# All Questions

**0**

votes

**0**answers

3 views

### Homology of infinite intersection

If $X_1\supseteq X_2\supseteq \ldots$ is a sequence of "nice" compact spaces, I would like to know whether the natural map from $H_*(\cap X_i)$ to the inverse limit $\lim \, H_*(X_i)$ is surjective. ...

**0**

votes

**1**answer

20 views

### Variations to Cayley's Embedding Theorem for Groups

Early in a course in Algebra the result that every group can be embedded as a subgroup
of a symmetric group is introduced. One can further work on it to embed it as a subgroup of a suitable (higher ...

**0**

votes

**0**answers

3 views

### Abstract Algebra [migrated]

Show that a group that has only a finite number of subgroups must be a finite group.(Fraleigh, A First Course in abstract Algebra-7th Edition,pg.67) I could not show properly so I need help. Thank ...

**0**

votes

**0**answers

15 views

### Morita equivalence via Kan extension

Are there necessary/sufficient conditions for a functor $f\colon \mathcal C\to \widehat{\mathcal A}$ to induce an equivalence $\text{Lan}_yf=F\colon \widehat{\mathcal C}\leftrightarrows ...

**0**

votes

**0**answers

9 views

### Existence of nonergodic polygonal billiard.

Let $P$ be a polygon in the plane. One can define the billiard flow on the unit tangent bundle of $P$, just following the trajectories of the billiard at speed one.
A standard conjecture is that a ...

**-1**

votes

**0**answers

18 views

### Maximum chi-square distance between norm vectors

What is the maximum possible chi-square distance between two normalized vectors? The representation of chi-square distance is below.
$d(x,y) = \sum_i \frac{(x_i-y_i)^2}{x_i+y_i}$

**0**

votes

**0**answers

22 views

### Kaehler form on weighted projective space

The Kaehler potential for the standard Fubini-Study Kaehler form in projective space $\mathbb{C} P^n$ is given by:
$$\log(\sum_{i=0}^n |z_i|^2)).$$
What is the analogous formula for a Kaehler ...

**1**

vote

**0**answers

19 views

### DGBV algebra of symplectic manifold

Let $(M,\omega)$ be a simply connected closed symplectic manifold. Then we have the symplectic codifferential operator $d^{\star}$. Furthermore, $(\Omega^{*}(M),d,d^{\star})$ is a differential ...

**-3**

votes

**0**answers

50 views

### The problem of Reimann zeta function [on hold]

$\zeta(2)=\sum_0^\infty 1/n^{2}<\pi^2/6=1.644934<2$
From the popular knowledge
$\zeta(2)\Gamma(2)=\int_0^\infty x/(e^x-1)dx$
but
$\int_0^\infty x/(e^x-1)dx=\int_0^\infty ...

**1**

vote

**0**answers

26 views

### K-theory of ringed spaces (including henselian and formal schemes); exision and Mayer-Vietoris

Given a ringed topological space $S$ one can easily define its K and K'-theory as the K-theories of the categories of locally free sheaves and of the category of coherent sheaves on it, respectively. ...

**-3**

votes

**0**answers

35 views

### Prove determinant of nxn matrix is (a+(n-1)b)(a-b)^(n-1)? [on hold]

Prove det(mat) is (a+(n-1)b)(a-b)^n-1 where matrix is nxn matrix with a's on diagonal and all other elements b, off diagonal?
For example, suppose matrix with diagonal composed solely of a's. All ...

**2**

votes

**0**answers

41 views

### $SL(n) \times SL(n)$-invariants of $m$-tuples of matrices

I work over field of complex numbers. Let $G=SL(n) \times SL(n)$, and $(A,B) \in G$ acts on $m$-tuples of matrices $M_{n \times n}(\mathbb{C})^{\oplus m}$ as follows
$$
(A,B) \cdot (M_1, \ldots, M_m) ...

**3**

votes

**1**answer

105 views

### Circle method on things other than the integers

The circle method is often used to estimate the number of solutions to the equation $$x_1 + x_2 + ... x_k = N$$ if for all $i$ $x_i\in A\subseteq\mathbb{N}_0$ and some subset of the nonnegative ...

**0**

votes

**0**answers

79 views

### Can we construct cohomolgy theory on noetherian separated schemes without Axiom of Choice?

The usual cohomology theory on schemes uses injective or flasque resolutions of quasi-coherent sheaves. Hence it uses Axiom of Choice.
However, if the base scheme is a noetherian separated scheme, the ...

**-2**

votes

**0**answers

76 views

### The problem of Riemann zeta function [on hold]

$\zeta(2)=\sum_0^\infty 1/n^{2}<1.8$
From the popular knowledge
$\zeta(2)\Gamma(2)=\int_0^\infty x/(e^x-1)dx$
but
$\int_0^\infty x/(e^x-1)dx=\int_0^\infty xe^{-x}/(1-e^{-x})dx$
$=\int_0^\infty ...

**2**

votes

**1**answer

75 views

### Suslin lines hereditarily Lindelof

I need to prove that every suslin line is hereditarily Lindelof. Any idea will be helpfull.

