#decomposing partial fractions

[polymorphemic-vector]

i'm so straight i'm an imhomogeneous second order partial differential equation

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In The Flesh

Five Hargreeves / Reader Insert

Imagine that Five wasn't alone the entire time he was in the apocalypse...

-This is a special reader request for an extended scene from my Five Centric fanfic 'The Anti Hero's Pitfall of Arrogance.' Set during the apocalypse and Five is only 21.

-This request is a bit of a spoiler alert to the story that inspired it. It's written with a non-descript female character with no name, only referred to as she or her, so it's sort of a reader insert/you sort of vibe, or you can think of it as simply someone that Five loved. Think of it as you or someone else, either way, it's sad. 😭

Heed the warnings and click the link in the summary to read the full story if you want to get the full picture of what led up to this very sad moment for our favorite guy.

Warning: possible triggers, suicidal thoughts/behavior issues, alcohol abuse/excessive drinking, extreme grief/loss, graphic description of death/corpse, we get some Dolores in this, meant to be very sad, this fic this is based on is not all gloom and doom but it's clearly not all pretty either.

(5312 words)

In The Flesh

The funny thing about rock bottom is I’d thought I’d hit it many times before she saved me but really there is no depth far enough down to describe where I was after finding her body and where I would be for a very long time after that.

Like I’d done every day since I saw her favorite baseball cap bobbing on that partially submerged branch stuck out in the depths of the churning flood waters, I was out looking for her. On my endless searches, I would yell her name, over and over, till my voice was nothing more than a pained screech of air.

It was as I was scouring a new area that the water had receded that I went to shout her name again but stopped with only the first faint syllable. 

The moment I saw her distinctly colorful sandal and what appeared to be the discolored fragments of flesh still clinging to the bones trapped in it, the wind shifted, and my nostrils were filled with a pungent, sickeningly sweet, earthy odor.

That is what the smell of death is like if a body has been exposed to the elements for ten days or more. The anatomy and physiology decomposition literature states, a body exposed to the elements begins to decompose within less than 1 hour postmortem. That rate is accelerated if the tissues are exposed to other factors such blunt force trauma or heat and moisture.

She had been exposed to all of it.

I could still hear the ominous sound of the huge trees snapping and boulders grinding over things in the swift current as I walked along the road, just hours after she’d gone, only then, I didn’t know she wasn’t coming back. I didn’t know what was being done to her.

Now her body was there, under the hardened soil, but her foot was the only part of her that was visible other than her twisted tangle of hair wrapped around a river beaten branch. 

For the last week I’d been lying to myself, trying to hang on to the idea that she was still out there, that she was just too mad at me to come home. But really, in that time, she’d been first submerged in the torrents of flood water decimating that landscape, and then after, (not long based on the murky pool of muck and the very small cracks in the clay at my feet), she’d been there, encased in the ground. 

I cried out her name.

I dropped the stick I’d been using to poke and prod the underbrush, my body instantly disappearing for a fraction of a second into the snapping vacuum of my portal. Stepping out of it a few yards away, I fell to my knees, my trembling hands not knowing what to do or what was safe to touch. I moved to her foot, then pulled back as the tiny black flies that were startled by my presence flew up in an angry swarm.

The temperature since the day she disappeared had been colder but that had done nothing to prevent her rapid decay.

Entomology and Body Decomp 101: A decomposing body will attract all manner of life forms within 24 after death. If allowed access, scavengers are ruthless in their pursuit of the flesh of the dead. 

Having been well read prior to my time in the apocalypse and being well acquainted with death in the years before this, I was still not prepared for what I saw or had to go through over the next several hours it took to free her.

Her body was no longer her anymore, but I couldn't accept that. My mind told me she was under there and she was so scared. 

Frantically, I started digging with my bare hands. No matter how careful I was clawing at the clay that had molded her in the ground, anytime my fingers came close to her, they crushed her slick, wet remnants of flesh, tearing it through.

At this point, she had surpassed the early stages of decomposition. Gone was the bloating. The gases and liquids had mostly expelled, and her skeleton was letting go of her skin, though in some areas it remained in denser sections that were identifiable but mostly because her clothes had embedded in her. Her jean shorts made clear where her abdomen was, what was left of her chest was now part of her t-shirt.

What I was seeing and touching and smelling made my stomach heave over and over but still I had to save her.

She had needed me, and I wasn’t there.

Stage 4 post-decay lacks some of the first levels of putridity, but even though I had seen hundreds of thousands of faces of death, seeing hers will always represent the loss of everything; even more so than the day I’d foolishly ran into the future, lost my family, and found I couldn’t get back.

“No, no, no,” I sobbed, my filthy, bloodied fingertips inching along her face, or what should have been her face. “I am so sorry… Please!  No! God, please!”

The mouth I had cherished was gaping, her once perfect teeth were more exposed than they should have been due to the skin around them receding or simply just not being there at all. 

Her eyes…

Where once someone had looked back at me with so much love and endless understanding, now there was horror, both mine and hers. 

Sickness took me again.

Dizzy, I frantically scrambled back, away from where I had unearthed most of her, my stomach emptied, but nothing but acid spilled onto the scattering of broken foliage off to my side. 

My ears were filled with the evil buzzing sound of insects that were warming themselves in the open area around us as the sun relentlessly beat down.

I couldn’t take it.

A feral sound of pure agony crawled out of my chest, getting eaten away by all the nothingness.

“Please, I am so sorry… Please forgive me, I never meant for…” 

She wouldn’t except my words and I couldn’t blame her.

My broken cries were lost in my delirium. On hands and knees, I came back to her, lifting her to me even though I shouldn’t have.

The gruesome sound of parts of her stickily pulling free from the ground and the sight of the parts of her that remained in the soil were enough to fracture what was left of my sanity.

“It’s okay. I’ve got you, we can go home now,” I shushed her, in my head believing I had the ability to soothe her pain. 

She still said nothing, and I told myself it was because she was just too weak.

She just needed my help. She was just mad. She was just…

“You are safe now,” I said, my hand sinking into her, her spinal column hitting my palm not even enough to shock me back into reality. 

After cradling her for far too long, I said, “I am not leaving you here.” 

Lightly as possible, I let my shaking hand touch her hair, seeing but not acknowledging that it was starting to detach from her scalp. Without thinking, I forced the massive amounts of energy I needed for a jump, the blue power expanding from my hands, then around us. 

I only took us across the drying riverbed, up the steep embankment and up the hill to where the road hadn’t been washed out, and that was far, but it was not even close to getting us back to our cabin. For that, I had planned to teleport again and again, as many times as it took but when my feet smacked the ground the force of it made the tendons holding her right thigh to her hip give way and the length of her leg landed at my feet. 

“Fuck!” I screamed, slamming to my knees to grab her.

Like a madman, I could at least put together that she was falling apart and that this wasn’t going to work. Even jumping with her was too much. She was so fragile; she’d always said she wasn’t, but she was…

“I am so-ssss-sorry,” my voice cracked as I carefully laid her down again. 

The sight of those tiny black bugs as they fought to get a piece of the woman I loved, caused me to feel the burn of violent anger and that almost brought me to my senses, but even that too, I washed away with another imaginary idea, that if I just covered her, somehow all the severed openings that were now more her than anything else, would be spared from further ruin.

In a frenzy, I stripped off my shirt, covering her with it the best I could. The moment I was able to get to my feet again, I swayed, the world spun, but when it came back into focus, I could see again like lightning struck my head, brightening the gray world around me, making the colors of her bright sandals and her hair and the tattered remains of her clothing stand out in stark contrast to the deep darkened purple of her rotting body.

My filthy hand came up, rubbing my face and my blurred eyes, then my fingers tore back as I painfully yanked at my hair. 

I had done this to her.

Sniffling and on the verge of a full screaming fit of rage, I turned and started making my way up the road, a few steps away, my hands coming together, my fingers like claws, I tried to gather the light in my hands to blink again, but instead I was met with the impotence of the faintest swirls of azure static crackling to life then fizzling out. 

Turning back to the motionless pile on the ground, I again assured her I’d be back. Then in a haze, like a zombie on empty, I mindlessly made my way back, my mud-covered boots trudging up the steep hill, my balance faltering over and over as I’d tripped over the uneven surface.

If you ask me what I was thinking during that walk, I couldn't tell you. All I knew was that I was empty and that a horrible numbness was taking hold.

Even still, I came back fast, like I’d promised. First, I placed her in a thick blanket, sure to get every bit that was her that was there, anything that wasn’t, I never found.

“There,” I breathed, positioning her leg that had been torn off at the hip in such a way that looked less painful. Then flapping away any visible bugs from her, I covered her completely. Knowing that she was in the later stages of decomposition but that it was far from over and she was seeping fluids, I lifted her, and laid the cocoon of wool on top of a tarp. 

I could have carried her the whole way but not wanting to hurt her or break her apart more than she already was, I only carried her to the cart I’d brought back with me, then I carefully laid her in. 

Though she didn’t answer no matter how much I wanted her to, I spoke to her the whole way as I tugged the wagon with her in it up the hill. 

Getting back to our home, the mud encrusted wheels clattered to a stop in the yard right next to the chair I had been sitting in the day we had gotten into our fight. It was dead silent and getting so dark by that point that the stars were coming out but as if in a time loop in hell, I could still hear the cruel things I’d said to her on that sunny morning. 

Looking down at the small mound of blanket with her in it, I said, “You have to forgive me. I don’t know what to do without you. I don’t want to live with-”

My heart was racing, I couldn’t breathe. My chest felt a new tightness where before, since the hours after she’d gone and not come back, I’d only felt the stabbing pain of regret and fear, now it was like an aching void as if there were an actual hole inside me.

I stood there blankly staring at the door, then back to her, my mind not working at all but somehow still functioning enough to make the start of a string of very bad decisions.

Taking her up in my arms, we went inside. “We’re back. You're not alone anymore. I never meant to leave you out there like that. I tried so hard to find you,” I said, smothering my words against her wrap. “It’s okay now…we are okay…”

I kicked the door closed then I moved straight for our bed, and I would have laid her down in it and climbed right in if not for the fact that Dolores was sitting in the chair next to it, staring at me looking horrified.

‘No, Five, don’t!’

Saying nothing, I spun around to instead place the bundle in my arms on the couch in front of the fireplace. It wasn’t lit and it needed to be. That’s what she and I did at night. That was our other special place.

Memories of sitting there together, her behind me, reaching around to place my fingers correctly to play the chords she was trying to teach me filled my head. I could almost trick myself into thinking I could hear her beautiful playing and that I could hear her laugh at me every time I’d try to get out of my lessons.

“This is okay. I’ll fix this. We are going to be okay,” I said, as I started to unwrap her.

Dolores panicked at the sight in front of us. ‘Five, no. She’s gone. This isn’t right. What are you doing?”

I stopped, leaving her under wraps but I ignored Dolores’ s warning and started to light the fire. 

Again, Dolores asked, ‘Five, what are you doing? She is dead. You can’t do this to yourself.’

“She’s not dead!” I shrieked, my eyes filling with welling tears as I clenched my hands, my broken fingernails slicing half-moons into the flesh of my dirty palms. 

‘I am sorry, Five, but she is. You knew that after she didn’t come back.”

My head turned back and forth as I shook away a flood of tears threatening to come out and drown me like the water had done to all that I loved. I pinched my eyes shut, a broken whimper squeaking out of my throat.

‘Look at yourself, Five… You are not okay. That is why she can’t stay here. I love her too, but she is gone.’

I opened my eyes and looked at myself. I had no shirt on, my body was covered in mud and death. 

The smell of me… 

The smell of her poor body…

‘You need to bury her. She wouldn’t want this.’

“No,” I whispered as my body trembled and I stared blankly at the floor. “No,” I said again, then screamed, “Stop!!!! Just stop! Don’t you fucking talk to me! I didn’t ask for your help! It didn’t ask for any of this!”

Refusing to look up and see the hurt on Dolores’s face, I looked to the motionless pile of fleece blanket.

“I am not putting you out there all alone again, sweetheart.”

With that affirmation, and me placing a kiss to her covered face, the night did not get better.

In the light of the fire, I sat there on the floor in front of the couch as close to her as I could be without touching her. I wanted to protect her. I needed to keep my promise that I wasn’t going to leave her. 

So many times, she and I had discussed the possibility of me being able to jump back in time and the fact that doing so with her was going to make it all the harder for me to pull off. Even with the right math, and just me, the energy needed to do it was something I hadn’t figured out how to achieve. Even though she had said that me getting back was all that mattered, I refused to consider leaving without her. 

I couldn’t leave her, not then and not now; that was what I kept telling myself.

Sometime late into the night, slumped against the plaid couch, my head resting near hers though she remained covered, my demented and wrong train of thoughts slipped away, and sleep took me but in it l found no solace. 

~~~

As I came to in the early hours of the next morning with my body crumbled on the cold floor, I knew instantly that everything I wanted to believe was okay was not. 

The dimly lit cabin smelled of death and I was graced with the buzzing sound of a half a dozen or more flies that had found their way in somehow in the tiniest of cracks.

The decay had been clinging to me since I found her, but I refused to acknowledge it even as the putrid odor only added to my ongoing nausea. I clumsily reached for the stale glass of water I’d left at some point on the end table. Drinking it burned my cracked lips and the taste of it felt laced with a bitter acid. I wanted to retch but managed to refrain.

Then, wanting to remain living in the land of make believe, I got up, went to our small kitchen area, and proceeded to grab several bottles of liquor.

Dropping down next to her again, I twisted a cap, sloshing the clear liquid as I tipped it back, dumping the alcohol down my raw throat. 

It was awful but that was not the only time I’d drank to forget, or that I’d drank things that were questionable in their quality.

“Remember when we found that stash of cheap wine with the seals broken,” I quietly asked. 

I took a long pull at the bottle, then another as I peered over my shoulder at her laying there on under her favorite blanket.

“Smarter than me as always, you refused to drink any of it, but not me… Stupid as always, I gave it a try and boy did I pay for it. You had to baby me for the entire next day. God, I am such a lightweight. I’d be dead if not for you.”

I laughed, the sound of it thick with irony.

“You were always so good to me…”

Eyeing the dried mud and smears of her flesh on my pants, my eyes blurred. 

“I didn’t deserve you and you didn’t deserve this.”

I started to cry. Then I started to hyperventilate, my breaths coming too fast and my head spinning. 

Shuddering, I drank more and more but I could never turn the image of my girl’s face staring back at me from that riverbed into the beautiful living version I wanted so badly to believe was still with me.

Hours later, I was disturbingly drunk. 

One minute I was musing to myself about our better times, talking out loud like a maniac about something so wonderful, like one night that she and I were out scavenging too far to come back, and we’d camped out under the stars. I’d told her the names of all the constellations I knew and there were many. She’d quietly listened, cuddled up next to me, both of us just happy to be in love and together even if our world was a landscape of tragedy. 

Together, we could have done anything. We were going to save the world.

Now she was gone.

I had nothing.

She’d been everything and now I had no one again.

With the room spinning, I abruptly got to my feet, stumbling towards the window above the sink basin. The flies zipped and buzzed in front of me, landing in the vomit I had left there after I’d finished the first bottle of liquor. Knowing that those same dirty insects were landing on my beautiful girl made me quake with not just sickness but unmeasurable self-hatred.

I was a fucking mess, and I wasn’t doing right by her. 

Dolores was right. 

Glancing back to where I had abandoned Dolores almost two days prior, the room tilted in my vision. I dizzily turned back, clutching the white cast iron basin.

The light outside was fading. I wanted to go along with it. I wanted all the horrible pain and debilitating heartache to stop.

Laying on the butcher block counter space where we prepared our meals, was a sharp kitchen blade. With where my head was at, seeing it, I immediately thought of my gun and other times of morbid desperation. 

My tears burned down my cheeks.

I hated myself so much for what I had caused. If I had not yelled at her, and if I could only have seen through my arrogance and own my deficiencies, she would still be here. I didn’t and instead did what I’d always done and blamed anyone but myself for my problems.

I’d taken out everything on her, again…

If I’d only learned from my mistakes, things that weren’t okay never would have been said. She never would have felt the need to be away from me. She never would have gone for that walk, and if she had, I would have been by her side. If I had just agreed with her to go to the city to try something new, I may not have had the breakthrough we needed so badly but at least she’d be there.

Feeling on the verge of vomiting again, I wanted to disappear into an alcohol induced coma.

I pushed off the sink, staggering like a drunken idiot the whole way back to the dresser that was next to my side of the bed. In a blur, I saw Dolores sitting there on her chair, but she didn’t say anything. She looked every bit the inanimate object she was.

It was as if I’d killed her too.

I yanked the top drawer open, my hand tearing through the clothes to find the heavy black metal object that my fucked-up mind craved. 

My fingers grazed the cold instrument of death. I could feel the barrel of the pistol sticking down my throat, the oiled slickness of it slipping past my parting lips. 

Just the thought made me gag but with sick fascination, and I didn't’ stop thinking about it.

All it would take is one second and my finger on the trigger and no more guilt. My brain would be a splatter of nothing, painting the bedspread behind me. The place we’d slept and loved would be ruined just like we were.

Images of us, heated tangled flesh, together in those same blankets filled my mind.

To get away from the hurt that memory caused, I looked up, the weapon in my hand but my eyes aimed at the small dresser mirror. It was as if a stranger was looking back at me. My stomach felt like it was trying to crawl out of my mouth and my vision was closing in with blackness threatening to pull me under.

I was seeing things and hearing things.

The loud pop of the bullet; the sound of my body hitting the floor. 

I saw bugs crawling out of the jagged rotting hole in my skull.

Then I saw her face, only not the destroyed one that was hidden under the blankets on the couch. 

That was when I finally came back to myself. 

“Don’t you fucking do it,” I furiously screamed at myself, throwing the gun back down in the drawer.

My ears were ringing from my own terrified voice reverberating in them, then a few seconds later, the silence of death and that room returned.  

It was just me, the mannequin and the body.

Dolores was right, I needed to let her go. 

I had to bury her.

