# All Questions

**0**

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2 views

### Elementary question of Group cohomology

Let $G$ be a finite group.
Assume $G$ acts on finite abelian module $M$ such that $(|G|,|M|)=1$.
Question: Why $H^i(G,M) = 0$ for $i > 0$?
Pierre MATSUMI

**2**

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6 views

### Relationship of ${\cal P}(\omega)/fin$ and ${\cal L}$

Define ${\cal L}$ as in this question: the set of functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $f(n)\leq f(n+1)\leq f(n)+1$, where two functions are considered equal if they differ at at ...

**-3**

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**0**answers

57 views

### Flower Arrangements [on hold]

We have a $n\times m$ grid with $k$ flowers (not necessarily distinct). The grid is assumed to have horizontal and vertical symmetry. What is the value of $A(n,m,k)$, where $A(n,m,k)$ is the number of ...

**-4**

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**0**answers

40 views

### Solve the recurrence formula $a_{n+1} = 2 a_n + 1/a_n$ with $a_1 = 1$ [on hold]

How to solve for general term of $a_{n+1} = 2 a_n + 1/a_n$ with $a_1 = 1$
Thanks in advance!

**5**

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49 views

### Brouwer's theorem for the Cauchy reals

Brouwer famously proved, using principles motivated by intuitionistic choice sequences, that every function $\mathbb{R}\to \mathbb{R}$ is continuous. In Sheaves in geometry and logic (section VI.9), ...

**0**

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28 views

### On the search for an explicit form of a particular integral

Let $f$ be integrable over the interval $(0, 1)$, and
$$I_n = \int_0^{1} x^n f(x) \, \mathrm{d}x.$$
Suppose $f(x) = f(1-x)$; we can then show that
$$I_n = \sum_{k=0}^{n} \binom{n}{k} (-1)^k \, ...

**-2**

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**0**answers

31 views

### are signs of coefficients arbitrary in 01-integer programming?

looking to understand more about full coverage integer programming i wondered if my research should include forms of the problem with the possibility for negative coefficients
i went looking for an ...

**3**

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60 views

### An inequality from the “Interlacing-1” paper

This question is in reference to this paper, http://annals.math.princeton.edu/wp-content/uploads/annals-v182-n1-p07-p.pdf (or its arxiv version, http://arxiv.org/abs/1304.4132)
For the argument to ...

**1**

vote

**0**answers

35 views

### Generalized identities of (soluble) groups

Let $G$ be a group. Let us say that $G$ satisfies a generalized identity of degree $n$ if there exist $a_1,a_2,\dots a_n \in G$ such that
$$x^{a_1}x^{a_2}\dots x^{a_n}=1,$$
for all $x\in G$.
...

**-1**

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17 views

### Optimization problem with an integral in the objective function

I would like to find $x$ that solves the following optimization problem:
$min \;L(x) = \int\limits_{-24}^{48} c(t)\cdot f(x,t) dt$
sa $ 0 \leq x \leq 24$
with
$c(t) = 5 + cos(\frac{\pi\cdot ...

**0**

votes

**0**answers

47 views

### Distribution of a transformed Gaussian random vector

Let $B$ be a random vector with $b_{i} \backsim N(m_i,\sigma_i) $ and $Y$ another random vector with $y_i \backsim N(r_i,\psi_i)$. Let $A$ be a symmetric and non-singular square matrix. What is ...

**-1**

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**0**answers

62 views

### Curvature in geometry-interpretation

Previously this question was asked on stack exchange: the answer contained only reference to the wikipedia page which I already read (as mentioned in my post). So here is the question:
The are ...

**1**

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47 views

### Vanishing natural transformation and strong generator

Let $X$ be a smooth projective variety (over the field of complex numbers). Let $T$ be strong generator of $D^b(X)$ : this means that every object in $D^b(X)$ can be obtained in a finite number of ...

**5**

votes

**1**answer

109 views

### For a 3-manifold $Y$, when does $Y\times S^{1}$ admits a Riemannian metric with positive scalar curvature?

Let $Y$ be an orientable, smooth 3-manifold and let $X=Y\times S^{1}$. My question is that: when does $X$ admits a Riemannian metric with positive scalar curvature?
An obvious case is when $Y$ ...

**0**

votes

**0**answers

51 views

### Properties of Coefficients of Order Polynomials

I am working on a problem involving determining the order polynomial $\Omega_P(k)$ of a partial order $P$, which counts the number of order-preserving transformations/maps from $P$ to the $k$-chain ...

**14**

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370 views

### A Linear Order from AP Calculus

In teaching my calculus students about limits and function domination, we ran into the class of functions
$$\Theta=\{x^\alpha (\ln{x})^\beta\}_{(\alpha,\beta)\in\mathbb{R}^2}$$
Suppose we say that ...