**0**

votes

**0**answers

120 views

### Recreating the wheel

I recently finished my Phd in pure maths and I am looking for open problems in my research area, functional analysis. Without going into the details, I stumbled onto an interesting problem and I ...

**0**

votes

**0**answers

26 views

### Cover one finite subset of integers by another one

Let $A$, $B$ be two finite subsets of integers. We denote by $C(A, B)$ the minimum number of shifts of $A$ to cover $B$. More formally, it can be written as
$$
C(A, B)=\min\{|S|: S\subseteq ...

**5**

votes

**1**answer

180 views

### Is there a sideways-walking rolling convex body?

Let $K$ be a solid, homogenous convex body in $\mathbb{R}^3$.
Place $K$ on an inclined plane, and let it roll down the plane,
under some reasonable assumptions of friction between $K$ and
the plane, ...

**0**

votes

**0**answers

23 views

### additive support functions of a convex set

Let $K \subset \mathbb{R}^d$ be a compact, convex set. It could be uniquely determined by its support function (for $u$ on the unit-sphere $S^{d-1}$), given by
$$h_K(u) = \sup \{ \sum_{i=1}^d x_i ...

**-2**

votes

**0**answers

36 views

### n-th prime in first order arithmetics [on hold]

Recently I have thought about formalizing Turing machine in first order arithmetics, step by step, starting from the most basic things. But I quickly struck a problem - to continue, I need to find a ...

**1**

vote

**0**answers

94 views

### A complicated combinatoric/probabilistic limit

I'm hoping to find a tractable expression for a limit of the following expression:
$P_i (\textbf{n},\textbf{U};M,N) =\frac{M U_i}{M^{\sum \limits_{j=1}^{N} n_j}} \sum \limits_{k_1 = \delta_{i,1}} ...

**3**

votes

**0**answers

52 views

### Positivity of Intersections in higher dimensions

"Positivity of Intersections" is a phenomenon in 4-dimensions, due to Gromov: Given two embedded $J$-holomorphic curves in an almost-complex 4-manifold $(X^4,J)$, all intersection points are isolated ...

**-1**

votes

**0**answers

78 views

### Why integer should have finite many digits? [on hold]

for example, if we take the real part of pi 3.1415926... and write it from right to left
like ...6295141, we can get a number, but this number is not a integer, why ? why it is not a integer?
Can we ...

**1**

vote

**1**answer

21 views

### a class of directed hypergraphs

I am interested in a certain class of directed hypergraphs, more precisely in the class of those hypergraphs each of whose hyperedges contain an even number of nodes (not necessarily the same even ...

**5**

votes

**0**answers

43 views

### When were bordered Heegaard Floer homology's DA bimodules invented?

This is less of a strictly mathematical question and more of a reference request.
In their paper "Bordered Heegaard Floer Homology (http://arxiv.org/pdf/0810.0687.pdf)," Lipshitz-Ozsvath-Thurston ...

**9**

votes

**2**answers

213 views

### What are the invariants of $U\otimes V\otimes W$ under action of $GL(U)\times GL(V) \times GL(W)$

The tensor product of some (finite dimensional real) vector spaces is acted on by the direct product of their general linear groups. I would like to know if there are explicit invariants in the case ...

**3**

votes

**1**answer

193 views

### What year was Hechler forcing created?

Hechler forcing is described on page 278, Jech.
Does anyone know when Hechler forcing was first used in a publication?

**-2**

votes

**0**answers

33 views

### Simplifying Trig Equation with Identifities [on hold]

I have an equation I have been given to solve, I know how to start but I do not know what to do after I use the Trig Identities. Any help?
Here is what I was given
(cos(A + B) + cos(A - B))
/
...

**4**

votes

**2**answers

119 views

### Can finitely generated subgroups of limit groups be detected in free group quotients?

In Henry Wilton's excellent paper "Hall's Theorem for limit groups" (Geom. Funct. Anal. 18, pp. 271–303, 2008 ) he proves the following result (see his paper or here and here for the relevant ...

**3**

votes

**0**answers

71 views

### Universal property of module categories over monads

Let $T$ be a monad on a cocomplete category $\mathcal{C}$. Let's assume that $T$ preserves reflexive coequalizers (or something weaker?). Then the category of $T$-modules $\mathsf{Mod}(T)$ is ...

**2**

votes

**1**answer

65 views

### Extremal graph theory for directed graphs

In extremal graph theory, there are results such as
$$t(C_4,G)\geq t(K_2,G)^4,$$
where $G$ is an undirected graph, $C_4$ is a cycle graph on 4 nodes, $K_2$ is a complete graph of $2$ nodes, and ...

**3**

votes

**0**answers

59 views

### What is the early history of the concepts of probabilistic independence and conditional probability/expectation?

In the 1738 second edition of The Doctrine of Chances, de Moivre writes,
Two Events are independent, when they have no connexion one with the other, and that the happening of one neither forwards ...