~~~

Over the next several hours, through the task of digging a hole in the ground, I sobered up significantly. Having done that, I re-entered the dank, horrid smelling cabin, removing the small pile of remains that had been the love of my life.

I was still covered in layers of filth and knowing that even if Dolores wouldn’t speak to me, she’d loved her as much as me and she’d want to be there to say goodbye, I quickly washed myself outside under the spout attached to the spring fed line that was rigged to the house. Splashing my face with a mix of soap and water, I cleaned my battered hands, and my arms, and I removed my soiled pants, tossing them in the woods. 

The water streaming down my body was ice cold and disgusting. My fleshly cleaned and very pale skin ran under my fingers, standing in stark contrast to the filth that I was and the sight of it only furthered the much-needed reality check I'd only recently found. 

Once I’d made myself somewhat more presentable, I redressed, then silently approached Dolores.

My voice cracked from being burned by stomach acid so many times and by my screams and lack of simply drinking or eating appropriately for days, but I had the strength and weakness to ask her for something I didn't deserve.

“Please come with me…I don’t want to do this alone.”

When Dolores responded with her softly spoken words of devotion, ‘You are never alone, Five. You will always have me,’ I was nearly beside myself with emotion. I’d thought I’d lost her along with everything else.

“Oh, my God, thank you,” I sobbed as I lifted Dolores up and carried her outside into the yard.

We approached the hole I’d dug. It wasn’t that deep, and it wasn’t that big, but it didn’t need to be. It was in front of an ancient but long dead ash tree that she had once told me had to have been something truly beautiful at one point in time when it was alive.

It was just like her.

The burial was silent, save for the sound of the blade of my shovel slicing through the softened pile of dirt I had removed and then replaced. 

The sky was getting dark, the woods full of shadows of monstrous things that looked like they could come out of the night and pull you away forever. 

I sat, folded in on myself at the base of the old ash tree, the disturbed soil at my feet as I looked up to the highest branches of the barren tree. Its flesh had been taken. Remanence of its bark were scattered all around me. It would someday be nothing but dust. 

We all would be, but it was not my time-yet.

