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Mean Score: 9.32

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Tsukipro The Animation

Yesterday, 4:07 PM

Completed 13/13 · Scored 8

The Rapeman

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The iDOLM@STER SideM

Mar 19, 2:09 PM

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Onanie Master Kurosawa

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Isekai Trip-saki de Tasukete Kureta no wa, Hitogoroshi no Shounen deshita.

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Reading 1/7 · Scored 10

Sokushi Cheat ga Saikyou sugite, Isekai no Yatsura ga Marude Aite ni Naranai n desu ga. ΑΩ

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Fukushuu wo Koinegau Saikyou Yuusha wa, Yami no Chikara de Senmetsu Musou suru Manga·2019

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Chronon Dec 15, 2022 8:27 PM

thanks, I learnt something new today ^^

Thanatos1 Dec 14, 2022 8:06 AM

Tychonoff Plank is a topological space which is defined as the product of the set of all ordinals which are less than or equal to ω (the first infinite ordinal) and the set of all ordinals which are less than or equal to ω1 (first uncountable ordinal) with the product topology that is induced on it.
The tychonoff plank is normal but its subset, the punctured tychonoff plank (tychonoff plank-(ω,ω1)) is not. It is an example that shows that normal spaces can have subsets that are not normal.

Green's Function

Nurguburu Dec 13, 2022 4:24 PM

All people are nothing but tools

Thanatos1 Dec 12, 2022 5:57 AM

A Hausdorff space is a topological is space in which for any two distinct points, there exist two disjoint open sets which include the points.

Normal Space

Thanatos1 Dec 11, 2022 6:31 AM

The Mittag-Leffler theorem says that any meromorphic function F(z) with given poles An can be expanded in the neighbourhood of one of its poles in terms of some entire function (function that's holomorphic on the finite complex plane) H(z) and the principal part (negative power part in the Laurent series) of that function for that pole.
F(z)=H(z)+∑(from n=1 to ∞)[Gn(z)+Pn(z)]
here Gn(z) is the principal part corresponding to the pole An and Pn(z) is chosen based on Gn(z) so that the series is uniformly convergent.

Uniform Convergence

Thanatos1 Dec 9, 2022 5:50 AM

The Cross Product (also known as vector product) of two vectors belonging to R3 is the vector that is orthogonal to the original vectors (orientation is given by right hand rule) and whose length is equal to the area of the parallelogram formed by the two vectors.
(I know there are other cross products but this was the easiest one :)

Essential Singularity

Domenico1620 Dec 8, 2022 11:05 AM

Thanatos1 Dec 8, 2022 6:30 AM

If a Group admits a principle series (satisfies ascending chain or descending chain conditions for normal subgroups), then any decomposition of the group as a direct product of indecomposable factors is centrally isomorphic,

didn't completely understand this either.

Jacobian

Thanatos1 Dec 7, 2022 7:08 AM

I found out after I wrote the previous reply that when physicists talk about "saddle-point approximation", they are referring to the method of steepest descent or what is referred to by mathematicians as Laplace's method. That is something that's conceptually different from and simpler compared to the maths "saddle-point approximation". .

The method of Lagrange Multiplers is a method that one uses to find extremas for a function of multiple variables under some equality constraints. It is based on the idea that at the extrema point, the gradients of the function that is being optimized and the constraints are linearly dependent. The proportionality factors between the gradients are known as the Lagrange Multipliers.

Cayley Graph

Thanatos1 Dec 6, 2022 5:31 AM

Was able to find a definition for this,

A Grothendieck Topos is a category that is equivalent to the category of sheaves of sets on some topologised category

but I don't know what this really means. I am too small brain for it.

Saddlepoint approximation method

Thanatos1 Dec 5, 2022 9:52 AM

Riemann Roch Theorem gives the formula to find the answer to the Riemann Roch Problem (The Riemann Roch Problem asks how many meromorphic functions (Holomorphic functions with only isolated poles) are there on a compact connected Riemann surface with given poles).
It states that if a Riemann surface has genus g and canonical divisor K then for any divisor D ,
l(D) − l(K − D) = deg (D) + 1 − g
Here, l(D) is the required answer to the Riemann Roch Problem.

Nagata–Smirnov metrization theorem

Thanatos1 Dec 2, 2022 1:05 AM

The Riemann Hypothesis is a hypothesis concerning the Riemann Zeta Function (The riemann zeta function looks just like the harmonic series (Harmonic series is the series given in the form of the sum of all the positive unit fractions) where each term has been raised to the power which is given by the argument of the function. This argument is complex where the real part is greater than 1) which hasn't been proven or disproven yet.
It says that the real part of all the non-trivial zeroes of the riemann zeta function is 1/2.

Bolzano–Weierstrass theorem

Thanatos1 Dec 1, 2022 5:29 AM

I sort of know about ramification because I studied a little bit about multivalued functions while studying complex analysis in my Mathematical Methods for Physics (yeah I'm a physics person) course but the rest of it is a little too advanced for me.

Cauchy Schwarz inequality says that the magnitude of the inner product of any two vectors is always smaller than or equal to the product of their norms. It is true for any vector space for which an inner product has been defined.

Riemann Sphere

Thanatos1 Nov 30, 2022 5:20 AM

I have no idea what that is. I don't know enough math to be able to understand that even when I read about it.

Thanatos1 Nov 29, 2022 7:48 AM

Cauchy-Kovalevskaya Theorem says that there exists a unique analytic (infinitely differentiable) solution to a Cauchy problem (an ordinary or partial differential equation problem with certain initial conditions given on the hypersurface (a surface of dimension n-1 compared to the domain space)) if the Cauchy data (all the functions involved and the initial conditions) is analytic.

Cauchy–Goursat theorem

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