#eischens

[mostlyyourlysander]

*knocks on office door and creaks the door open while peeking inside* …Is this Professors’ Valerian office?

— R. Eischen

Yes, this is he. *shuts suitcase on desk and looks over shoulder to see him* Young Eischen? What is a student like yourself still doing upon school grounds? Have you lost something, perhaps?

[jockloverspics]

[missgossiper]

Are this Remus guy and Cicero on a slow burn to sleepovers and wrestling parties?

Dearest Anonymous,

Ah, the halls of academia are abuzz with the latest intrigue. It plays out exactly like an academic rivals to lovers AO3 fic — Two young History Students, dazzled in Dark Academia, fierce Rivals in Intellect and Debate, find themselves at the center of a most tantalizing Speculation. Their heated exchanges and sharp intellects have long been the talk of the university, but could there be more than just animosity simmering beneath the surface? Observers have noted a peculiar tension, one that hints at a passion not yet acknowledged. As they clash over historical narratives, might they be on the brink of writing a new chapter in their own story? For with erotic fights and subtle flirting veiled beneath witty banter?

[postcard-from-the-past]

Hotel Tonteling-Robert and view of Eischen, Luxembourg

Luxembourgish vintage postcard, mailed in 1913 to Arlon, Belgium

[duranduratulsa]

Oklahoma Treasures: Eischen's Bar in Okarche Oklahoma #eischensbar #chicken #friedchicken #okarche #Oklahoma #okarcheoklahoma

[foreveryour-remus]

*places a hand on his shoulder gently* Young Eischen?

—E.Lys. Valerian

*blowing books down with hairdryer* Damn sprinklers… This is what I get for taking library books! *looks up and turns off hairdryer* Professor Valerian, I wasn’t expecting to see you— Need something?

[columbiauniversity-schoolboard]

Attention all Columbia students — A new arrival has joined us here at the college; everyone remember to give a warm welcome to Remus Eischen [@foreveryour-remus], a freshman student in Art History.

First impressions are always most important.

Sincerely,

Columbia Staff

[jessecmckeown]

Whence Fabulous Faulhaber?

should I promise not to make this a habit?

Dear Mr. Haran, I'm grateful to you and correspondent Eischen (and Conway) for putting the name of Faulhaber on a calculation which heretofore I'd only known quoted, without attribution, by Heinrich Dörrie in Triumf der Mathematik---(which I've only read in translation). However, I'm most frustrated that neither Dörrie nor Eischen give any satisfying motivation for why the postulate should work.

For bystanders still catching up, this postulate is that if one defines a sequence of numbers $B_k$ "by expanding" $$(B-1)^{k+1} = B^{k+1}$$ and transcribing exponents to subscripts... one finds that the differences $$ (n + B)^{k+1} - B^{k+1} $$ similarly treated are equal to cumulative power sums, $$(k+1) \sum_{j \leq n} j^k$$

So the calculation is doable. My Beef is Dilemmimorphic: Either the notational abuse of $(n + B)^k$ suggests that $B$ should be Some Kind Of Linear Operator, in which case what is it? Or else there's an Amazing Coincidence being Overlooked!

It's a comparative Triviality that the power sums $\sum_1^N n^k$ should be polynomials of $N$, and that the leading term be $\frac{1}{k+1} N^{k+1}$ , so indeed it is perfectly reasonable to consider coefficients $B_{k,j}$ defined by $$ \sum_1^N n^k = \frac{1}{k+1} \sum \binom{k+1}{j} B_{k,j} N^{k+1-j} $$ BUT WHY SHOULD WE ASSUME that in fact $B_{k,j}$ depends only on $j$? That's STAGE MAGIC, and the fact that indeed it somehow works does not explain "where it comes from" (Eischen's favourite phrase on the matter).

