Tagged Questions

6
votes
0answers
58 views

Is this combination of generalized polygamma and dilogarithm actually zero? $\Im\;\psi^{(-2)}(1+i)+\frac1{4\pi}\text{Li}_2(e^{-2\pi})-\log\sqrt{2\pi}+\frac{5\pi}{24}+\frac12$

I encountered this quantity in my calculations and tried to simplify it. Approximate numeric calculations suggested it could be zero (more precisely, it is certainly less than $10^ …
13
votes
7answers
957 views

What math institutes offer research in pairs/research in teams?

Some math institutes offer programs in which a small number of researchers are enabled to meet at the institute for a week or more. A list seemed as if it could be useful.
0
votes
1answer
31 views

Is there any result concerning on the metric dimension of inverse limit?

To be specific, my question is as follows: Question: Let X be an inverse limit of compact metric spaces (X_i, d_i), then does it hold dim(X, d) \leq sup_i {dim (X_i, d_i)} for so …
0
votes
0answers
9 views

how to get the class interval given the distribution starts at 1, 3 as the highest value and 0.65 as the lowest?

Good day. I know getting the class interval given 3 as the highest value and 0.65 as the lowest value is easy. Here's the catch, the distribution of the interval starts at 1 which …
2
votes
1answer
59 views

Lipschitz map of the ellipse

Is there a L-Lipschitz homeomorphism of the Elipse $x^2/4+y^2=1$ onto the unit circle $x^2+y^2=1$ such that $L<1$?
0
votes
0answers
15 views

Free resolution for Lie algebras (reference)

What is a reference for the subject of "free resolutions for Lie algebras"? Does the term "standard resolutions" means "free resolutions"? What is a "bar resolution"? Is there o …
1
vote
1answer
54 views

sequences of non-crossing matchings by mutation

In Polynomials, meanders, and paths in the lattice of noncrossing partitions, they talk about sequences of non-crossing matchings related by "flips". Savitt counts "maximal chains …
2
votes
0answers
101 views

Reference request: Minimal Axiomatizations of PA over (+,x,<=).

Many years ago, when I was still a high school student, I came up with a certain first-order axiomatization of PA over the signature (+, x, ≤). Out of nostalgia, I've decided t …
11
votes
3answers
2k views

Proof of the weak Goldbach Conjecture

What are the main ideas of Harald Helfgott's proof that all odd $n \geq 5$ is the sum of 3 primes? This is breaking news, but is there a general feeling that the proof is correct? …
4
votes
0answers
70 views

What are the main structure theorems on finitely generated commutative monoids?

I should read J. C. Rosales and P. A. García-Sánchez's book Finitely Generated Commutative Monoids and L. Redei's book The Theory of Finitely Generated Commutative Semigroups. I h …
1
vote
2answers
130 views

The relations between the Perelman’s entropy functional and notions of entropy from statistical mechanics

I am looking for the relations and analogies between the Perelman's entropy functional,$\mathcal{W}(g,f,\tau)=\int_M [\tau(|\nabla f|^2+R)+f-n] (4\pi\tau)^{-\frac{n}{2}}e^{-f}dV$, …
39
votes
7answers
8k views

How many orders of infinity are there?

Define a growth function to be a monotone increasing function $F: {\bf N} \to {\bf N}$, thus for instance $n \mapsto n^2$, $n \mapsto 2^n$, $n \mapsto 2^{2^n}$ are examples of grow …
2
votes
0answers
70 views

Why are affine Lie algebras called affine?

Hi. I was wondering if someone could explain why we call affine Lie algebras affine. Thanks! Oliver
28
votes
9answers
1k views

Why is Set, and not Rel, so ubiquitous in mathematics?

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations. Why was there the n …
4
votes
1answer
297 views

Doubt in the proof of Stickelberger’s Theorem

I was going through the proof of Stickelberger's Theorem, as given in the book 'Algebraic Number Theory' by Richard A Mollin, and I am having some problem in understanding the proo …

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