Burying my head in my hands, I kept telling myself that. 

~~~

In the days that came after that, it rained and rained. My mind tormented me constantly with the flawed idea that she was trapped out there in the crushing wet ground. One second, I’d be haunted by images of her so scared and trying to breath and break free as then dirty water filled her lungs, and then the next, I’d come back to the dimly lit room I was in; Dolores worriedly watching me as I slowly organized things and cleaned up my many messes.

We couldn't stay there, but I couldn't bring myself to leave either, not when everything I had that she'd ever touched was right there. All around me were parts of her life that she’d shared with me. I’d clung to every trinket; every item of fabric that bore her scent. 

Lying in bed at night, I’d break down into sobbing fits of anguish with my face buried in her pillow. I could stay like that for hours on end, fading in and out, tricking my mind and heart into thinking I hadn't lost her and that she was right there in bed next to me. But it would never last because the damp coldness of the empty space around me that had once been warmed by everything that was her was an inescapable reminder that I had failed the woman I loved and who had saved me.

It was in a notion during one of these times of despair that I realized the only thing I could do to redeem what I had done was to fix this like I'd always promised her I would. Out there somewhere in time there was a place where the world was still alive, and she was in it and everyone I ever cared about was still flesh and blood and filled with life.

I had to get back.

The pain that happened here was real and always would be but somewhere out there, there was a chance of better things.

There was a chance of seeing her again.

That idea of saving her and my family was the only way, and it was my reason for breathing again.

Broken, but somehow still standing, my heart though not the same was still beating. The flesh covering my hand could still feel hers in it and it was while cherishing that feeling that I made the decision that it was time to go. 

On our final day, I got up like every day since I’d put her in the ground under that tree. I came outside, picking up the wildflowers I had left for her the day before, then I went for a short walk, talking to her in my mind the entire time, making my usual promises while I worked through ideas and math and things that gave me hope. Then I’d come back, refill her favorite vase with new water and place the colorful blooms there above her.

Alone, the sun shone down on me, my shadow stretching across the earth above her, giving the illusion that we were laying there together.  

“I love you,” I whispered, my eyes blinking back the enormous weight I felt from her loss and would always feel.

I liked to think I heard her say she loved me back, but I knew she didn’t; it was just a memory of her words tickling my ear as her lips gently kissed along my neck.

I shivered from head to toe as I felt the ghost of her touch but not in a bad way.

I smiled, sniffing like a baby as I rubbed my eyes.

Then, making one last promise I said, “You will be okay. I’ll fix this.”

Going back in the house, with Dolores watching all the while, obedient and loyal and loving with words of encouragement, I packed my final things.

I left our cabin spotless and set up as if we were coming back to it. It was as if I could see us in there again, spending our nights in front of that fireplace, laughing and endlessly teasing each other; our bed ready for us to lay down in and explore each other in new and exciting ways that only made our love stronger. I saw all that but in the back of my head I knew I was never going to come back to that place because it was gone, and if I did return, I may never leave her.

So, it was with that in mind, late in the morning, I loaded Dolores with our supplies, setting her next to the hard black guitar case that held her cherished Christmas present I'd given her and so many other things I couldn’t let go. I pulled a blanket around Dolores and the case, as if the instrument inside it had become something in a way of being the woman I’d lost, so much the way Dolores was a real thing that needed my care and love. 

I walked to the old, grayed ash tree, its wind worn and smooth branches shone in the warm sun as I looked down at the ground where I’d left a piece of my heart. I could almost hear the sound of her playing my favorite sone and I knew that when I plucked those strings, a piece of my heart would break a little more with each strum, but I’d be back with her.

My lower lip trembled, and my nose burned with the same heat as my eyes.

“Until we meet again, my love…”

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[placeslong]

Decompose into partial fractions calculator

You may switch on the 'Show details' toggle of the calculators above to study the procedure steps using an example. create and solve the system of linear equations to obtain a jk, b jk,c jk.equate each coefficient of P 2(x) to the linear expression with a jk, b jk,c jk corresponding to the same degree of x Integration by Partial Fraction Decomposition is a procedure where we can decompose a proper rational function into simpler rational functions that are.expand the numerator polynomial factors and express the numerator polynomial coefficients in terms of linear expression of unknown constants a jk, b jk,c jk.reduce the right side numerator to a common denominator., where a jk, b jk,c jk are real numbers. then the partial fraction decomposition takes the form:.find the denominator factorization as l linear factors for real roots of Q 1(x) and n quadratic factors for complex roots of Q 1(x):.if the degree of P 1(x) is greater than or equal to the degree of Q 1(x), do the long division to find the common polynomial term (quotient) and the new numerator P 2(x) (remainder), which degree is less than Q 1(x) degree:.convert the denominator polynomial to monic by dividing P (x) and Q (x) by the leading coefficient of Q (x).Note that it is Bx + C on the numerator of the fraction with the squared term in the denominator.The partial fraction decomposition procedure of a polynomial fraction P(x)/Q(x) is as follows: This method is for when there is a square term in one of the factors of the denominator.įind A, B and C in the same way as above. Note that we have put a (x - 1) and a (x - 1) 2 fraction in.Īs before, all we do now is find the values of A, B and C, by putting them over a common denominator and then substituting in values for x. When there is a repeated factor in the denominator, such as (x - 1) 2 or (x + 4) 2, the following method is used. Remember, the above method is only for linear factors in the denominator. Find the partial fractions given the numerator and denominator. Now cover up (x + 1) and substitute -1 into what's left to discover that the other partial fraction is 1/(x + 1). WolframAlpha Widgets Overview Tour Gallery Sign In. This tells you that one of the partial fractions is 4/(x + 6). To put 5(x + 2) into partial fractions using the cover up method:Ĭover up the x + 6 with your hand and substitute -6 into what's left, giving 5(-6 + 2)/(-6+1) = -20/-5 = 4. The "cover-up method" is a quick way of working out partial fractions, but it is important to realise that this only works when there are linear factors in the denominator, as there are here. In this example, if we substitute x = -6 into the identity, the A(x + 6) term will disappear, making it much easier to solve. When trying to work out these constants, try to choose values of x which will make the arithmetic easier. This means that we can substitute any values of x into both sides of the expression to help us find A and B. An identity is true for every value of x. The above expression is an identity(hence º rather than =). Step 3: In the new window, the partial fraction decomposition of the given polynomial rational function will be displayed. Step 2: To obtain the expansion, click the button Submit. (putting the fractions over a common denominator)ĥ(x + 2) º A(x + 6) + B(x + 1) (we have cancelled the denominators) To use the partial fraction decomposition calculator, follow these steps: Step 1: Enter the numerator and denominator polynomials in the respective input fields. This leaves us with two possibilities - either accept the complex roots, or find a way to. So now, all we have to do is find A and B. The second term in the denominator cannot be factored into real terms. This method is used when the factors in the denominator of the fraction are linear (in other words do not have any square or cube terms etc). The method of partial fractions allows us to split the right hand side of the above equation into the left hand side. Partial fraction decomposition is basically the opposite of adding fractions. This has many uses (such as in integration). It is possible to split many fractions into the sum or difference of two or more fractions. The method is called Partial Fraction Decomposition, and goes like this: Step 1: Factor the bottom.

[phantomrose96]

Joyrider

(Welcome to another warm-up writing piece. cw for mild body horror)

...

The mall food court doubled rather nicely as a battle-dome.

It fit the bill: a flat and circular arena, crowned two-stories up by a hemisphere of glass windows which lapsed iridescent in the maelstrom of ecto-fire.

Spectator chairs sat empty, hastily shoved back and knocked over by the Amity Park mall patrons who knew to leg it at the first sound of explosions and the first sign of the atmosphere tipping dark. Admittedly, the patron evacuation took longer than Danny anticipated, and he backed himself into a corner playing defense for the 50 some-odd people who, worn-out on the every-day mundanity of ghost alarms, took their time gathering belongings, or shutting off burners, or working in a few last bites of a burger.

So with the crowd gone and the stage their own, Danny found himself pressed back against a vat of french fry oil, hands braced against the handle of a broom he held out horizontally, which the ghost gripped with equal measure and shoved her full weight against.

“Oh, why not take a little dip, Ghost Boy? I hear the water’s nice.”

“No thanks,” Danny answered, shoving harder. “I never was much of a hot tub guy. You on the other hand—”

Danny set a foot forward and pivoted, body fueling the torque as he spun the broom, and tore the ghost with him, a pirouette to swap their spots and jam the ghost back-pressed to the fryer.

“—you seem like you’d like it hot.”

The ghost barked a laugh, jaw stretching lower and loose than Danny was comfortable with.

“Ha! You sure? Not very heroic of you to deep fry this girl I’m possessing.”

Danny faltered. His grip slipped. His blood chilled to ice as the information clicked in place – as he recognized the sensation of a ghost talking through someone. This wasn’t the ghost’s own form. This was some girl. How had he not felt—

A blast took him by the ribs. Danny doubled over, immediately kicked back. A foot found contact with his face, driving him down, until the girl’s wet and slippery fingers pinned him down by the wrists.

Danny strained. He could pivot his wrist a fraction of an inch left or right, but he could not break the hold.

“Get off me!”

And a voice answered from behind him.

“I can help with that.”

Danny craned his neck. Upside down, vantage point from the floor, he registered Sam’s combat boots slam into focus. She bent to one knee, a bazooka locked on the other. It charged, whined, and erupted with an explosion of green light.

The ghost shrieked. It took only an instant of resistance before the ghost tore cleanly from the girl possessed.

“Now if you don’t mind me—” Tucker, by the voice. Danny heard the whine of a Fenton Thermos heating up. “—I’d officially like to change my order from fries to soup.”

The beam burst forth, and the writhing, shrieking, yelping form of the exorcised ghost clawed and scratched in Danny’s direction before the thermos consumed her in full.

“Really? ‘Fries to soup’? Even Danny can do better than that.”

“Hey,” Danny answered.

“I was thinking on my feet, Sam. I didn’t hear any witty quips from you.”

The conversation fell away from Danny’s focus as the full human weight of the possessed girl dropped down on him. Gently, Danny gripped her by the shoulder, lifting her as he pushed himself into a sitting position.

“Your parents’ anti-possession gear is getting good. I don’t think I’ve seen an exorcism work that quickly.” Sam’s voice, now at his side. Danny glanced over, finding her kneeling beside him. “Is she hurt?”

Danny gave the girl a once-over. She was pale, cold, lips seeping blue. A mottled, blackish bruise spread across her temple, partially hidden beneath loose red bangs.

“I don’t… totally know. I didn’t land any hits on her, thankfully. But who knows what that ghost might have done. We should call an ambulance.”

“On it,” Tucker, from behind.

“Do you… do you think the bazooka might have hurt her?” Sam asked.

Danny shook his head. “Mom and Dad have blasted each other with that thing a hundred times. Dad got himself possessed by the box ghost for a trial run. It doesn’t hurt people. …Maybe she just needs a minute.”

“Lay her down, maybe?”

“Good idea.”

Danny eased forward, careful in his movements. Something about his grip slipped, sliding loose and rolling forward, and she fell unceremoniously from his arms, shoulder knocking ground as she lay there partially turned on her side.

“Danny!”

“Sorry! I didn’t—something slipped!”

“Well don’t leave her like—” Sam gripped a hand to the girl’s shoulder, weight behind her wrist to roll the girl fully onto her back. Sam’s hand froze, and then yanked away.

“What?” Danny asked.

“That didn’t feel right.” Sam only stared down, her hand hovering, twitching in increments. “Way too cold… and loose.”

“Loose?”

“Danny, look at her hands. What’s wrong with her hands?”

Danny looked. The skin stretched and wrapped the bones of her fingers as if rotated partway around. Her fingernails sat off-center, twisted around and bunched up like a glove. Sam’s hand came back into view, and she clamped it to the girl’s wrist.

“It’s like jelly. Danny it’s like jelly. Why is she this cold? Danny, I don’t think she’s—”

Something new caught Danny’s eye, a purple discoloration peeking out from the bottom ruffles of the girl’s shirt. His hands seemed to move on their own as he reached down, and pinched the bottom of her shirt, and pulled it back.

Black bruising consumed her torso, caving deep and bloating, pruning around the trails of heavy stitching that ran along the tracks of surgical cuts carving through her abdomen.

Danny yanked his hand away as if burned.

“Danny, she’s not breathing.”

The rest of Danny’s thoughts drowned in the swelling wail of the approaching ambulance siren.

…

Outside the Fenton Portal, green lighting doused the only part of Danny’s form not hidden in shadow, and danced with the fire of his glowing green eyes. Danny uncapped the thermos in his hand, and he trailed his thumb along the eject switch.

A new consuming green light belted forth, lasting only a moment until it vanished with a twin-braided ghost in its wake. The ghost blinked, smoothing over her hair and pulling the ends of her braids over her shoulders.

“Oh, it’s the Ghost Boy again. I thought you’d just throw me back in the Ghost Zone. Are you interested in a round 2?”

“No, not interested,” Danny answered, tone colder than ice.

“Yeesh, you’re quite sour. No more puns?”

“Why were you possessing that girl?”

“Hmm?”

“Why were you possessing her?”

The ghost blinked, green portal light mixing murkily with her purple eyes. “No particular reason. It was just a joyride.”

“A joyr—she was dead.”

Another blink. “Yeah I know. She was sitting in the morgue. She was in like a car crash or something and they already took all her organs. They didn’t need her. And I was gonna give her back, but you had to go and make it a whole thing.” The girl swooped forward, eyes wide and roving over Danny. “You seem mad. Wanna call a truce?” She stuck a hand forward. “I’m Melissa, by the way.”

Danny jolted, eyes flashing brighter. “No, you’re not. That girl was Melissa.”

“Oh for real?” Melissa let out a chuckle. “Crazy coincidence. I like don’t even know that many Melissas. Anyway truce?”

“No.” Danny ran his fingers through his hair. “You were possessing the body of a dead girl and you made me fight her! Don’t you see how that’s—that’s so—how fucked up—that you’d even—”

“Well I mean, I didn’t make you fight me. You made that happen. I was minding my business.”

“Doing what?”

“Shopping. Why else would I take a body for a joyride? I stole some cute clothes to wear. Stole some food to eat. Oh! That outfit I was wearing when we were fighting? Yeah I picked that out. She was in like a hospital gown when I found her. Super cute improvement right?”

An ectoblast sounded and connected with the wall behind Melissa, missing her a foot to the right. Danny’s hand glowed, and his eyes focused with a razor sharpness.

“Stop talking like that, okay? It’s pissing me off. I need you to tell me you know this was fucked up.”

Melissa put a finger to her chin. “I mean I guess stealing is kinda wrong. They were all like, big box corporate stores don’t worry.”

“The. Dead. Body.”

And Melissa fell silent a moment, violet eyes probing deep into Danny’s before widening. “Oh. Oh you’re like for-real mad about that. Like actually. I thought you were like, making an ironic joke.”

“Why the hell would I be joking about this??”

Melissa cocked her head to the side. “Well because you’re doing it too, duh. Like, duh.”

A huff of air cut against Danny’s teeth, an involuntary noise, incredulous, a guffaw he didn’t consciously make. The jelly sensation of decomposing flesh was back under his fingers. “I am not—would never—I’ve never even seen a dead body before this thing with you and I’d never in a million years even think for even a fucking second that I’d want to possess a dead body. What’s wrong with you?!”

Melissa bobbed a little in the air, ends of her braids trailing over the straps of her ephemeral sundress. “See this is why I really can’t tell if you’re joking or not. What are you talking about? You’re doing it right now.” She clasped her hands behind her back. “The black-haired boy whose corpse you’re possessing. Why are you allowed to do it?”

Danny froze. He laughed, heavy, with an uncomfortable force. “Myself, you mean? I’m not possessing myself. I am myself. I’m a half-ghost.”

Melissa met his laugh. “Oh what? No way like, that’s your own corpse? How’d you even get back to it in time? That’s crazy lucky like you must have died right near a portal or something.”

An involuntary shiver traced down Danny’s spine.

“…I’m not dead.” His eyes shifted around, and Danny dropped to the floor. He set a hand against the wall, throwing on the lights to the Fenton basement. Rings swept around his form, green iridescent eyes sweeping blue, white hair seeping black. “Look. Literally look at me. I’m not dead.”

And Melissa swooped closer. She set a finger to her bottom lip and hovered a foot in front of Danny, drinking him in. She swept to the side, like a swimmer in the water, sweeping around him in a full arc. She edged closer and pinched her fingers against the exposed skin on Danny’s arm. He flinched.

“Oh wow there’s like, not even any decay or anything. Your human brain even feels like it’s working it’s all like, electro-magnety. How long were you dead before you got back to your body?”

“I didn’t die.”

“Then what did happen?”

“I got shocked by the Fenton Portal, okay? It was just a lab accident and it gave me powers.”

“Oh. Oh.” Melissa’s eyes shot wide. “Oh you didn’t die near a portal… You died in a portal. You didn’t even have to get back to find your body at all. You must have appeared like practically on top of your own body. That’s crazy lucky. That’s so lucky. Your body was like, probably only dead a microsecond before you hopped back in. No wonder it’s so well-preserved.”

Danny swatted her away. “You’re not listening to me.”

“You’re not listening to me.” Melissa floated backwards. “What do you think is more likely? A bajillion ecto-volts somehow gave you superpowers that exactly mirror everything a regular dead ghost can do? …Or you died, and became a regular old ghost, and did what any regular old ghost can do, which is possess a freshly-dead dead body?”

“…I’m half-ghost,” Danny answered, human heart pounding in his chest. “I know what I am.”

Melissa bobbed back, feet pointed backwards until the soles of her feet skimmed the matrix of the portal. “I see you’ve made up your mind. That’s alright. But it was still pretty mean of you to accuse me like a big hypocrite like that.”

“I’ll destroy you if you ever try that again.”

“Oh I’ll try asking permission next time okay? Promise.” Melissa’s feet sank into the surface of the portal. “But, before I go, I’ve just got one more question to leave you with.”

“Go.”

“Why should a lethal accident do anything other than kill you?”

“Go.”

“Maybe you’ll have an answer for me next time I see you. Byeee!”

A spark of white erupted from the portal, consuming, absorbing, and fizzling out as Melissa’s form vanished into the ether beyond.

…

“Hey! Yo! Danny, come check this out!”

Danny rounded the stairs, unsocked feet creaking the floorboards with each step. Danny yawned, and blinked, and rubbed at his bruised eyes with the sleeve of his pajama top.

“Still asleep? That’s fine! You don’t have to do anything. Just come over here and look at what your old pop’s been up to.”