**3**

votes

**1**answer

71 views

### Zero currents localized along a submanifold

Let $\mathcal{D}(\mathbb{R})$ be the continuous dual of $C^\infty_c(\mathbb{R})$, the space of compactly-supported smooth functions. There is a nice characterization of distributions ...

**0**

votes

**0**answers

21 views

### Grassmann algebra morphism with universal property

I'm pretty sure that the following doesn't work, but nevertheless i wanted to ask, maybe this is a kind of well-known construction i've never heard of:
Let $\Lambda(\mathbb{R}^n)$ be a finite ...

**0**

votes

**0**answers

38 views

### Is there inverse FFT algorithm for Fourier transform of a integer-valued random variable?

In many applications, it is possible to derive an explicit expression for the
fourier transform of a random variable $X$
$$\varphi (\theta ) = \sum\limits_{n = 0}^\infty {{p_n}} {e^{in\theta }}$$
...

**1**

vote

**0**answers

33 views

### A comparison principle for degenerate parabolic equation

Let $\Omega$ be a bounded smooth domain and let $p < 0$ be real. Suppose that $u, v \in L^2(0,T;H^1(\Omega) \cap L^2(0,T;L^2(\partial\Omega))$ with $|u|^{p+1} \in L^2(0,T;L^2(\partial\Omega))$ and ...

**3**

votes

**1**answer

74 views

### Simple example of isolated critical point with non-semisimple monodromy

Consider a polynomial map $f :\mathbb{C}^{n+1} \rightarrow \mathbb{C}$ with $f(0)=0$ (no constant term) and with isolated critical point at $0 \in \mathbb{C}^{n+1}$. We can choose a disc $D$ of some ...

**-1**

votes

**0**answers

11 views

### regu tools l_curve regularization stanford ee 263 [migrated]

I am trying to solve one of the famous stanford EE263 problems, which gives me matrix A representing blurring of an image and y, representing the blurred image. For that I have been trying to use ...

**4**

votes

**1**answer

317 views

### Advice for number theory library

Hi I just got a faculty position and it comes with a generous start up funds for "office supplies", which I must use or lose. What does a pure mathematician need? I have good computers already. I ...

**3**

votes

**0**answers

72 views

### Infinite series of determinants

I am interested in what is known about the following class of sums. For a sequence of matrices $A_i$ (which possibly have different size), I am wondering about examples and methods for evaluating sums ...

**2**

votes

**0**answers

53 views

### $p$-groups with $\Omega_1(G)\leq\Phi(G)$

Let $G$ be a finite $p$-group with $\Omega_1(G)\leq\Phi(G)$.
What do we have information about this group?

**1**

vote

**0**answers

59 views

### Are the only discrete groups with nontrivial p-adic Haar measure finite?

Let K be a complete non-archimedean field (say $\mathbb{C_p}$) and let G be a discrete group. Since {e} is an open p-compatible compact subgroup of G, G admits a (left) K-valued Haar measure $\mu$. ...

**2**

votes

**0**answers

36 views

### Reference for Frobenius’s proof of Schur’s finite version of the Rogers - Ramanujan identities

In his paper “Ein Beitrag zur additiven Zahlentheorie und zur Theorie der Kettenbrüche” I. Schur has stated that Frobenius has communicated to him a simple direct proof of his finite version of the ...

**0**

votes

**0**answers

34 views

### First-countable topological monoids without local absorbing elements whose topology is induced by a semimetric

This is a follow up of Question 163246. For the reader's convenience, let me first copy&paste some basic definitions.
We let a semimetric on a set $X$ be a function $d: X \times X \to [0,\infty]$ ...

**1**

vote

**1**answer

113 views

### What are finite groups $H$ such that $H^n(H,\mathbb{Q/Z}) \cong H_n(G,\mathbb{Z})$?

Let $G$ be a finite group and $G^{\prime}$ be its commutator subgroup. Let $\mathbb{Z}$ and $\mathbb{Q}$ denote the integers and rationals. $\mathbb{Z}$ and $\mathbb{Q/Z}$ treated as trivial ...

**-5**

votes

**1**answer

57 views

### An elementary question in abstract algebra [on hold]

Let K be a field and A be a K-algebra, then how can we show that $\lambda1_A=\lambda$ for $\lambda\in$K and $1_A$ is the identity of A?

**-2**

votes

**1**answer

37 views

### How to find a matrix by its characteristic value and characteristic vectors? [on hold]

Now I am studying linear algebra course, In that for a given matrix we are finding the characteristic values (eigen vlaues) and characteristic vectors (eigen vectors). But my qustion is why cant we ...

**1**

vote

**0**answers

32 views

### A counterpart of Karhunen theorem

According to the Karhunen theorem, if the correlation function of a process $X(t)$
can be represented as
$$
R(t,s)= \int_{\Lambda} f(t, \lambda) \overline{f(s, \lambda)}d\nu(\lambda)
$$
then the ...

**-1**

votes

**0**answers

22 views

### departure time/overlap algorithm [on hold]

i'm looking for "departure time/overlap algorithm" or any other idea.
Suppose you have n trains and each one has a performance profile(how much electricity they need at the current time while driving ...