So, in my customary way of starting with the actual problem and throwing at it what seems to me the minimum of thought, let's first explicate that "comparative triviality": the sequence of polynomials $p_k(j) = \binom{j+k}{j}$ are integral generators for the Integral-valued polynomials, and are recursively definable as iterated cumulative sums of the constant polynomial $p_0 \equiv 1$: $$\binom{j+k+1}{j} = \binom{j+k}{j} + \binom{j+k}{j-1}$$. Hence, cumulative sums of any polynomial, written in the binomial basis, can be obtained just by incrementing: $$\sum_{j=1}^N \sum a_n p_n(j) = \sum a_n p_{n+1}(N)$$

Next, cumulative sums are themselves defined by induction: $"\sum_{j=1}^0" P(j) = 0$ and $\sum_{j=1}^{N+1} P(j) = P(N+1) + \sum_{j=1}^N P(j)$, or said differently, by the Difference equation $$ SP(N+1) - SP(N) = P(N+1).$$ In other words we are trying to solve the Difference Equations $$ S_k(N) - S_k(N-1) = N^k,$$ but in the basis of Monomials $N^j$ instead of Binomials $p_j(N)$.

The binomial theorem, $$ (x+y)^k = \sum \binom{k}{j} x^{k-j} y^j $$ makes the Taylor-MacLaurin formula a Theorem for polynomials $$ (x+y)^k = \sum y^j \frac{1}{j!} \frac{d^j}{dx^j} x^k $$ which is fruitfully abbreviated $$ P(x+y) = e^{y\\, d/dx} P(x) $$ the Backwards Difference, then, is similarly $$ P(x) - P(x-1) = (1 - e^{- d/dx}) P(x) $$

Shall we say, The kernel of the Backward Difference is reasonably well understood? The differential operator is the retract of the Integral operator $\int_0$, so the Taylor-MacLaurin formula provides us also a section for the Forward Difference operator, $$ 1-e^{-x} = \frac{d}{dx} + A\frac{d^2}{dx^2} $$ where, for now, the main point is that the unbounded-degree differential operator $A$ commutes with $d/dx$, so that, for example $$ (1 - e^{-d/dx}) \left(\int_0 \sim dx - A + A^2 \frac{d}{dx} - A^3\frac{d^2}{dx^2} + - \cdots \right) P(x) = P(x)$$

Of course, there are various paths to the power series, other than via expansion of the powers of $A$, but there is a (Laurent) power series $$ \frac{1}{1-e^{-t}} = \frac{1}{2}\coth(\frac{t}{2})+\frac{1}{2} = \frac{1}{t} + \sum \frac{B_j}{j!} t^{j-1} $$ where $B_j$ are the faBulous Bernoulli numbers.

In any case, applied to simple powers, $$ \left( \int_0 \sim dx + \frac{1}{2} + \sum_{j=2}^{\infty} \frac{B_j}{j!} \frac{d^{j-1}}{dx^{j-1}} \right) x^k = \frac{1}{k+1} x^{k+1} + \sum_{j=1}^{k} \frac{k!}{j!(k-j+1)!} x^{k-j+1} B_j \\\\ {} = \frac{1}{k+1} \sum_{j=0}^{k} \binom{k+1}{j} B_j x^{k+1-j} $$ Finally, the power sum polynomials $S_k$ vanish both at zero (formally an empty sum) and at $-1$ (since $S_k(0) - S_k(-1) = 0^k$), so that in particular, $$ \sum_{j=0}^k \binom{k+1}{j} B_j (-1)^{k-j} = 0$$ THAT'S WHERE THIS IS COMING FROM.

[reisegruppekaenguru]

Beach-City-Life

Diesen Tag beenden wir mit einem Knall. Es fing ganz harmlos und entspannt heute Morgen an, als wir uns alle mit dem Bus in Richtung Bondi Beach auf machten. Den haben wir uns nach einer holperigen Fahrt dann erst mal angeschaut und schön viel Sonne für die nächsten Stunden, die wir viel im Auto verbringen werden, getankt. Manch eine/r auch etwas zu viel Sonne. Nach einer kurzen Erkundungstour und etwas Shopping in Bondi Junction, dem Stadtteill in dem sich der Bondi Beach befindet, ging es auch schon zurück und zum uns schon bekannten Darling Harbour, an dem uns der Knall erwartete. Ein Feuerwerk, welches im Frühling und Sommer jeden Samstag für Touristen und Einheimische gezündet wird. Dazu gab es dann für jeden einen Burrito in die Tatze, ein kleines Eischen wurde sich geteilt und der Tag so perfekt beendet.

[madeinoklahomaproducts]

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[mostlyyourlysander]

https://www.tumblr.com/local-child-prodigy/757807966638555136/blinks-pushing-glasses-up-nose-aanderson

School bullying was not what I expected in a college😭😭

*eyes widen and quickly stands up, hissing under his breath* Eischen–!