Danny entered the living room, where Jack sat hunched on the couch surrounded by an arsenal of power tools, rags, oil, soldering equipment, and scrap metal. From beside him he hefted a bazooka into view.

“This is the Fentonzooka 3.2.17. Amped up and equipped with all the latest in ghost-busting and human-saving technology.”

Danny blinked. “3.2.17?”

“Yep. This baby’s got 17 bug patches, tweaks, and internal improvements since the 3.2.0. The 3.2.0 was the advent of the snack compartment in the side. Look!” Jack spun a dial, revealing a chamber half-filled with pistachios.

Danny only stared.

Jack hefted the bazooka onto his shoulder. “Even better, Mads and I finally got rid of the last little sting humans feel when it’s fired. It’s now completely 100% harmless to humans. It feels like the breeze from a standing fan when it hits ya.” Jack turned, and he aimed the barrel at Danny. “Wanna try it out?”

Danny stood, and Danny stared, and Danny said nothing.

What might happen when it hit him?

Would it hit like the gentle breeze of a fan? Wash over him like air conditioning? Tingle cool and pleasant against his human fingers, human face, human skin?

Would it do something else?

Why should a lethal accident do anything other than kill you?

Jack eased the bazooka a bit off center, pulling his eyes away from the sight. He stared directly at Danny. “Danny?”

“Yeah?”

“Do you want to try it out?”

Danny stood.

Danny stared.

Danny wondered if he’d have an answer for Melissa the next time he saw her.

[irispublishersagriculture]

Iris Publishers - World Journal of Agriculture and Soil Science (WJASS)

Remediation Methods of Crude Oil Contaminated Soil

Authored by Ding Xuezhi,

Crude oil is a quick and easily accessible source of energy, making our life comfortable and raising the standards of living. It can be found naturally in many parts of the world, particularly in the USA, Russia, Romania, Iran, Mexico, Iraq, Saudi Arabia, Kuwait, Libya, and Nigeria [1]. The petroleum industries generate billion tons of crude oil, natural gas and its derivatives every year. All of these are then undergone further processing for the production of refined products such as diesel, gasoline, petrol and lubricants [2]. It is recorded by international energy agency that demand of oil all over the world in 2015 was 97 million barrels/day which is expected to be 100 million barrels/day up to 2021 [3].

Crude oil is composed of volatile liquid hydrocarbons with varying molecular weight and structure. It contains more than 17,000 hydrocarbons and its classification are based on the most prevalent compound present in it. The three main hydrocarbons components present in crude oil are compiled in Table 1 [4-6].

Crude oil contamination is one of the major environmental problems effecting aquatic and terrestrial environments. At present, approximately 80% of lands are affected by petroleum origin products i.e., hydrocarbons and these products are used in oil and chemical industries as energy source [7]. Crude oil makes a covering on the surface of soil and causes the retention of carbon dioxide produced by soil organisms. It also decreases the soil porosity by sticking the soil particles together. The amount of loss depends on the amount and grade of oil spilled [1].

Many accidental spillages of crude oil have threatened the nature. The largest accident in the history of mankind that caused environmental disaster is “Gulf war oil spill” (1991). This accident caused the spill of millions of gallons of crude oil from destroyed oil wells into the water and surrounding land covering 49 square km of an area [8]. Similarly, “Keystone pipeline accident” (2017) is another disaster of oil spillage. This spill caused the spread of 210,000 gallons of oil on the grass as well as in the agricultural area at southeast of the small town of Amherst in northeast South Dakota [9].

Polycyclic aromatic hydrocarbons (PAH) present in crude oil, declared as primary environmental pollutant by the United States Environmental Protection Agency are mutagenic and carcinogenic [10]. A prolonged contact time of stable PAH with soil stimulate the phenomenon called soil aging, leading to the resistant of soil to any treatment [11]. Leakage of these contaminants from the soil to the ground water can pose risk to human health, vegetation and biological environment [7]. So, it is very important to clean the soil from these harmful substances to guard life from their deadly effects. Besides, by remediating oil contaminated sites more land can be available for residence as well as agricultural activities.

Numerous countries are developing their own strategies to cope with the soil contamination done by crude oil e.g., Lebanon, Kuwait and some other middle east countries have organized oil spill working groups by the aid of environment research organizations for assessment and future remediation of the affected areas [2]. Numerous methods for the removal of crude oil from the contaminated soil have been devised. A quick, nature friendly and cost-effective method is required for this purpose. This review focuses on the current developments of some generally accepted remediation techniques used to treat crude oil contaminated soil.

Chemical Methods

Chemical oxidation is an efficient method to remove dangerous wastes from the soil at the oil spilled sites. The efficiency of this method strongly depends on the soil matrix. Fenton’s reagent, a mixture of Hydrogen peroxide and Ferric ion, is used for chemical oxidation. Hydrogen peroxide is a strong oxidizing agent that generates hydroxyl ions during Fenton’s reaction while ferric ion acts as catalyst. Hydroxyl ions are very powerful and effective agents that destroy the contaminants present in the soil [12,13] demonstrated that removal of oil from sand at lower pH by using Fenton’s reagent is much efficient than at natural pH or peat.

Another efficient oxidant that is used for the removal of crude oil from soil is ozone. It is easy to generate, store and handle for in situ treatment. Polycyclic aromatic hydrocarbons are more reactive with ozone in comparison o alkanes. Reactivity of poly aromatic hydrocarbons depends on the number of rings, heteroatoms presence or absence and alkylation level. Ozone also support microbial community present in the soil as it generates oxygen on its degradation, so it can be helpful in bioremediation method to aid microbial growth [14]. Chemical method is a quick way to treat contaminated soil, but chemicals may pose a serious threat to the nearby soil and living beings due to leaching or side reactions.

Physical Methods

Excavation of crude oil contaminated soil is the quickest and safe way but not a sophisticated and cheap method. The contaminated soil is removed and transported to appropriate landfill for the disposal. The samples are collected from bottom and sidewalls of the excavated area to check if the site is clean or not [15-17].

Another physical method is the washing of contaminated soil. Washing with organic solvents such as ethanol- water mixture and ethyl acetate-acetone-water mixture exhibited significant removal of hydrocarbons from the contaminated soil [18-20]. Soil washing does not only treat the oil contaminated soil but also remove the heavy metals from the soil. The efficiency of washing can be enhanced by the addition of surfactants. Studies showed that both artificial and natural surfactants are helpful in the removal of crude oil. Different surfactants remove different fractions of crude oil e.g. artificial surfactant sodium dodecyl sulfate (SDS) removed aliphatic hydrocarbons while natural surfactants saponin and rhamnolipid removed polycyclic aromatic hydrocarbons from the contaminated soil [21]. This method no doubt is simple and efficient, however, it is very prolonged, time consuming and very costly. Transportation of contaminated soil to disposal site is another big problem. Surfactants might be dangerous due to their possibility of adhesion to soil particles.

Thermal Methods

In Thermal stripping/low temperature thermal desorption/soil roasting contaminated soil is heated to very low temperature (200- 1000 °F) to increase the vaporization and separation of low boiling point contaminants from the soil. By this process organic contaminants can be completely or partially decomposed depending upon the thermal stripping temperature and organic compounds present in the soil. [22]. This method can remove approximately 90% of the contaminants but it is very costly and not eco-friendly.

Another way to remove crude oil from the soil is incineration. The contaminated soil is burned by using fire at high temperature (1600-2500 °F) [1]. This method is also not environmentally friendly as volatile and flammable compounds present in crude oil will cause the environment pollution.

Biological Methods

Bioremediation is a traditional method that involves the use of living organisms (bacteria, fungi and plants) to degrade harmful substances present in the environment. Bioremediation of crude oil from the soil is very efficient, cheap and environmentally friendly solution. The effectiveness of this method is depended on hydrocarbon concentration, soil characteristics and composition of pollutants [8].

PAH are the most resistant and toxic group of soil pollutants present in the crude oil. PAH get trapped in the soil pores after they enter into the soil and retained by the soil matrix. So, their removal from the soil is very difficult [23]. Bioremediation is the most suitable method to remove PAH from the soil as microbes and plant roots can access these tiny pores easily.

Microbe assisted remediation

Soil is a diverse ecosystem as it inhabits various microbial populations. The composition of naturally residing microbes change with the composition and concentration of contaminants, so only resistant consortium of microbes survives and work actively in the cleaning of polluted soil [24]. Hydrocarbon degrading microbes are extensively present naturally in the contaminated soil and breakdown complex hydrocarbons into simple form by the use of their enzymatic systems.

Different bacterial genera chose different types of hydrocarbons for the degradation (Table 2) and they can also work in both aerobic and anaerobic condition. In anaerobic condition, bacteria present in the deepest parts of the sediments use nitrates, sulfates and iron as electron acceptor to degrade the hydrocarbons. Some of the species of anaerobic bacteria belonging to genus Desulfococcus, Thauera, Dechloromonas and Azoarcus exhibit hydrocarbon degradation ability [25-26].

While in aerobic condition, bacterial dioxygenase enzymes incorporate oxygen into carbon molecule through a series of enzyme catalyzed reactions to generate hydrocarbon with alcohol group. Alcohol groups are oxidized to aldehyde and then converted into carboxylic group by the action of other enzymes which in turn is degraded to acetyl co-A by beta oxidation [27].

The major bacterial genera that showed crude oil degrading capability are Alcaligenes, Sphingomonas, Pseudomonas, Bacillus, Nocardia, Acinetobacter, Micrococcus, Achromobacter, Rhodococcus, Alcaligenes, Moraxella, Mycobacterium, Aeromonas, Xanthomonas, Athrobacter, Flavobacterium, Micrococcus, zospirillum [1, 2,8,27- 30].

Fungal mycelium is very helpful in the degradation of hydrocarbons because of their penetration ability, it also aids in the entrance of bacteria to the deep soil. Fungal laccase, lignin peroxidase and manganese peroxidase enzymes degrade the hydrocarbons by its oxidation [31]. Crude oil degradation has been shown by some members of the following fungal genera: Candida, Stropharia, Rhodotorula, Pleurotus, Penicillium, Phanerochaete, Fusarium [8, 14, 32,27].

Microbial remediation of contaminated soil is affected by many factors such as water amount, temperature and pH of soil, concentration of oxygen, soil quality and amount of nutrients. Change in any of these factors can decrease the population of microbes and in turn decreases the bioremediation [33].

Microbial activity can be accelerated by using bioaugmentation and bio stimulation strategies. In bioaugmentation exogenous oil degrading bacteria are supplemented to enhance soil microbiota while in bio stimulation addition of nutrients, aeration and optimization of physical conditions like pH and temperature is performed. Research has shown that bioaugmentation and bio stimulation when used together effectively remediate crude oil hydrocarbons polluted soil. It has been observed that the number of exogenous bacteria decreases after sometimes because of nutrient unavailability or other abiotic factors (pH, temperature or oxygen). So, bio stimulation incorporation with bioaugmentation provided effective results in the degradation of crude oil pollutants (Figure 1) [1,23,30,34-36]. Different types of surfactants produced by many microorganisms are called biosurfactants. These biosurfactants enhance the bioavailability of hydrocarbons to the microbes and in turn increases its degradation. Use of biosurfactants producing microbes is a good bioremediation choice as this process is cheap, nontoxic with efficient degradation rate. So, researchers have turned their focus towards such microbes that can degrade crude oil and produces biosurfactants at the same time [37].

Phytoremediation

Phytoremediation is an effective, solar driven and low-cost strategy that uses plants for the removal of contaminants from the soil of large contaminated area. Plants have the ability to grow in polluted soil by metabolizing or accumulating the harmful compounds in their roots or shoots [45].

Plants with extended root systems, minimum water requirement, adaptability to a variety of environmental conditions and fast growth rate are appropriate for this purpose [46]. Phytoremediation efficiency depends on the plant species selection, environmental conditions and rhizobacteria [47].

Analysis of soil of the Possession Island after diesel leakage in 1997 showed that area with vegetation has 10% low concentration of hydrocarbons as compared to non-vegetation area [48].

Different mechanisms are devised by plants for the removal of contaminants i.e., phytoaccumulation (absorption of contaminants into the roots or shoots), phytodegradation (degradation of pollutants by utilization of plant enzymes such as laccase, oxygenase and nitroreductase), phytovolatization (release of volatile metabolites into the atmosphere) and phytostabilization (decrease the movement of contaminants) [11,49,50] reported that two plant species i.e., Eleusine indica and Cynodon dactylon significantly eliminated some low to medium molecular weight PAH from the soil by phytoextraction process, indicating their use in the removal of PAH.

Maize plants showed enhanced biodegradation in association with Cynanchum laeve. This symbiotic relationship between maize roots and Cynanchum laeve degraded 4-6 rings PAH more efficiently than any other treatment [11].

Vetiver grass, belongs to the Poaceae family, is a perennial grass. It decontaminates the soil by extraction of PAH and other toxins from the soil and accumulating it in the roots and shoots. This plant showed negative effect on its growth and other physical activities when grown on soil contaminated with diesel [51] Mirabilis jalapa, is also considered a good candidate for phytoremediation. [52] investigated that M. jalapa can remove 41-63% of saturated hydrocarbons within 127 days when compared with natural attenuation process (Figure 2).

Similarly, ryegrass, alfalfa, tall fescue, prairie grasses, meadow fescue, yellow medick, soybeans, Gazania, Mimosa pudica, Cyperus rotundus have shown good crude oil remediation [53-60].

With all the advantages, phytoremediation also has some drawbacks i.e., it is a time-consuming process, limited remediation in high pollutants concentration and limited area of success [47].

Rhizoremediation (Plant-microbe assisted remediation- recent technology)

Rhizoremediation requires such plants that can grow in oil contaminated soil and also provide favorable environment to contaminants degrading microbes by exudates secretion or aeration. Plant-microbe strategy not only increases the metabolic activity of rhizosphere microbes, but it also improves the soil physical and chemical properties and increases microbial access to the contaminants present in the soil [56].

PAH degrading bacterial strain Rhodococcus ruber Em1 showed enhanced degradation rate when combined with Orychophragmus violaceus during the period of 175 days in a controlled environment (mesocosms). The expressions of linA and RHD like genes, coding PAH-ring hydroxylating dioxygenase, increase 3-5 times in the mesocosoms [42]. Enhanced degradation of contaminants by maize plant was observed when maize plant was provided with indigenous microbial biomass inoculum [61].

Glycine max (Soybean) plant is among those plants that exhibit hydrocarbon remediating capability. Research showed that soybean remediation of crude oil was not because of the phytoaccumulation but it was a mutual action of G. max and rhizospheric microbes. It was observed that Glycine max growth in the contaminated soil effect the total number of bacteria, amount of water, pH and organic matter quantity [62].

A study conducted on wheat plant in hydroponics condition showed that wheat seedlings eliminate more than 20% of oil from the medium, but this remediating ability enhances to 29% when grown in association with Azospirillum [63].

Bioremediation of oil contaminated soil by using yellow alfalfa in combination with Acinetobacter sp. strain S- 33 improved the remediation efficiency 39% in comparison to alone alfalfa (34%) and Acinetobacter sp. S-33 (35%). Fractional Contaminants analysis showed that plant microbe association is the most efficient strategy in the cleanup of aromatic hydrocarbons from the soil [63].

Plant growth promoting bacteria (PGPR) promote the tolerance and resistance of plants against contaminants present in the soil. Ryegrass when grown with PGPR showed increased degradation of hydrocarbons to 61.5% for 3 years when 13% TPH content was used. It was observed that low concentration enhanced the degradation and vice versa [3,64].

Crude oil after leakage gets trapped or physically bound with the soil particles; access to these micro spaces is made possible by plant roots. Roots of plants harbor microbes in the rhizosphere as well as on the surface. So, root generates a pathway for these microbes to have access to these contaminants. Once in the soil micropores, GPR increases the solubility of oil droplets by producing biosurfactants or by adhering to the surface of the oil droplets. Microbial surface membrane oxygenase’s than generate fatty acid analogues by adding oxygen atoms into PHC. In this way microbes keep on growing and degrading contaminants. Tentatively, microbes use 150mg of nitrogen and 30mg of potassium to degrade 1g of PHC [65]. Utilization of plants and microbes in collaboration is indeed a good strategy to recovery contaminated soil. It might be a long process, but it is safer and environment friendly. Further field experiments must be performed to develop good models.

Conclusion

Crude oil is a quick and easily accessible energy source found in most of the countries. Its leakage during extraction and transportation has posed danger to the environment because it contains mutagenic and carcinogenic compounds. Soil contamination due to crude oil leakage has adverse effects on human and vegetation growth so its removal is essential. Many methods have been developed to remove crude oil from the soil i.e., physical, chemical, thermal and biological. Many alterations and development have been introduced in Physio-chemical and thermal methods to enhance their efficiency and reduce their demerits. Still these methods have many drawbacks and less acceptable by the society. On the other hand, bioremediation methods are preferred because they are efficient, cheap and nature friendly. In the recent technology i.e., rhizoremediation, microbes and plants are combined together in synergistic relationship to efficiently remove the crude oil contaminants from the soil. Research has shown that rhizoremediation is more efficient than microbial and phytoremediation techniques separately.

To read more about this article: https://irispublishers.com/wjass/fulltext/remediation-methods-of-crude-oil-contaminated.ID.000595.php

Indexing List of Iris Publishers: https://medium.com/@irispublishers/what-is-the-indexing-list-of-iris-publishers-4ace353e4eee

Iris publishers google scholar citations: https://scholar.google.co.in/scholar?hl=en&as_sdt=0%2C5&q=irispublishers&btnG=

[sleepyfloor]

partial fraction decomposition makes me want to decompose

[livingcorner]

Organic Garden Soil: Use Organic Compost +more | Gardeners.com

The healthy soil in this bed is ready for planting.

Though some gardeners may be blessed with perfect soil, most of us garden in soil that is less than perfect. If your soil has too much clay in it, is too sandy, too stony or too acidic, don’t despair. Turning a poor soil into a plant-friendly soil is not difficult to do, once you understand the components of a healthy soil.

You're reading: Organic Garden Soil: Use Organic Compost +more | Gardeners.com

Soil is composed of weathered rock and organic matter, water and air. But the hidden “magic” in a healthy soil is the organisms—small animals, worms, insects and microbes—that flourish when the other soil elements are in balance.

Minerals. Roughly half of the soil in your garden consists of small bits of weathered rock that has gradually been broken down by the forces of wind, rain, freezing and thawing and other chemical and biological processes.

Vegetable gardeners understand the importance of healthy garden soil.

Soil type is generally classified by the size of these inorganic soil particles: sand (large particles), silt (medium-sized particles) or clay (very small particles). The proportion of sand, silt and clay particles determines the texture of your soil and affects drainage and nutrient availability, which in turn influence how well your plants will grow.

Organic Matter. Organic matter is the partially decomposed remains of soil organisms and plant life including lichens and mosses, grasses and leaves, trees, and all other kinds of vegetative matter.

Although it only makes up a small fraction of the soil (normally 5 to 10 percent), organic matter is absolutely essential. It binds together soil particles into porous crumbs or granules which allow air and water to move through the soil. Organic matter also retains moisture (humus holds up to 90 percent of its weight in water), and is able to absorb and store nutrients. Most importantly, organic matter is food for microorganisms and other forms of soil life.

You can increase the amount of organic matter in your soil by adding compost, aged animal manures, green manures (cover crops), mulches or peat moss. Because most soil life and plant roots are located in the top 6 inches of soil, concentrate on this upper layer. To learn more about making your own compost, read All About Composting.

Be cautious about incorporating large amounts of high-carbon material (straw, leaves, wood chips and sawdust). Soil microorganisms will consume a lot of nitrogen in their efforts to digest these materials and they may deprive your plants of nitrogen in the short run.

Soil life. Soil organisms include the bacteria and fungi, protozoa and nematodes, mites, springtails, earthworms and other tiny creatures found in healthy soil. These organisms are essential for plant growth. They help convert organic matter and soil minerals into the vitamins, hormones, disease-suppressing compounds and nutrients that plants need to grow.

Their excretions also help to bind soil particles into the small aggregates that make a soil loose and crumbly. As a gardener, your job is to create the ideal conditions for these soil organisms to do their work. This means providing them with an abundant source of food (the carbohydrates in organic matter), oxygen (present in a well-aerated soil), and water (an adequate but not excessive amount).

Air. A healthy soil is about 25 percent air. Insects microbes, earthworms and soil life require this much air to live. The air in soil is also an important source of the atmospheric nitrogen that is utilized by plants.

Well-aerated soil has plenty of pore space between the soil particles or crumbs. Fine soil particles (clay or silt) have tiny spaces between them – in some cases too small for air to penetrate. Soil composed of large particles, like sand, has large pore spaces and contains plenty of air. But, too much air can cause organic matter to decompose too quickly.

To ensure that there is a balanced supply of air in your soil, add plenty of organic matter, avoid stepping in the growing beds or compacting the soil with heavy equipment and never work the soil when it is very wet.

Water. A healthy soil will also contain about 25 percent water. Water, like air, is held in the pore spaces between soil particles. Large pore spaces allow rain and irrigation water to move down to the root zone and into the subsoil. In sandy soils, the spaces between the soil particles are so large that gravity causes water to drain down and out very quickly. That’s why sandy soils dry out so fast.

Read more: Learn Which Plants to Avoid If Rabbits Are a Problem in Your Garden

Small pore spaces permit water to migrate back upwards through the process of capillary action. In waterlogged soils, water has completely filled the pore spaces, forcing out all the air. This suffocates soil organisms as well as plant roots.

Ideally, your soil should have a combination of large and small pore spaces. Again, organic matter is the key, because it encourages the formation of aggregate, or crumbs, or soil. Organic matter also absorbs water and retains it until it is needed by plant roots.

Every soil has a different combination of these five basic components. By balancing them you can dramatically improve your soil’s healthy and your garden’s productivity. But first, you need to know what kind of soil you have.

Soil Texture and Type

Soil texture can range from very fine particles to coarse and gravelly. You don’t have to be a scientist to determine the texture of the soil in your garden. To get a rough idea, simply place some soil in the palm of your hand and wet it slightly, then run the mixture between your fingers. If it feels gritty, your soil is sandy; if it feels smooth, like moist talcum powder, your soil is silty; if it feels harsh when dry, sticky or slippery when wet, or rubbery when moist, it is high in clay.

Every soil has unique physical characteristics, which are determined by how it was formed. The silty soil found in an old floodplain is inherently different from stony mountain soil; the clay soil that lay under a glacier for millions of years is unlike the sandy soil near an ocean. Some of these basic qualities can be improved with proper management—or made worse by abuse.

Identifying your soil type: Soils are generally described according to the predominant type of soil particle present: sand, silt or clay. By conducting a simple soil test, you can easily see what kind of soil you’re dealing with. You may want to repeat this test with several different soil samples from your lawn and garden.

1. Fill a quart jar about one-third full with topsoil and add water until the jar is almost full.

2. Screw on the lid and shake the mixture vigorously, until all the clumps of soil have dissolved.

3. Now set the jar on a windowsill and watch as the larger particles begin to sink to the bottom.

4. In a minute or two the sand portion of the soil will have settled to the bottom of the jar. Mark the level of sand on the side of the jar.

5. Leave the jar undisturbed for several hours. The finer silt particles will gradually settle onto the sand. You will find the layers are slightly different colors, indicating various types of particles.

6. Leave the jar overnight. The next layer above the silt will be clay. Mark the thickness of that layer. On top of the clay will be a thin layer of organic matter. Some of this organic matter may still be floating in the water. In fact, the jar should be murky and full of floating organic sediments. If not, you probably need to add organic matter to improve the soil’s fertility and structure.

Improving Soil Structure

Even very poor soil can be dramatically improved, and your efforts will be well rewarded. With their roots in healthy soil, your plants will be more vigorous and more productive.

Sandy Soil. Sand particles are large, irregularly shaped bits of rock. In a sandy soil, large air spaces between the sand particles allow water to drain very quickly. Nutrients tend to drain away with the water, often before plants have a chance to absorb them. For this reason, sandy soils are usually nutrient-poor.

A sandy soil also has so much air in it that microbes consume organic matter very quickly. Because sandy soils usually contain very little clay or organic matter, they don’t have much of a crumb structure. The soil particles don’t stick together, even when they’re wet.

To improve sandy soil:

Work in 3 to 4 inches of organic matter such as well-rotted manure or finished compost.

Mulch around your plants with leaves, wood chips, bark, hay or straw. Mulch retains moisture and cools the soil.

Add at least 2 inches of organic matter each year.

Grow cover crops or green manures.

Clay Soil. Clay particles are small and flat. They tend to pack together so tightly that there is hardly any pore space at all. When clay soils are wet, they are sticky and practically unworkable. They drain slowly and can stay waterlogged well into the spring. Once they finally dry out, they often become hard and cloddy, and the surface cracks into flat plates.

Lack of pore space means that clay soils are generally low in both organic matter and microbial activity. Plant roots are stunted because it is too hard for them to push their way through the soil. Foot traffic and garden equipment can cause compaction problems. Fortunately, most clay soils are rich in minerals which will become available to your plants once you improve the texture of the soil.

To improve clay soil:

Work 2 to 3 inches of organic matter into the surface of the soil. Then add at least 1 inch more each year after that.

Add the organic matter in the fall, if possible.

Use permanent raised beds to improve drainage and keep foot traffic out of the growing area.

Minimize tilling and spading.

Silty Soil. Silty soils contain small irregularly shaped particles of weathered rock, which means they are usually quite dense and have relatively small pore spaces and poor drainage. They tend to be more fertile than either sandy or clayey soils.

To improve silty soil:

Add at least 1 inch of organic matter each year.

Concentrate on the top few inches of soil to avoid surface crusting.

Avoid soil compaction by avoiding unnecessary tilling and walking on garden beds.

Consider constructing raised beds.

Soil pH

The pH level of your soil indicates its relative acidity or alkalinity. A pH test measures the ratio of hydrogen (positive) ions to hydroxyl (negative) ions in the soil water. When hydrogen and hydroxyl ions are present in equal amounts, the pH is said to be neutral (pH 7). When the hydrogen ions prevail, the soil is acidic (pH 1 to pH 6.5). And when the hydroxyl ions tip the balance, the pH is alkaline (pH 6.8 to pH 14).

Most essential plant nutrients are soluble at pH levels of 6.5 to 6.8, which is why most plants grow best in this range. If the pH of your soil is much higher or lower, soil nutrients start to become chemically bound to the soil particles, which makes them unavailable to your plants. Plant health suffers because the roots are unable to absorb the nutrients they require.

To improve the fertility of your soil, you need to get the pH of your soil within the 6.5 to 6.8 range. You can’t, and shouldn’t try, to change the pH of your soil overnight. Instead, gradually alter it over one or two growing seasons and then maintain it every year thereafter. Liberal applications of organic matter is a good idea too, because it helps to moderate pH imbalances.

Acidic Soil. If the pH of your soil is less than 6.5, it may be too acidic for most garden plants (although some, such as blueberries and azaleas require acidic soil). Soils in the eastern half of the U.S. are usually on the acidic side.

The most common way to raise the pH of your soil (make it less acidic) is to add powdered limestone. Dolomitic limestone will also add manganese to the soil. Apply it in the fall because it takes several months to alter the pH.

Wood ash will also raise the pH, and it works more quickly than limestone and contains potassium and trace elements. But if you add too much wood ash, you can drastically alter the pH and cause nutrient imbalances. For best results, apply wood ash in the winter, and apply no more than 2 pounds per 100 square feet, every two to three years.

To raise the pH of your soil by about one point:

Read more: 10 Top Gardening Tips for Beginners

In sandy soil: add 3 to 4 pounds of ground limestone per 100 square feet.

In loam (good garden soil): add 7 to 8 pounds per 100 square feet.

In heavy clay: add 8 to 10 pounds per 100 square feet.

Alkaline Soil. If your soil is higher than 6.8, you will need to acidify your soil. Soils in the western U.S., especially in arid regions, are typically alkaline. Soil is usually acidified by adding ground sulfur. You can also incorporate naturally acidic organic materials such as conifer needles, sawdust, peat moss and oak leaves.

To lower soil pH by about one point:

In sandy soil: add 1 pound ground sulphur per 100 square feet.

In loam (good garden soil): add 1.5 to 2 pounds per 100 square feet.

In heavy clay: add 2 pounds per 100 square feet.

Soil Testing

A professional soil test will provide you with a wealth of information about your soil, including the pH and amount of different nutrients.

Your local Cooperative Extension Service office may offer a professional soil testing service. The advantage is low cost and results that are specifically geared to your location. If this service is not available, you can also have your soil tested by an independent soil lab. If possible, choose one in your own region of the country.

Soil test results usually rate the levels of soil pH, phosphorus, potassium, magnesium, calcium, and sometimes nitrogen. (Most labs do not test for nitrogen because it is so unstable in the soil.) Some labs also offer tests for micronutrients such as boron, zinc and manganese. Unless you feel there may be a deficiency problem, you probably won’t need micronutrient testing. As a preventative measure, you can apply organic fertilizers that include micronutrients (such as greensand and kelp meal).

To get the most accurate test results, take a soil sample from each garden area: lawn, flower garden, and vegetable garden. Spring and fall are the best times to perform a soil test. The soil is more stable, and these are good times to incorporate any recommended fertilizers. Many labs will give recommendations for specific organic amendments upon request. If not, you will have to compare labels to find organic substitutes for the chemical fertilizers that may be suggested.

Soil Testing Labs

Woods End Soil Labs RFD 1, Box 4050 Old Rome Road Mt. Vernon, ME 04352 207-293-2457

A & L Agricultural Labs 7621 White Pine Road Richmond, VA 23237 804-743-9401

Green Gems P.O. Box 6007 Healdsburg, CA 95448 707-431-1691

Frequently Asked Questions

What are cover crops and green manures? Cover crops are used primarily to protect fallow (unused) soil. In the North, gardeners usually plant them at the end of the season so their soil is not bare over the winter. Cold-hardy crops such as vetch and winter rye are best for overwintering. They will begin growth again in spring, and need to be tilled in before you can plant your garden.

Green manures can also be planted on a new garden area the year before you plan to use it. They will choke out weeds and add a wealth of organic matter. Legumes, including field peas, soybeans, and alfalfa, will contribute both nitrogen and organic matter to the soil. Fast-growing grains and buckwheat produce the most organic matter and will smother competing weeds as they grow.

If your soil will be fallow for more than one growing season, you can plant perennial or biennial green manures, such as clover or alfalfa. All cover crops should be tilled-in at least three weeks before the area is to be replanted, so the organic matter will already be partially decomposed at planting time.

What are liquid soil conditioners? Liquid soil conditioners typically contain a blend of humic acid and catalytic enzymes, which are produced in a controlled environment by the same sort of microorganisms that are at work in your compost pile. When applied to your soil, their effect is similar to the effect you get when you add compost. Clay soils become easier to work and nutrients become more available; sandy soils are able to retain more water and nutrients.

Researchers have now isolated specific organic substances that solve specific soil problems. Soon you will be able to buy organic soil conditioners that have been specially selected for their effectiveness in opening up heavy soils or dislodging salts and other elements that have become tied up in the soil.

What is hardpan? Hardpan is a dense layer of soil that restricts root growth and the movement of moisture, air and beneficial organisms through the soil. Hardpan is usually created by glacial action, heavy rain, or heavy equipment, and typically lies between 6 and 25 inches below the soil surface.

Farmers often cope with hardpan by using a chisel plow to cut and break up this dense layer of soil. Home gardeners can break up and mix the hardpan layer by “double digging” the soil. This involves removing 10 to 12 inches of topsoil, and then working organic matter into the 12-inch layer of material that lies below. If the hardpan layer is not too deep, you can use a digging fork to puncture it and open up passages for air and water.

What does chelated mean? Chelation is a process that joins a nutrient, such as iron, to a non-nutrient compound that can be easily absorbed by your plants.

What does 5-8-3 mean? The numbers refer to the percentage by net weight of total nitrogen (N; always the first number), available phosphorus (P; the second number), and soluble potash (K; the third number). In other words, a 5-8-3 fertilizer contains 5 percent nitrogen, 8 percent available phosphorus, and 3 percent soluble potash.

Labeling laws allow only the immediately available nutrients to be listed. That is why the nutrient analysis for organic fertilizers tends to be low. Most organic fertilizers actually have a higher nutrient content, but these nutrients gradually become available to plants over a period of months or even years.

What are the benefits of seaweed? Seaweed contains at least sixty micronutrients, including iron, copper, zinc, boron, and manganese. Seaweed also contains a high concentration of natural growth hormones which allow it to grow rapidly in its natural environment. When applied to plants, these growth hormones stimulate root growth, reduce transplant shock, promote more rapid fruit set, increase frost resistance and improve storage life. Research has also revealed that seaweed contains antitoxins that help plants fend off bacteria, viruses and pests.

Powdered seaweed (kelp meal) releases its nutrients gradually into the soil. Liquid seaweed makes these nutrients immediately available. Seaweed is not a complete fertilizer because it doesn’t provide adequate nitrogen and phosphorus for most plants. But it is an excellent part of a balanced soil-building program.

Source: https://livingcorner.com.au Category: Garden

source https://livingcorner.com.au/organic-garden-soil-use-organic-compost-more-gardeners-com/

[doyouthatknow]

Ecosystem: Energy Flow

Life is dependent on energy from the sun. The organisms that use the chemical as it flows all life forms, except for roads , high-energy organic nutrients are obtained directly or indirectly from photosynthesis. The solar energy that reaches the Earth's surface of 1% less than 1/10 of a portion of the products of photosynthesis to be converted to total primary (first) gets the name of the production. Plants, the total production is 15-20% of their respiration are used. The rest is used to make new textures, and net primary production is known as. Per year approximately 6X1020 gr. kal energy as predicted, the total biosphere net primary production, heterotrophic forms the basis for the energy of life in the world. Animals fungi protists bacteria and heterotrophic organisms, which are almost all of the energy they need ototrophic and most of the organisms, other organisms, called detritus or other ototrof who heterotrof the rotten parts (waste products, or dead tissues) by eating. In a community of energy that can be moved an array of organisms, the food chain is called in the usual way. In most real communities, there are many complex food chains together as in the past. These together they are the foundation of a community's food web. However, a food chain or food regardless of how complex of a network can be how it is always that you have certain basic features. Every food chain or food web for the community ototrophic the producer organisms (usually plants Yesil) at each level of each food web begins with and or chain, usually scavenger organisms such as bacteria and fungi (decomposer) called parser ends with. Also centipedes, earthworms, termites, flies, lobsters, mussels and some fish feed on detritus and partially release. All heterotrof like scavengers, they release CO2 and NH3 which can be reused by manufacturers such as simple substances. The connections between the parser and shows the diversity of manufacturers. Directly to manufacturers or producers may be processed by the parser after the death of the primary consumers which are herbivores, they can be eaten by; terrestrial plant production is about 10% is consumed in this way. In contrast, herbivore, or directly exposed to the impact of the parser may or may not be carnivores, parasites, carrion eaters, and are eaten by secondary consumers like. Ecology scientists, community, the steps of feeding in the food chain, trophic levels 