[rotterdamvanalles]

Gezicht op het sportterrein met de Chr. H.B.S. en Het Marnix Gymnasium op het Henegouwerplein. Op de achtergrond de huizen aan de Henegouwerlaan en het bovenste gedeelte van het Groothandelsgebouw in aanbouw, 1951.

Omstreeks 1880 had Rotterdam ongeveer 150.000 inwoners. Er bestond nog geen voortgezet onderwijs. Wel bestond sinds de veertiende eeuw de Latijnse school. Deze openbare school bereidde voor op universitair onderwijs en werd bezocht door een zeer klein aantal leerlingen uit de hoogste kringen.

In 1898 maakten de oprichters van de vereniging die de voorloper van het huidige CVO is, propaganda voor een christelijke middelbare school. Aan overtuiging ontbrak het hen niet, aan doorzettingsvermogen evenmin. Drie jaar later ging een klasje van tien jongens in de binnenstad van Rotterdam van start: de eerste christelijke HBS in Nederland was een feit! Onderdak werd gevonden in het catechisatielokaal van de gereformeerde kerk aan de Hovenierstraat, een zijstraat van de Jonker Fransstraat.

In 1903 stelde de ledenvergadering voor een gymnasium op te richten. Als naam voor de nieuwe school koos men Marnix. Tegenover het humanistische Erasmianum was er nu ook een gereformeerd gymnasium. De school werd gehuisvest in het pand Jonker Fransstraat 71, naast het bovenhuis waarin de HBS intussen haar intrek had genomen. Beide scholen zaten nu gezamenlijk boven een sterk geurende onderbouw: onder de HBS bevond zich namelijk de slagerswinkel Joh. Dirkzwager en onder het gymnasium was een vishandel gevestigd.

In 1905 werd voor de leraren een instructie opgesteld welke onder meer de volgende formulering bevatte (artikel3): ‘’De leeraar heeft zich te beijveren om steeds op de eischen van opvoeding en onderwijs te letten, in overeenstemming met de beginselen der Vereeniging (…)

In 1927 werd het door architect Anema ontworpen schoolgebouw aan het Henegouwerplein geopend. Hierin werden zowel de HBS als het Marnix Gymnasium ondergebracht.

De foto is gemaakt door de Fototechnische Dienst Rotterdam en komt uit het Stadsarchief Rotterdam. De informatie komt uit het Stadsarchief Rotterdam en van http://www.cvo.nl/cgi-oic/pagedb.exe/show?no=837

[missgossiper]

Give us some tea on all the new peeples

Dearest Anonymous,

Ah, the evening tea has rolled around yet again! There are quite so many to choose from with the towns population ever growing as a rabbits family—I shall name the most notable to spare us the tiring reading.

Nothing is ever quite sure surrounding the towns most infamous historian (@cicero-defacto), shrouded in as many myths as there are laced in history itself. But if one thing can be speculated, it is their apparent prejudice towards blondes. Why else is it that they have made many of the piss heads around their sworn enemy? To name a few a particular Colonel, an archduke, a Rockefeller, and now... a nobody of much importance unless you are teaching an anger management class. Who is this particular Eischen lad (@foreveryour-remus)? Why does his name sound like Uranus? And be that why he is frightfully so angry?

In other news, if one Royally Spoiled Fetus was not enough... Congratulations! It appears the school has a very well known Grand Duchess on it's hand (@grand-duchess-of-russia). The young lady seems inclined on spending her days in America running from her footman and abiding by absolutely no rules. I would cheer "slay queen", if not for the fact that she is as many miles away from the throne physically as she is heritarily.

[ifreakingloveroyals]

Through the Years → Maria Teresa, Grand Duchess of Luxembourg (520/∞) 22 June 2024 | The festivities organized on the occasion of the public celebration of the anniversary of the birth of The Grand Duke opened this year in the commune of Kehlen (7,000 inhabitants). The Grand Duke and the Grand Duchess were warmly welcomed this Saturday by Mayor Félix Eischen and the residents. The President of the Chamber of Deputies, Claude Wiseler, Ministers Gilles Roth and Max Hahn were also present. (Photo by Maison du Grand-Duc)

[judocritics]

ECup u18 Bielsko-Biala: VJF weggeblazen op sterk tornooi.