denote. Thus, all manufacturers together the first traffic level; primary consumers (herbivores) at the second trophic level; herbivore-eating carnivores form the third level, traffic. A community of species at each trophic level to another vary. Apart from that, many types of different food, such as omnivores fed a single food within a network the level of traffic the level of traffic that might be functional in two or more categories are not immutable themselves. For example, seeds, herbivorous insects, carnivorous insects, and a breed that eats tit, second, third, and fourth works on the traffic levels. In spite of this complexity, the concept of trophic levels, the community retains the value in the analysis. At each successive trophic level, there is loss of energy from the system. This loss, in part, the biomass of the consumer population is the lack of capable of obtaining more energy from a piece of; partly, omissions assimilasyon capabilities (e.g., ruminants and termites except for most of the herbivores can't metabolize the cellulose wall of plant cells); partly in accordance with the second law of thermodynamics, respiratory, and as a result in the form of heat due to the loss of energy (usually heat energy loss in each Energy Transfer that can be used as required. As a result, only a part of the energy at one trophic level, can be transferred to other levels. The fraction of the transmitted energy, the most effective animals to consume other animals ektotermik 35% with a high rate of the plants, and some small endothermic animals that fed on 0.1% to the bottom of a falling rate varies between. Backwards, almost all of the remaining energy, the parser, or is lost as heat. Therefore, less of a community the herbivores feeding on plants; a herbivore carnivore shows a less than efficiency, and so on. Thus, the distribution of productivity within a community, at the base of the first trophic level (producers) at the top of the latest consumer can be represented by a pyramid where the level of traffic. From a traffic efficiency quickly drops to the next level, because in a food chain are more rare than four or five digits; the fifth digit, the first digit in the efficiency of 0.0001% is more than rarely, and a top nutrient density of a new stage of support available is very low. The pyramid of productivity (also called the pyramid of energy flow) is a feature of all ecosystems. Many other features of ecosystems, energy flow in the system is associated with, since the pyramid may be reduced in accordance with the model; however, results may deviate from the model, because secondary productivity of the distribution pyramid. The pyramid of biomass is an example. In general, each successive traffic steps means that less biomass can be supported at each level of energy reduction. Therefore, the total mass of carnivores in a particular community is always less than the total mass of herbivores. However, traffic between the different steps of a community type, body size, growth rates and life lengths of the model pyramid, the biomass is important in determining whether those communities will cover. For example, manufacturers with high metabolic and reproductive rates, small algae and some aquatic communities, at a certain time, beyoba consumers, manufacturers can be much more; the total mass of all the algae that live but a year of living in that year will be larger than the total consumer mass.

The mutual relations between organisms at different traffic levels, it can have some effect on the size of the organism. Therefore, carnivores than herbivores usually are bigger. Secondary carnivores, feed on primary carnivores are larger than they usually where. In this case, the total biomass, consecutive traffic levels tend to decrease, so if the size of individuals increases at each level if it should decrease the number of individuals (too many parsers are excluded from this).As a result, some communities n herbivores, plants from herbivores and carnivorous individuals that number less than the pyramids show. As we mentioned earlier, killer whales, such as wolves, lions or top predators (predators at the top of the food chain) they can not hunt over both of their types. they make a very wide distribution, and because these animals are very few; and very little energy to find and hunt their own breeds. However, many community does not have a pyramid of numbers. For example, biomass is less, because a much greater number of consumer the insect is close to the plant manufacturer. Because plant-eating insects, feed on plants are usually much smaller; for example, the single large spring fed by thousands of eating a leaf on a tree-boring caterpillars and insects can be found. Including parasites in the food chain, because they are generally smaller and more numerous the parasites of the hosts, population—magnitude relationship is reversed. When considering the inability to transfer energy from a level to another traffic our remote ancestors kalitlanan both animal and vegetable diet, instead of eating vegetables entirely, if we stopped being omnivorous world seems to accommodate more people. However, this common belief there are some shortcomings. First, for example, large areas of the world —Argentina, Australia, Africa, South America, Western and Western— unfit for human consumption, however, the large herbivores that can feed this kind of habitat plants which are adapted to low quality pasture. Another problem, related to human nutritional requirements, whether vegetarian diet is animal protein daily that usually requires some additional. In Western societies most individuals consume much more animal protein than is necessary to sustain their lives, in fact, cattle meat for a few weeks before slaughter to enhance the taste of high-quality feed with seed. In the United States, total grain production (mostly corn), 30% cattle and the nutrition of chickens is divided into. Cattle is fed only by beslense was a significant portion of the world that can be done in the area of Agriculture, milk production 

who want to provide food for their dairy cattle for the continuation of high quality weed, it would be necessary . Another questionable part of cattle, animal farms along with that they are the main source of methane that might contribute to global warming. Malthus's other dilemma is a persistent problem in developing countries and a significant reduction in the birth rate, without any increase in World Food Production, After all, can serve to increase the number of people that will be hungry again. Any increase in the top of the pyramid; however, at lower traffic levels, a proportionally larger increase can be supported. Bibliography: https://www.sciencedirect.com Read the full article

[lesbianrewrites]

The Martian Chapter 6

*disclaimer* This is a project done for fun, and none of these characters/works belong to me. I do not claim to own any of the material on this page.

This is a Lesbian edit of The Martian by Andy Weir.

Chapters will be posted every day at 2pm EST.

Google doc version can be found here. The chapter can also be found under the cut. Enjoy!

CHAPTER VI

Venkat returned to his office, dropped his briefcase on the floor, and collapsed into his leather chair. He took a moment to look out the windows at his scenic view of the Johnson Space Center.

Glancing at his computer screen, he noted 47 unread emails urgently demanding his attention. They could wait. Today had been a sad day. Today was the memorial service for Maia Watney.

The President had given a speech, praising Watney’s bravery and sacrifice, and the quick actions of Commander Lewis in getting everyone else to safety. Commander Lewis and the surviving crew, via long range communication from Hermes, gave eulogies to their departed comrade from deep space. They had another ten months of travel yet to endure.

The Director had given a speech as well, reminding everyone that space flight is incredibly dangerous, and how we will not back down in the face of adversity.

During preparation for the service, they’d asked Venkat if he was willing to make a speech. He’d declined. What was the point? Watney was dead. Nice words from the Director of Mars Missions wouldn’t bring her back.

“You ok, Venk?” came a voice from the doorway.

Venkat swiveled around. “Guess so, ” he said.

“You could have given a speech.”

“I didn’t want to. You know that.”

“Yeah, I know. I didn’t want to, either. But I’m the director of NASA. It’s kind of expected. You sure you’re ok?”

“Yeah, I’ll be fine.”

“Good, ” Teddy said, walking in. “Let’s get back to work, then.”

“Sure, ” Venkat shrugged. “Let’s start with you authorizing my satellite time.”

Teddy leaned against the wall with a sigh. “This again.”

“Yes, ” Venkat said. “This again. What is the problem?”

“Ok, run me through it. What, exactly, are you after?”

Venkat leaned forward. “Ares 3 was a failure, but we can salvage something from it. We’re funded for five Ares missions. I think we can get Congress to fund a sixth.”

“I don’t know, Venk…”

“It’s simple, Teddy, ” Venkat pressed on. “They evac’d after six sols. There’s almost an entire mission worth of supplies up there. It would only cost a fraction of a normal mission. It normally takes 14 presupply probes to prep a site. We might be able to send what’s missing in three. Maybe two.”

“Venk, the site got hit by a 175 km/h sandstorm. It’ll be in really bad shape.”

“That’s why I want imagery, ” Venkat explained. “I just need a couple of shots of the site. We could learn a lot.”

“Like what? You think we’d send people to Mars without being sure everything was in perfect working order?”

“Everything doesn’t have to be perfect, ” Venkat said quickly. “Whatever’s broken, we’d send replacements for. The only thing that needs to work is the MAV. And we’d have to send a fresh one anyway.”

“How will we know from imagery what’s broken?”

“It’s just a first step. They evac’d because the wind was a threat to the MAV, but the Hab can withstand a lot more punishment. It might still be in one piece.

“And it’ll be really obvious. If it popped, it’d completely blow out and collapse. If it’s still standing, then everything inside will be fine. And the rovers are solid. They can take any sandstorm Mars has to offer. Just let me take a look, Teddy, that’s all I want.”

Teddy looked down, “You’re not the only guy who wants satellite time, you know. We have Ares 4 supply missions coming up. We need to concentrate on Schiaparelli Crater.”

“I don't get it, Teddy. What's the problem here?” Venkat asked. “I’m talking about securing us another mission. We have 12 satellites in orbit around Mars, I’m sure you can spare one or two for a couple of hours. I can give you the windows for each one when they’ll be at the right angle for Ares 3 shots-“

“It’s not about satellite time, Venk, ” Teddy interrupted.

Venkat froze. “Then… but… what…”

Teddy looked down. “We’re a public domain organization. There’s no such thing as secret or secure information here.”

“So?”

“Any imagery we take goes directly to the public.”

“Again: so?”

“Maia Watney’s body will be within a twenty meters of the Hab. Maybe partially buried in sand, but still very visible, and with a comm antenna sticking out of her chest. Any images we take will show that.”

Venkat stared. Then glared. “This is why you denied my imagery requests for two months?”

“Venk, come on-“

“Really, Teddy?” he said. “You’re afraid of a PR problem?”

“The media’s obsession with Watney’s death is finally starting to taper off, ” Teddy said evenly. “It’s been bad press after bad press for two months. Today’s memorial gives people closure, and the media can move on to some other story. The last thing we want to do is dredge everything back up.”

“So what do we do, then? She’s not going to decompose. She’ll be there forever.”

“Not forever, ” Teddy said. “Within a year, she’ll be covered in sand from normal weather activity.”

“A year?” Venkat said, rising to his feet. “That’s ludicrous. We can’t wait a year for this.”

“Why not? Ares 5 won’t even launch for another five years. Plenty of time.”

Venkat took a deep breath and thought for a moment.

“Ok, consider this, ” he said. “Sympathy for Watney’s family is really high. Ares 6 could bring the body back. We don’t say that’s the purpose of the mission, but we make it clear that would be part of it. If we framed it that way, we’d get more support in Congress. But not if we wait a year. In a year, people won’t care any more.”

Teddy rubbed his chin. “Hmm…”

Mindy stared at the ceiling. She had little else to do. The 3am shift was pretty dull. Only a constant stream of coffee kept her awake.

Monitoring the status of satellites around Mars sounded like an exciting proposition when she took the transfer. But the satellites tended to take care of themselves. Her job turned out to be sending emails as imagery became available.

“Master’s Degree in Mechanical Engineering, ” she grumbled to herself. “And I’m working in an all-night photo booth.”

She sipped her coffee.

A flicker on her screen announced another set of images were ready for dispatch. She checked the name on the work order. Venkat Kapoor.

Posting the data directly to internal servers, she composed an email to Dr. Kapoor. As she entered the latitude and longitude of the image, she recognized the numbers.

“31.2°N, 28.5°W… Acidalia Planitia… Ares 3?”

Out of curiosity, she brought up the first of the 17 images.

As she suspected, it was the Ares 3 site. She’d heard they were going to image it. Slightly ashamed of herself, she scoured the image for any sign on Maia Watney’s dead body. After a minute of fruitless searching, she was simultaneously relieved and disappointed.

She moved on to perusing the rest of the image. The Hab was intact; Dr. Kapoor would be happy to see that.

She brought the coffee mug to her lips, then froze.

“Um…” she mumbled to herself. “Uhhh…”

Quickly bringing up the NASA intranet, she navigated through the site to the specifics of the Ares missions. After some quick research, she picked up her phone.

“Hey, this is Mindy Park at SatCon. I need the mission logs for Ares 3, where can I get ‘em?... Uh huh… uh-huh…. Ok… Thanks.”

After some more time on the intranet, she leaned back in her seat. She no longer needed the coffee to keep awake.

Picking up the phone again, “Hello, Security? This is Mindy Park in SatCon. I need the emergency contact number for Dr. Venkat Kapoor… Yes, the Director of Mars Missions… Yes it’s an emergency.”

Mindy fidgeted in her seat as Venkat trudged in.

“You Mindy Park?” He asked, looking mildly annoyed.

“Yeah, ” she quavered. “Sorry to drag you in.”

“I’m assuming you had a good reason. So?”

“Um, ” she said, looking down. “Um, it’s. Well. The imagery you ordered. Um. Come here and look.”

He pulled another chair to her station and seated himself. “Is this about Watney’s body? Is that why you’re shook up?”

“Um, no, ” she said. “Um. Well… uh.” She pointed to the screen

Venkat inspected the image. “Looks like the Hab’s in one piece. That’s good news. Solar array looks good. The rovers are ok, too. Main dish isn’t around. No surprise there. What’s the big emergency?”

“Um, ” she said, touching her finger to the screen. “That.”

Venkat leaned in and looked closer. Just below the Hab, beside the rovers, two white circles sat in the sand. “Hmm. Looks like Hab canvas. Maybe the Hab didn’t do well after all? I guess pieces got torn off and-“

“Um, ” she interrupted. “They look like rover pop-tents.”

Venkat looked again. “Hmm. Probably right.”

“How’d they get set up?” Mindy asked.

Venkat shrugged. “Commander Lewis probably ordered them deployed during the evac. Not a bad idea. Have the emergency shelters ready in case the MAV didn’t work and the Hab breached.”

“Yeah, um, ” Mindy said, opening a document on her computer. “This is the entire mission log for Sols 1 through 6. From MDV touchdown to MAV emergency liftoff.”

“Ok, and?”

“I read through it. Several times. They never threw out the pop tents.” Her voice cracked at the last word.

“Well, uh…” Venkat said, puzzled. “They obviously did, but it didn’t make it in to the log.”

“They activated two emergency pop tents and never told anyone?”

“Hmm. That doesn’t make a lot of sense, no. Maybe the storm messed with the rovers and the tents autodeployed.”

“Um, ” Mindy stammered, “So after autodeploying, they detached themselves from the rovers and lined up next to each other 20 meters away?”

Venkat looked back to the image. “Well obviously they activated somehow.”

“Why are the solar cells clean?” Mindy said, tears forming. “There was a huge sandstorm. Why isn’t there sand all over them?”

“A good wind could have done it?” Venkat said, unsure.

“Did I mention I never found Watney’s body?” She said, sniffling.

Venkat’s eyes widened as he stared at the picture. “Oh…” he said quietly. “Oh god…”

Mindy put her hands over her face and sobbed quietly.

“Fuck!” Director of Media Relations Annie Montrose said. “You have got to be fucking kidding me!”

Teddy rubbed his forehead. “How sure are we of this?”

“Nearly 100%, ” Venkat said.

“Fuck!” Annie said.

“Not helping, Annie, ” Teddy said.

“Do you have any idea the magnitude of shitstorm this is gonna’ be?” She retorted.

“One thing at a time, ” Teddy said. “Venk, what makes you sure she’s alive?”

“For starters, no body.” Venkat explained. “Also, the pop-tents are set up. And the solar cells are clean. You can thank Mindy Park in SatCon for noticing all that, by the way.

“But, ” Venkat continued, “her body could have been buried in the Sol 6 storm. The pop tents might have autodeployed and wind could have blown them around. A 30km/h windstorm some time later would be strong enough to clean the solar cells but not strong enough to carry sand. It’s not likely, but it’s possible.

“So I spent the last few hours checking everything I could. Commander Lewis had two outings in Rover 2. The second was on Sol 5. According to the logs, after returning, she plugged it in to the Hab for recharging. It wasn’t used again, and 13 hours later they evac’d.”

He slid a picture across the table to Teddy.

“That’s one of the images from last night. As you can see, Rover 2 is facing away from the Hab. The charging port is in the nose, and the cable isn’t long enough to reach.”

Teddy frowned. “She must have parked it facing the Hab or she wouldn’t have been able to plug it in, ” he said. “It’s been moved since Sol 5.”

“Yeah, ” Venkat said, sliding another picture to Teddy. “But here’s the real evidence. In the lower right of the image you can see the MDV. It’s been taken apart. I’m pretty sure they wouldn’t have done that without telling us.

“And the clincher is on the right of the image, ” Venkat pointed. “The landing struts of the MAV. Looks like the fuel plant has been completely removed, with considerable damage to the struts in the process. There’s just no way that could have happened before liftoff. It would endanger the MAV way too much for Lewis to allow it.”

“Hey, ” Annie interrupted. “Why not talk to Lewis? Let’s go to CAPCOM and ask her this shit directly.”

Venkat looked to Teddy knowingly. After a few moments, Teddy sighed.

“Because, ” he said. “If Watney really is alive, we don’t want the Ares 3 crew to know.”

“What!?” Annie said. “How can you not tell them?”

“They have another ten months on their trip home, ” Teddy explained. “Space travel is dangerous. They need to be alert and undistracted. They’re sad that they lost a crewmate, but they’d be devastated if they found out they’d abandoned her alive.”

Annie looked to Venkat. “You’re on board with this?”

“It’s a no-brainer, ” Venkat said. “Let ‘em deal with that emotional trauma when they’re not flying a spaceship around.”

“This’ll be the most talked-about event since Apollo 11, ” Annie said. “How will you keep it from them?

Teddy shrugged. “Easy. We control all communication with them.”

“Fuck, ” Annie said, opening her laptop. “When do you want to go public?”

“What’s your take, ” he asked.

“Mmm, ” Annie said, “We can hold the pics for 24 hours before we’re required to make them public. We’ll need to release a statement along with them. We don’t want people working it out on their own. We’d look like assholes.”

“Ok, ” Teddy agreed, “put together a statement.”

“This is so fucked up, ” she said.

“Where do we go from here?” Teddy asked Venkat.

“Step one is communication, ” Venkat said. “From the pics, it’s clear the comm array is ruined. We need another way to talk. Once we can talk, we can assess and make plans.”

“All right, ” Teddy said. “Get on it. Take anyone you want for any department. Use as much overtime as you want. Find a way to talk to her. That’s your only job right now.”

“Got it.”

“Annie, make sure nobody gets wind of this till we announce.”

“Right, ” Annie said. “Who else knows?”

“Just the three of us and Mindy Park in SatCon, ” Venkat said.

“I’ll have a word with her, ” Annie said.

Teddy stood and opened his cell phone. “I’m going to Chicago. I’ll be back later today.”

“Why?” Annie asked.

“That’s where Watney’s parents live, ” Teddy said. “I owe them a personal explanation before it breaks on the news.”

“They’ll be happy to hear their daughter’s alive, ” Annie said.

“Yeah, she’s alive, ” Teddy said. “But if my math is right, she’s doomed to starve to death before we can possibly help her. I’m not looking forward to the conversation.”

“Fuck, ” Annie said, thoughtfully.

“Nothing? Nothing at all?” Venkat groaned. “Are you kidding me? You had 20 experts working for 12 hours on this. We have a multi-billion dollar communication network. You can’t figure out any way to talk to her?”

The two men in Venkat’s office fidgeted in their chairs.

“She’s got no radio, ” said Chuck.

“Actually, ” said Morris, “She’s got a radio, but she doesn’t have a dish.”

“Thing is, ” Chuck continued, “without the dish, a signal would have to be really strong-“

“Like, melting-the-pigeons strong-“ Morris supplied

“-for her to get it.” Chuck finished.

“We considered Martian satellites, ” Morris said. “They’re way closer. But the math doesn’t work out. Even SuperSurveyor 3, which has the strongest transmitter, would need to be 14 times more powerful-“

“17 times, ” Chuck said.

“14 times, ” Morris asserted.

“No it’s 17. You forgot the amperage minimum for the heaters to keep the-“

“Guys, ” Venkat interrupted. “I get the idea.”

“Sorry.”

“Sorry.”

“Sorry if I’m grumpy, ” Venkat said. “I got like 2 hours sleep last night.”

“No problem, ” Morris said.

“Totally understandable, ” Chuck said.

“Ok, ” Venkat said. “Explain to me how a single windstorm removed our ability to talk to Ares 3.”

“Failure of imagination, ” Chuck said.

“Totally didn’t see it coming, ” Morris agreed.

“How many back-up communication systems does an Ares mission have?” Venkat asked.

“Four, ” Chuck said.

“Three, ” Morris said.

“No, it’s four, ” Chuck corrected.

“He said back-up systems, ” Morris insisted. “That means not including the primary system.”

“Oh right. Three.”

“So four systems total, then, ” Venkat said. “Explain how we lost all four.”

“Well, ” Chuck said, “The primary ran through the big satellite dish. It blew away in the storm. The rest of the backups were the MAV.”

“Yup, ” Morris agreed. “The MAV is, like, a communicating machine. It can talk to Earth, Hermes, even satellites around Mars if it has to. And it has three independent systems to make sure nothing short of a meteor strike can stop communication.”

“Problem is, ” Chuck said. “Commander Lewis and the rest of them took the MAV when they left.”

“So four independent communication systems became one. And that one broke, ” Morris finished.

Venkat pinched the bridge of his nose. “How could we overlook this?”

Chuck shrugged. “Never occurred to us. We never thought someone would be on Mars without a MAV.”

“I mean, come on!” Morris said. “What are the odds?”

Chuck turned to him. “One in three, based on empirical data. That’s pretty bad if you think about it.”

“Thank you all for coming on such short notice, ” Annie said. “We have an important announcement to make. If you could all take your seats, ”

“What this about, Annie?” A reporter asked. “Something happen with Hermes?”

“Please take your seats, ” Annie repeated.

The reporters mingled a bit, argued over seats for a short time, then finally settled down.

“This is a short, but very important announcement, ” Annie said. “I won’t be taking any questions at this time, but we will have a full press conference with Q&A in about an hour. We have recently reviewed satellite imagery from Mars, and have confirmed that astronaut Maia Watney is, currently, still alive.”

After one full second of utter silence, the room exploded with noise.

“I’m getting sick of daily press conferences, ” Venkat said.

“I’m getting sick of hourly press conferences, ” Annie countered.

“Sorry I’m late, ” Teddy said, entering the crowded press room. Managers from every department stood shoulder to shoulder in the back, while reporters crammed the pit.

Teddy pulled some flash cards from his pocket, then cleared his throat.

“In the nine days since announcing Maia Watney’s survival, we’re received a massive show of support from all sectors. We’re using this shamelessly every way we can.”

A small chuckle cascaded through the room.

“Yesterday, at our request, the entire SETI network focused on Mars. Just in case Watney was sending a weak radio signal. Turns out she wasn’t, but it shows the level of commitment everyone has toward helping us.

“The public is engaged, and we will do our best to keep everyone informed. I’ve recently learned CNN will be dedicating a half-hour segment every weekday to reporting on just this issue. We will assign several members of our Media Relations team to that program, so the public can get the latest information as fast as possible.

“We have adjusted the orbits of three satellites to get more view time on the Ares 3 site, and hope to catch an image of her outside soon. If we can see her outside, we will be able to draw conclusions on her physical health based on stance and activities.

“The questions are many: How long can she last? How much food does she have? Can Ares 4 rescue her? How will we talk to her? The answers to these questions are not what we want to hear.

“I can’t promise we’ll succeed in rescuing her, but I can promise this: The entire focus of NASA will be to bring Maia Watney home. This will be our overriding and singular obsession until she is either back on Earth, or confirmed dead on Mars.”

“Nice speech, ” Venkat said as he entered Teddy’s office.

“Meant every word of it, ” Teddy said.

“Oh, I know.”

“What can I do for you, Venk?”

“I’ve got an idea. Well, JPL has an idea. I’m the messenger.”

“I like ideas, ” Teddy said, gesturing to a seat.

Venkat sat down.

“We can rescue her with Ares 4. It’s very risky. We ran the idea by the Ares 4 crew. Not only are they willing to do it, but now they’re really pushing hard for it.”

“Naturally, ” Teddy said. “Astronauts are inherently insane. And really noble. What’s the idea?”

“Well, ” Venkat began, “It’s in the rough stages, but JPL thinks the MDV can be misused to save her.”

“Ares 4 hasn’t even launched yet. Why misuse an MDV. Why not make something better?”

“We don’t have time to make a custom craft. Actually, she can’t even survive till Ares 4 gets there, but that’s a different problem.”

“So tell me about the MDV.”

“JPL strips it down, loses some weight, and adds some fuel tanks. Ares 4’s crew lands at the Ares 3 site, very efficiently. Then, with a full burn, and I mean a full burn, they can lift off again. It can’t get back to orbit, but it can go to the Ares 4 site on a lateral trajectory that’s, well, really scary. Then they have an MAV. This would require a massive design and construction effort, but JPL says they can make it happen.”

“How are they losing weight?” Teddy asked. “Don’t they already have it as light as it can be?”

“By removing safety and emergency equipment.”

“Wonderful, ” Teddy said, “So we’d be risking the lives of six more people in a very dangerous landing, re-liftoff, re-landing process.”

“Yup, ” Venkat said. “It would be safer to leave the Ares 4 crew in Hermes, and only send the pilot down with the MDV. But that would mean giving up the mission and they’d rather risk death.”

“They’re astronauts, ” Teddy said.

“They’re astronauts, ” Venkat confirmed.

“Well. That’s a ludicrous idea and I’ll never ok it.”

“We’ll work on it some more, ” Venkat said. “Try to make it safer.”

“Do that. Any idea how to keep her alive for four years?”

“Nope.”

“Work on that, too.”

“Will do, ” Venkat said

Teddy swiveled his chair and looked out the window to the sky beyond. Night was edging in. “What must it be like?” He pondered. “She’s stuck out there. She thinks she’s totally alone and that we all gave up on her. What kind of effect does that have on someone’s psychology?”

He turned back to Venkat. “I wonder what she’s thinking right now.

LOG ENTRY: SOL 61

How come Aquaman can control whales? They’re mammals! Makes no sense.

[mathematicianadda]

How to determine algebraically whether an equation has an infinite solutions or not?

I was learning for the first time about partial fraction decomposition. Whoever explains it, emphasises that the fraction should be proper in order to be able to decompose the fraction. I was curious about knowing what happens if I try to decompose an improper fraction, So I tried to do one:

$\frac{x^2 - 4}{(x + 5)(x - 3)}$

I got the equation: $\frac{(Ax + B)(x - 3) + (Cx + D)(x + 5)}{(x + 5)(x - 3)} = \frac{x^2 - 4}{(x + 5)(x - 3)}$. I have 4 unknowns: A, B, C and D.

$\therefore (Ax + B)(x - 3) + (Cx + D)(x + 5) = x^2 - 4$

After expanding and regrouping the coefficients:

$(A + C) x^2 + (-3A + B + 5C + D)x + (-3B + 5D) = x^2 - 4$

Here the coefficient of the term $x^2$ is 1 therefore:

$(A+C) = 1$

similarly:

$(-3A + B + 5C + D) = 0$

$(-3B + 5D) = -4$

I still have to get one more equation to be able to solve this system so I substituted 1 for x and I got this equation:

$-2A - 2B + 6C + 6D = -3$

After getting four equations I used this site to solve the system of equations. Unfortinetly I got no soultion. Tried another site and also the same result.

I've tried to use different values for x and got another equaitons like:

for x = 2 : $-2A - B + 24C + 7D$

for x = -1 : $4A - 4B - 4C + 4D$

for x = -2 : $10A - 5B - 6C + 3D$

But also that didn't work. Always the system of equations have an infinite solutions.

After tring to figure out why this is happening, I've managed to prove logically that this equation:

$(Ax + B)(x - 3) + (Cx + D)(x + 5) = x^2 - 4$

has an infinite solutions and my approach was as follows:

After doing polynomial long division and decomposing the fraction using the traditional way, the result should be:

$\frac{5}{8(x - 3)} - \frac{21}{8(x - 5)} + 1$

Now I can add the last term (the one) to the first term and get the follows:

$\frac{8x-19}{8(x-3)} - \frac{21}{8(x+5)}$

From that solution I can see that $A = 0, B = \frac{-21}{8}, C = 1, D = \frac{-19}{8}$. After all these are just the coefficients of the terms. and this solution worked fine.

Alternatively I can add the one to the second term instead and get:

$\frac{5}{8(x-3)} + \frac{8x + 19}{8(x+5)}$

Now $A = 1, B = \frac{19}{8}, C = 0, D = \frac{5}{8}$

Generally, after adding the one to any of the terms, I can add any number to one of the terms and add its negative to the other term and the equation will remain the same, But the value of the 4 constants (A, B, C, and D) will change. And from that I got convinced that there are an infinite solutions to this equation.

But Algebraically? I'm not able to prove that it has an infinite solutions algebraically. And my questions is how to prove algebraically that this equation has an infinite solutions? Or generally how to know whether the equation has just one solution or an infinite?

from Hot Weekly Questions - Mathematics Stack Exchange from Blogger https://ift.tt/340waBL

[9-11luria-blog]

Week of: April 1

9-11 Class Learning Highlights

Language Arts

4th grade: This week we launched our new writing unit: literary essay! Students analyzed three stories (Eleven, The Marble Champ, and Fox) then chose one story and decided on a theme using text evidence.

5th grade: This week we launched our new writing unit: memoir! Students compared four different memoirs, noticing what makes a memoir and all of the many different formats that a memoir can have, such as essay, hybrid of narrative and essay, or list-like structure.

Math

Shelby 4th grade: We continued our investigation of fractions this week and decomposed fractions using area models and multiplication to show equivalence of two fractions. We also contributed to the Luria Haggadah Companion and created math puzzles that are related to the Pesach seder and story. We are excited for you to see them over the holiday!

Jen 4th grade: This week students continued finding equivalent fractions using area models and number lines. As a group, we discovered that the rule for finding equivalent fractions is that you can multiply or divide both the numerator and the denominator by the same number. We also contributed to the Luria Haggadah Companion and created math puzzles that are related to the Pesach seder and story. We are excited for you to see them over the holiday!

5th grade:  This week students focused on partial quotients and multi-digit decimal division.  Students used basic facts to approximate decimal quotients with two-digit divisors, and reasoned about the placement of the decimal point. Students also divided decimal dividends by two-digit divisors, estimated quotients, reasoned about the placement of the decimal point, and made connections to a written method.

Science

Our journey back in time continues, this time to the beginning of first life as it branches out into the five main kingdoms of life: Prokaryotae, Protoctista, Fungi, Plantae, Animalia. These five kingdoms over time have given us all the living things we have today. Let’s see if any of these organisms are recognizable in the twenty-first century.

History

4th grade: Students had the chance to showcase their presentations and posters from our Native American history research project this week. Each student walked around and took notes on their classmates’ research and then we sat together and gave and received feedback.  It was amazing to see how seriously the students took this process and how much they were able to learn from each other! We also began our next unit on slavery and the slave trade, focusing on its beginnings and how it impacted settlement of the British Colonies.

5th grade: This week, students took a close look at the preamble of the U.S. constitution.  Each student read through the text and highlighted words or phrases which jumped out at them and then created a poster which illustrated and explained some of these concepts.  

Hebrew

Dorit’s groups: This week we finalized our long term projects and we got to read and play with each other’s work. Some games were played on the computers, others are recorded and are available to be watched on replay.

Daphna’s group: We continued our kinneret unit and compared kibbutzim past and present, focusing on verb conjunction in past and present tense.

Chumash

Rashi, Eben Ezra and Ramban: We learned a piece of text from the Haggadah and a commentary on it based on our own questions. We then wrote a Dvar Torah about what we learned.

Kindness: Students are hard at work to finish out Dvar Torahs for the school’s Haggadah companion. We explored and compared the characters of Paroah and Lavan, seeing how they affected the course of Jewish history. Finally we brought in personal connections and how everyone can contribute at their own seder.

The Dreamers: As our Dvar Torahs finish up, students begin to examine how the four children can be found in each and every one of us. Each student discussed this connection and how they can contribute at the seder, whoever they are having it with.

Mishnah

4th grade: Students finished learning the second mishnah in the first perek of Mishnah Brachot.  We focused on the final lines of the mishnah, which explain that if one is not able to recite the Shemah on time, that they still get a different kind of “credit” for having read a Torah text.

5th grade: Students completed the first mishnah in the 5th perek of Mishnah Brachot, which explains the concept of mitoch koved rosh, or being in a serious state of mind while praying.  Students went through a reflection and journaling process where they checked in with themselves on their own focus and presence during Tefillah and had the opportunity to set some goals for themselves.

Community Time

We discussed the Pesach story and how strong the Jewish people must have been. Using modern inspirational quotes, students highlighted meaningful words and illustrated quotes in small groups. The goal was to imagine going back in time to encourage the Jewish people to persevere through this difficult time.

Questions

Language Arts

4th grade: Which story are you writing your literary essay about? What is the theme of that story?

5th grade: What makes a memoir? What is your memoir going to be about and what will be the message?

Math

Shelby 4th grade: Can the numerator be larger than the denominator?  How is the size of a unit fraction related to the denominator?  

Jen 4th grade: Which is bigger - 2 thirds or 2 fifths? Which fraction is closer to 1 whole - 4 sixths or 9 tenths?

5th grade:  Noa bought a bag of 3 dozen toy animals as party favors for her birthday party. The bag of toy animals cost $28.97.  Estimate the price of each toy animal. The Aon Centre in Chicago, Illinois, is one of the world’s tallest buildings. Built in 1973, it is 1,136 feet high and has 80 stories. If each story is of equal height, how tall is each story?

Science

Can we see any connection between the first life and what we see today?

History

4th grade: Why did Slavery start in America?

5th grade: What were some of the goals of the Preamble to the U.S. Constitution?

Hebrew

Dorit’s groups: What did you learn about the process of making a final draft and presenting it to the class?

Daphna’s group:מה שונה בין קיבוץ של היום לקיבוץ של פעם?

Chumash

Rashi, Eben Ezra and Ramban: What is your Dvar Torah about?

Kindness: How can we help shape the course of Jewish history moving forward?

The Dreamers: What is the best way to communicate with people, regardless of their background and connection to Pesach?

Mishnah

4th grade: What happens to me if I forget to say the Shemah on time? Do i still get “credit”? Have I completed the mitzvah?

5th grade: What is one thing that you can do differently in Tefillah to be in a more serious state of mind?

[crayonlead2-blog]

The Inconvenient Truth about Climate Change and the Economy

By Gregor Semieniuk, Lecturer in Economics, SOAS, University of London and Associate Research Faculty, Science Policy Unit (SPRU), University of Sussex; Lance Taylor, Arnhold Professor of International Cooperation and Development, New School for Social Research; and Armon Rezai, Assistant Professor, Environmental Economics, Vienna University of Economics and Business. Originally published at the Institute for New Economic Thinking website

The recent report from the Intergovernmental Panel on Climate Change (IPCC, 2018) rightly raises the alarm about the dangers of global warming of 1.5 °C beyond the “pre-industrial” temperature level circa 1850-1900. Unfortunately, the present situation is far worse than the Panel suggests. Its projections regarding reductions in energy use while maintaining historically observed productivity and income growth patterns into the future are inconsistent with historical experience. They understate the impact of continued economic growth on carbon dioxide emission and climate damage.

On the other hand, sufficient mitigation of emission could offset the damage. It would require new spending, large but lying within the range of macroeconomically feasible reallocations. Political consensus could be another story.

We begin with two sets of background observations, then describe the IPCC’s scenarios, and conclude by examining potential macroeconomic repercussions.

Background Observations

The first point is that increasing CO2 emissions from combustion of fossil fuels has gone hand in hand with industrialization and increases in the real output/employment ratio (or “labor productivity”) for more than 250 years. Compared to traditional sources (waterpower, wood, animal and human traction) coal and subsequently petroleum and natural gas are readily available, relatively easy to handle, and have high energy density.[1] Here is a capsule history:

18th– 19th Centuries: coal-fired steam engines provided the motive power for the first wave of industrialization in Great Britain and subsequently around the world.

19th – 20th Centuries: transport was reorganized around steam engines on railroads, and steel production relied on blast furnaces. Electricity came from steam turbines coupled with generators; internal combustion engines later revolutionized transportation by road. Central heating and air conditioning spread widely. Coal was the main original source of energy, later supplemented by petroleum and natural gas.20th – 21st Centuries: hydro and nuclear electricity generation emerged, followed by solar and wind power.

The bottom line is that fossil fuels have been built into the core of modern technology, required by essentially all prime movers with the partial exception of electricity. (One-third of supply comes from non-fossil sources including nuclear and hydro but it also uses coal, the dirtiest and most harmful of fossil fuels). Over 90% of primary energy supply comes from CO2–producing fossil and biofuels.[2]

Second, this technological bias means that world energy utilization per person has risen in direct proportion to output per capita: A one percent increase in income is associated with nearly a one percent increase in energy use.[3] With fossil energy sources built into the economy in such a fundamental manner, CO2 emissions go up in direct proportion to output, with Earth only absorbing a fraction in natural “sinks.” Remaining emissions add to greenhouse gas (or GHG) in the atmosphere. Since the 19th century it has been known that atmospheric GHG causes global warming. Through various channels (i.e., reduced health, increased diseases, and the more direct economic consequences of lower profits and the direct destruction of capital) warming causes reductions in the flow of world gross domestic product, not to mention the devastating impacts on ecosystems described by the IPCC.

Myriad details underlie this macro level causal loop: a positive effect of output on GHG accumulation, and a negative feedback of the rising atmospheric stock of GHG on output growth.  Complications notwithstanding, unless this loop is severed, it will inevitably lead to worldwide economic collapse. The recent IPCC report suggests that, as we learn more about the climate’s response to emissions, the crash can come sooner than was previously expected.

There are two ways to sever the loop. One is to mitigate atmospheric GHG accumulation created by burning fossil fuels to supply energy—either by avoiding carbon-emitting energy sources or by finding ways to sequester emissions once they occur. The other is to employ less energy to raise output. The two are complementary, and the IPCC relies heavily on both to keep to the 1.5°C target. While transforming the energy system to create no (or preferably negative) emissions is a daunting challenge already, the second is even harder given the historical record mentioned above.

IPCC scenarios

In very round numbers, current world population is 7.5 billion, and real output or GDP in 2010 at market exchange rates is $75 trillion per year. Hence GDP per capita is $10 thousand. It is convenient to measure the rate at which energy is consumed in terms of kilowatts per person.[4] Worldwide, energy is consumed at the rate of 18 terawatts (trillion watts) or roughly 2.5 kilowatts per capita.