(21-May-2023)

>> 2023 ECup u18 Bielsko-Biala, Pol (IJF results) 

Van de 9 VJF-judoka’s bereikte er niemand de kwartfinales, en werd uiteindelijk ook slechts één iemand (en die dan nog met eigen middelen kwam) met amper 1 overwinning heropgevist, nl. laatstejaars Andreas Declercq (°06 /-55kg; 2°BK’23); dat leverde vervolgens nog één repechage-winst op, en een uiteindelijke 9°-plaats.    

Line Martens (°06; /-52kg; 2°ECup Strasbourg’22; 7°ECup Bucharest’22; JC Nevele): out (1 own)

Milan Peeters (°07; /-50kg; Gruitrode): out (1 own)

Aschab Isayev (°07; /-50kg; 2°BK’23; Eindhout): out (2 own) >> in de /-50kg slechts 2 Europeanen in de top-8 (5° Ita & 7° Sui); de rest is Kaz, Aze, Bra.

Andreas Declercq (°06; /-55kg; Bavikhove): 9° (2 own) - eigen kosten

Xzeno Eischen (°??; /-60kg; 5°VK’23; Merksem): out (0 own) - eigen kosten

Sofiane El Hajouti (°06; /-60kg; 3°BK’23; Boom/Schelle): out (0 own) - eigen kosten

Bjarne Wellekens (°07; /-66kg; 3°BK’23; 3°DOE’23; 2°Leverkusen’22; 1°BK’21 u15/-66kg;  Boom/Schelle): out (2 own; tegen Baltics)

Alhamzah Hassoun (°06; /-73kg; 3°Bremen’22; 3°Harnes’22; 1°DOE’23; 3°BK’23; 3°Bremen’23; Gruitrode): out (0 own) ps: Jambes-Gishi 1°BK & 2°BK  

Kenzo Cremers (°07; /-81kg; 1°BK’23; 1°Leverkusen’22; 2°Harnes’22; 7°ECup Teplice’23; Gruitrode): out (1 own; verliest van Liam Le Gallou, Fra, hier 5°)  

Met landen als Frankrijk, Georgië, Kazakhstan, Azerbaijan, Brasil en Ukraïne was dit een erg sterk tornooi ! Frankrijk met 15 medailles levert een prachtprestatie; thuisland Polen, Hongarije en Duitsland waren verdienstelijke EU-landen. Maar Nederland bvb. met 33 deelnemers oogstte enkel 1 medaille: brons met Noor Noufal (u18/-48kg), naast 2x 5° (Megan Warners /-40kg & Zef Jansen /-60kg). 

De VJF werd weggeblazen in dit gezelschap van 781 deelnemers !! : 9 overwinningen in totaal van deze 9 judoka’s (de eigenlijke VJF-selectie van 6, won 7 maal). Je kan er moeilijk naast kijken: Wallonië zet systematisch zijn middelen véél efficienter in: enkel 2 meisjes maakten de tornooi-verplaatsing:  -- Lena Antoine 5° 3 own (°07; /-44kg; 2°BK’22; 2°Maubeuge’22; 3°Venray’22; 1°BK’23; 3°Thuringia’23; 1°Maubeuge’23; 7°ECup Teplice’23): verloor haar 1ste kamp tegen winnares Sarah Mendes (Bra), maar kon dan 3 repechages winnen om te sneuvelen voor brons. -- Marielle Bouvier out 0 own [°06; huidig 2-voudig Belgisch kampioene u18/-70kg en 2°BK Seniors tegen... Maxine Heyns (AUJ); 2x 7°ECup’22 (Coïmbra; Strasbourg); 2°Thuringia’23; 1°DOE’23; 3°Harnes’22)]; verliest van Coco-Mia Baur (7°), die verliest van de winnares en bronzen medaille.

PS: de beste jongere uit deze lichting is eigenlijk Amsar Dzhamaldinov (°06; /-55kg, recentelijk /-60kg; inderdaad, uit Wallonië - Jambes-Gishi), die als Cadet #4 ECup top-8 plaatsen behaalde (3° Coïmbra’22 /-55kg).

[foreveryour-remus]

who are you!?

Remus Eischen, A new student here at the University. Why… who’s asking?