These numbers explain the labels on the axes in Figure 1. The world currently operates at 2.5 kilowatts and $14.5 thousand at purchasing power parity[5] at the top right end of the historical trajectory (from 1960 to 2016), the solid black line. The dashed and dotted lines illustrate future prospects, if the average growth rates from 1970-2016, and from 2000 to 2016 were to continue until 2050. They are labeled ex 1970 and ex 2000 respectively. These trajectories show proportionality between energy and real income per capita.

Figure 1: Historical and scenario trajectories of output per capita and energy demand per capita.

Source: International Energy Agency 2017, Huppmann et al. 2018. 

The IPCC enters with a “reference” or “business as usual” (BAU) scenario in red which is supposed to mirror past dynamics, even though it is evident that it falls below the extrapolation from the 2000s and grows much faster than the extrapolation from the 1970s. It implies that a given level of output per capita (horizontal axis) can be supported by lower-than-historically- observed energy per capita (vertical axis). A dot shows where the scenario is in 2050, with output in the upper range of extrapolations at a substantially lower power level. All these trajectories would spell continued global warming, several degrees above the envisaged 1.5°C target.

The two blue curves represent IPCC scenarios in which global warming is held below 2.0 and 1.5 degrees, respectively, by the year 2100 (with a possibility of some overshoot in the interim).[6] The trajectories show a very substantial reduction in energy demand relative to a high level of GDP per capita. The implied output growth rate is about 3.0% per year until 2050—similar to or faster than historical rates.

If, as in Figure 1, the energy/labor ratio falls while labor productivity rises, then the growth rate of energy productivity must exceed that of labor productivity. For sustained growth rates, such a situation is historically unprecedented.

In the scenarios, renewable substitutes for fossil fuels only come online gradually, playing a smaller role in the next two decades which are decisive for climate change. Table 1 quantifies the contribution in the reduction of fossil fuel use from BAU to the 1.5 scenario. Until 2040, around three quarters of reduced energy demand comes from fossil fuel reductions relative to baseline. Renewable energy starts to become more important only at mid-century, when the critical window to reduce emissions has all but passed.

Table 1: Reductions in Fossil Fuels in 1.5 degree scenario relative to baseline, decomposed into absolute and percent contributions from renewable energy and reduced energy demand.

All figures in Exajoules per year. Source: Huppmann et al. 2018.

An Alternative Mitigation Scenario

In a macroeconomic model of economic growth designed to analyze the implications of reducing global warming with greater reliance on shifting the fuel mix rather than reducing energy demand (Rezai et. al., 2018), we used an initial mitigation cost of $160 per metric ton of carbon, or $44 per ton of CO2, in the mid-range of current estimates. Net carbon emissions are now on the order of 10 gigatons (billion tons) per year.

The model is built around the feedback loop described above. Output is broadly proportional to capital, so that the “state” variables, which evolve over time, are stocks of capital and atmospheric CO2. Labor productivity grows with the level of capital, and also increases in response to higher employment. In line with the historical pattern in Figure 1, growth of the ratio of energy use to employment is proportional to the growth of productivity—i.e. to make people more productive, they need more energy per person.

There is doctrinal dispute among economists about whether output in the medium run is set by forces of supply (typically assumed to involve full employment of labor and determination of investment in new capital by available saving) or whether it responds to effective demand (full employment not assumed and saving follows investment). Our model incorporates the latter assumptions. Outlays on mitigation add to demand, and so generate more output and employment.[7]

Figure 2 summarizes results from three runs of the model: BAU with no mitigation, mitigation set to hold the global temperature increase to 2°C, and full mitigation from the start to maintain the increase at the level of 1.3°C to which we are committed today (i.e., the level of warming that will materialize due to the emissions in the atmosphere already).

Figure 2: Simulations of the impact of different mitigation scenarios on the economy.

Source: Rezai et al. (2018)

Unsurprisingly, BAU runs the economy into a climate crisis. Net emissions go up for nearly a century and then trail off in the wake of an output collapse (upper left diagram). In the upper right-hand panel, the global mean temperature increase rises steadily by almost 5°C over a century. The underlying cause for this rise in emissions is a growing capital stock and income per capita, which start to fall precipitously as the climate worsens (middle panels), holding the output/capital ratio relatively stable (bottom left). The share of employment in population collapses as well.

The two scenarios with mitigation avoid the crisis. Cumulative net emissions stay close to current levels so that the temperature increase is held down.  Capital stock and income per capita increase exponentially and the employment/population ratio is stable.

Is Mitigation Feasible?

Figure 3 illustrates the timing of mitigation outlays. Full mitigation holds the temperature increase to 1.3°C. An initial mitigation “big push” is built into the timing, with outlays starting out at six percent of GDP and tailing off to about two percent. The simulation amounts to a more extreme version of the IPCC 1.5°C package, also because we are less optimistic regarding the deployment of negative emissions technology (i.e., the ability to reduce atmospheric carbon levels directly) within this century. The initial push in the model’s 2°C run is not as big as with full mitigation, but still peaks at three percent of GDP.

Figure 3: Mitigation shares and expenditures for the mitigation scenarios.

Source: Rezai et al. (2018)

In absolute terms, these outlays are large but comparable to other forms of spending. Three percent of current world GDP at market prices is $2.25 trillion. This magnitude compares to the world total of $1.74 trillion spent on the military. In several large countries the military’s share of GDP is in the range of two to four percent. Fossil fuel subsidies worldwide are estimated to be in the range of $5 trillion.

These numbers suggest that a big mitigation push, perhaps financed by carbon taxes and/or reductions in subsidies, is possible macroeconomically even if the link between energy use and output is not severed. This, however, would require considerable modifications of countries’ macroeconomic arrangements. Needless to say, military establishments and recipients of energy subsidies wield political clout. Fossil fuel producers have at least as much. Whether national preferences will permit big shifts in the use of economic resources is the key question. The IPCC report may help lead to a rational answer.

Footnotes

[1] Burning a kilogram of coal yields twice the energy as comes from the same amount of wood. Gasoline yields three times as much.

[2] For detail on energy see a new MIT textbook by Jaffe and Taylor (2018), largely accessible to the “intelligent layperson.”

[3] See Semieniuk (2018) for a review of the evidence. Recent investigation suggests that the correlation between the component of energy delivering useful work (in the physics sense of applying a force over a distance) and GDP is even higher (Serrenho et al. 2016).

[4] Power as measured in kilowatts is the flow of energy per unit time (a traditional 100-watt lightbulb uses 0.1 kilowatts or 100 joule per second). A standard metric for energy itself is kilowatt-hours (kilowatts times hours). Power absorbed by a typical US household is 1.2 kilowatts, or 11 thousand kilowatt-hours of energy per year.

[5] GDP at “purchasing power parity” or PPP is based on the idea that relatively inexpensive goods and services produced by cheap labor allow higher levels of real consumption (think of the comparative costs of haircuts in Mumbai and Manhattan). Estimated income in India, China, and all other poor countries is thereby adjusted upward, increasing the world total. The IPCC presents results in terms of PPP.

[6] All three IPCC curves are based on the marker implementation of the “middle of the road” scenario of future growth, energy demand, and technical change which is to continue past trends (Fricko et al. 2017), and are supposed to be comparable to historical data. The second of the five ‘shared socioeconomic pathways’ or SSPs (O’Neill et al. 2017)  underpins the integrated assessment models used in the new IPCC report.

[7] See Mercure et al. (2018) for an integrated assessment model where output is demand-determined.

See original post for references

This entry was posted in Doomsday scenarios, Dubious statistics, Economic fundamentals, Free markets and their discontents, Global warming, Guest Post, The dismal science on December 7, 2018 by Yves Smith.

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Source: https://www.nakedcapitalism.com/2018/12/inconvenient-truth-climate-change-economy.html

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IGCAR Admit Card 2018 Download IGCAR Kalpakkam Hall Ticket 2018 at www.igcar.gov.in

IGCAR Admit Card 2018

The Indira Gandhi Centre for Atomic Research is going to release IGCAR Admit Card for applied aspirants of Postman/Mail Guard Post. The IGCAR Admit Card 2018 can be downloaded before this written examination to get an entry in examination hall. Huge numbers of applicants applied for IGCAR Recruitment 2018 and waiting for Hall Ticket from very long time. Here is good news for all participants; The Indira Gandhi Centre for Atomic Research is going to upload IGCAR Kalpakkam Admit Card 2018 of Kalpakkam for all applicants on the official website of Indira Gandhi Centre for Atomic Research. As per the received information, the online registration has been finally closed. Candidates are suggested to download their call latter from official web portal which is www.igcar.gov.in. After becoming part of the recruitment, applicants are now looking for the IGCAR Admit Card 2018 that is likely to be available before some days of the examination date. Candidates can check more connected information regarding hall ticket, examination, selection process by reading this webpage. How to Prepare For Examination Best Tips All those applicants had who applied for this IGCAR Recruitment 2018 they need to download IGCAR Admit Card 2018 to attend the exam because it contains will deliver you all essential information such as time & date of exam, examination venue location, roll number, sit number etc. The Kalpakkam Written Exam Date is not yet announced by the Indira Gandhi Centre for Atomic Research.  Dear contenders who have filled their application form for becoming part of the organization can check the full information of examination as soon as possible from here.

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[letsbriefstrangercollector-blog]

modalert

Peken (slime) Bodily energy Peken (slime) corresponds to the liquid aspect of the body and therefore represents an element of water. All bodily fluids depend on mucus, which is responsible for the lubrication of the entire body (modalert). As a result, it maintains the connections (connections in the body, and also gives the body its softness and elasticity (flexibility), it is responsible for all factors of moisture and dampness in the body.Peken (slime) also provides strength to the body and mind (in the form of patience). it provides a solid foundation and in this respect corresponds to the element of the earth.In humoral pathology it is classified as phlegma.The desire to sleep is also conditioned by this bodily energy.With these characteristics it becomes clear why this energy is also associated with the fog GOVERNMENTAL and blunted feelings. Consequently-tion, energy Peken is heavy and static. The main repository of this energy level is considered to be "above the heart." Energy Peken (slime) has the following main characteristics • cool, • heavy, • dull, • oily, • gentle, • smooth (smooth), • static, • sticky, • dense (stable), • slow acting.

The body energy of Peken (slime) is divided into five subcategories:

1. Supportive mucus Its receptacle is located in the chest, primarily it is located along the sternum. It supports all four other types of mucus and is responsible for the equilibrium of water, which is the general level of moisture in the body. 2. Decomposing mucus This type of mucus can also be called "mixing" or "softening mucus". It is located in the upper part of the digestive tract, directly at the point where unheated food is collected - especially in the upper part of the stomach. In order that food can slowly move into the stomach through "supporting mucus," it "holds" at a point between the esophagus and enters into the stomach, up to the first compartment of the stomach. Then, "decomposing mucus" causes mixing of solid and liquid food. After that, she breaks down the food mixture, which is considered an important phase of food separation in the digestive tract. 3. "Perceiving" mucus It is also called "slime, which provides experience of taste sensations." It is located in the tongue and oral cavity. This mucus provides the perception of six different flavors: sweet, sour, salty, bitter, hot and astringent. (This topic is discussed in more detail in the chapter "Types of Tastes"). 4. Slime that brings satisfaction It is located in the head area and satisfies the senses. As a result, we perceive tones as pleasant sounds, smells as pleasant, tastes as good, and also see the beauty in objects that we perceive as beautiful, etc. 5. Bonding mucus It is placed in the joints, where it ensures their mutual connection so that they can bend and straighten.

Conclusions: Three basic energies can be considered as physiological and biochemical processes in the body. Lung (wind) is associated with the activity of the nervous system, as well as with the exchange of substances in general. Tripa (bile) is more associated with catabolic (decomposition processes) metabolic processes. Peken (mucus) is associated with anabolic (structuring, organizing) metabolic processes.

When three bodily energies in the appropriate proportions are in the receptacles assigned to them, health and balance are ensured. This means that imbalances and violations of body energies can arise as a result of increasing or decreasing their proportions, as well as as a result of "flowing" of energies from their respective containers. Seven body parts The seven bodily components form the body, thereby supporting its vital functions. Each of these components exists in an exactly specified amount. Therefore imbalances and disturbances in the body can result from an increase or decrease in the number of basic components.

According to the theory of Tibetan medicine, these basic constituent bodies are formed as a result of metabolic processes "consumed" by the absorbed food. In this process, one of the types of feeding essence and one product of processing are constantly formed. This means that one cleaned and one uncleaned part is created. With the exception of the slags that are formed at the very beginning of the metabolic process (feces and urine), both parts (or fractions) are always of fundamental importance for maintaining the body's functions. With a decrease in the quality of the relevant entities, there may also be disruptions in the form of diseases. The successive metabolic chains of the purified entity, as well as the processing products, will be described later in this chapter. First, you need to explain the principles of digestive heat and digestive process. Digestive heat In the texts on Tibetan medicine four or seven categories of digestive heat are described. However, in the context of this book, you can equate digestive heat with "digestive bile." This metabolic heat makes up the whole thermoregulation of the body, as well as the digestive process proper. If the digestive heat is too weak, most of the absorbed food will remain undigested. As a result, part of the food will be uselessly spent because of its inadequate separation and disposal, which exerts additional strain on the body. This can be expressed in the form of flatulence, etc. Moreover, over time, certain symptoms of modafinil will develop due to a lack of nutrients due to weak digestive heat. Consequently, the intake of additional food additives, vitamins, etc., without simultaneous maintenance of edible heat, is meaningless.

With the help of warm and light foods described in the "Habits of Nutrition" section, digestive heat can be protected and maintained. According to the principles of Tibetan medicine, this is a necessary condition for health and longevity. However, digestive heat can become too active. In such cases, it "attacks" the body components and practically "burns" them, which in the end can lead to symptoms of insufficiency and general exhaustion of the body. Digestive heat performs the following functions: • Provides heat (it provides a general thermoregulation of the body). • Separates nutrients (essence) from excess (products) processing). • Displays excess substances from the digestive area after the completion of the digestive process. • Prevents ingested undigested substances in the way of pro¬ circulation of digested food. • Increases the level of bodily components. • Responsible for good skin color, and also for strong charisma. • Gives the body physical strength. Effects on digestive heat by the predominance of one of the bodily energies In the case of an excess of energy Lung (wind), the digestive heat will be unstable.

In the case of the predominance of energy Tripa (bile), digestive heat will be very fluid and overactive.

In the case of a predominance of Peken (mucus) energy, digestive heat will slow down.

In the case of excessive combination of energies Lung / Tripa (wind / bile), the digestive heat will be too turbulent and very active.

In the case of an excess combination of Tripa / Peken energies (bile / mucus), the digestive heat will have an average level.

In the case of health an excessive combination of Lung / Peken energies (wind / mucus), the digestive heat will be weak.

PREVALENCE OF PHYSICAL ENERGIES AND FOOD HEAT: Excess energy: Influence on digestive heat: Lung Unstable, irregular Tripa Accelerated, overactive Peken Slowed Lung / Tripa Very active and stormy Tripa / Peken Average Lung / Peken Weak

With a balanced state of the three bodily energies, edible heat will also be optimal. The process of digestion According to the Tibetan manuscripts, the whole process of digestion occurs in the stomach. However, it can be assumed that the term "stomach" is used to refer to the entire gastrointestinal tract, that is, the stomach, duodenum, small intestine, and a certain portion of the large intestine. In addition, pointing to a specific "receptacle" of each of the three bodily energies does not mean that the energy is constantly there in a "fixed" position, but rather indicates the prevailing position of this energy in this specific area of ​​the body. In Tibet, the word denoting the process of digestion also has the meaning of "dissolution, melting." In the process of digestion, the nature of the chyme (a mushy mass of partially digested food) changes. Consequently, the proportions of the elements also vary. In accordance with the principles of Tibetan medicine, it can be said that "taste changes" (see "Types of Tastes"). As will be described in detail below, since the beginning of the functioning, under the influence of some stimuli, the entire digestive system is self-activated and its activity is intensified. It means that:

1. Slime produces a new mucus. 2. Bile produces a new bile. 3. The wind produces a new wind.

This process can be compared in some way with the western system of skin hormones. 1. Absorbed food and drinks move from the esophagus down, in the stomach by means of a wind that sustains life. I mix-¬ Slime is in the upper compartment of the stomach. She is responsible for re- mixing of solid and liquid fractions of absorbed food. Liquid fractions contribute to the breakdown of food, and oily fractions

[mathematicianadda]

How to quickly solve partial fractions equation?

Often I am dealing with an integral of let's say:

$$\int\frac{dt}{(t-2)(t+3)}$$

or

$$\int \frac{dt}{t(t-4)}$$

or to make this a more general case in which I am interested the most:

$$\int \frac{dt}{(t+\alpha)(t+\beta)} \quad \quad \alpha, \beta \in \mathbb{R}$$

Basically any integral with decomposed polynomial of second degree in the denominator. Obviously this leads to sum of two natural logarithms.

What I do is write down partial fractions equation and then solve system of linear equations (2 variables here):

$$\frac{1}{(t+\alpha)(t+\beta)} = \frac{A}{t+\alpha} + \frac{B}{t+\beta}$$

After solving this I end up with some $A, B$ coefficients and I can solve the integral.

Is there faster way to find $A, B$ ? Some algorithm or anything that I can follow and would always work for such case? Surely, solving that does not take much time but I just wonder if it could be done even faster.

(bonus question: what if there were more variables, like 3 variables?)

I would greatly appreciate all feedback as it could help me save countless number of minutes in the future.

from Hot Weekly Questions - Mathematics Stack Exchange from Blogger http://bit.ly/2IfX8O7