**2**

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**0**answers

31 views

### Compensated compactness for system of conservation laws?

As far as I knew, the method of compensated compactness can be used only for one-dimensional scalar and $2\times 2$ systems of conservation laws, i.e. $u_t+f(u)_x=0$. But if I understood correctly ...

**1**

vote

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24 views

### When do positively invariant subset contain a given set?

Non-triviality of the Conley index for an isolating neighborhood $N$ and a flow $\varphi$ can be used to prove non-emptyness of the related isolated invariant set. In particular, if $N$ doesn't ...

**-3**

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40 views

### How to find $B$ by solving the following linear system: $s_k$ $B$ ${s_k}^T$ $=1,$ [on hold]

How to find $B$ by solving the following linear system:
$s_k$ $B$ ${s_k}^T$ $=1,$ $\qquad$ for $k=1 ... ,p$.
Where $s_k$ is a $1\times3$ row_vector from the matrix
$S= [s_1 ... ...

**2**

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**0**answers

51 views

### Finding combintorial models / statistics

In many cases in combinatorics and especially algebraic combinatorics with some representation theory, the main problem is about finding the correct statistic on a mathematical object.
For example, ...

**3**

votes

**1**answer

125 views

### Construction of coherent sheaf such that $\text{Proj}\,\text{Sym}\,(\mathcal{F}) = \text{Sym}^n X$

Let $X$ be a smooth projective curve. How do I construct a coherent sheaf $\mathcal{F}$ on $\text{Pic}^n X$ (i.e., the component of the Picard scheme of $X$ parametrizing line bundles of degree $n$) ...

**2**

votes

**1**answer

216 views

### Bateman-Horn, continued even further

As before, consider the "singular series", which shows up in the Bateman-Horn conjecture: for an irreducible polynomial $f,$ this is equal to
$$
s(f) = \prod_p \frac{1-\frac{n_f(p)}p}{1-\frac1p},
$$
...

**3**

votes

**1**answer

61 views

### symmetric measurable 2-cocycles on compact abelian groups vanish?

Is the following result true? If it is, could you plese give me a reference for it? Thanks in advance!
Let $(G, \mu)$ be any compact abelian group with Haar measure $\mu$ (The case I am interested ...

**0**

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**0**answers

31 views

### Eigenvalue bounds from eigenvalues of Schur complement

Is it possible to lower bound the minimal eigenvalue of a symmetric PSD matrix
$M= \begin{pmatrix}A & C\\ C^*&B\end{pmatrix}$
from the knowledge of the eigenvalues of $M$'s Schur complement ...

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16 views

### what is formula of cumulative distribution function of hypergeometric distribution? [on hold]

sorry if this question seams ridiculous but I can't understand what does F means in the CDF formula for hypergeometric distribution in this wiki page. can somebody help me?

**8**

votes

**2**answers

169 views

### Quantum Hamiltonian for an Inverse Cube Force Law

If you have a nonrelativistic quantum particle in $\mathbb{R}^3$ in an attractive inverse cube force, its Hamiltonian is
$$ H = -\nabla^2 - \frac{c}{r^2} $$
where I'm keeping things simple by ...

**3**

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**1**answer

195 views

### Asymptotic $\int_M \mathrm{exp}[\mathbf{e}\left(n -\frac{t}{2\pi i}\right)] \left( 1 + \frac{5}{6} \mathbf{e}^2 \right)^{1/2} $ on quintic Calabi-Yau

Let $M = \{ G(x) = 0 \} \subseteq \mathbb{P}^4$ be a quintic Calabi-Yau and $\mathbf{e} \in H^2(M, \mathbb{Z})$ such that $\int_M \mathbf{e}^3 = 5$. Then as $t \gg 1$:
$$
\int_M
e^{n \mathbf{e}}
...

**1**

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58 views

### System of congruences

I have a system of $n$ congruences.
the generic $m$_th congruence of the system ($m = 1,\dots,n$) is in the form:
$(p_n\#)^2(\displaystyle\sum_{\substack{i=1\\i\neq ...

**-4**

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**0**answers

36 views

### Differentiability of the function $\frac{x}{1+\|x\|}$ [on hold]

Is the function $f:\mathbb{R}^n\to\mathbb{R}$ given by $$f(x)=\frac{x}{1+\|x\|},\;\;\forall x\in \mathbb{R}^n,$$ where $\|x\|=\sqrt[]{\sum_{i=1}^n{x_i}^2}$,, for all $x=(x_1, x_2,...x_n)$ in ...

**5**

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**0**answers

62 views

### A “universally non Hypercomplete” $\infty$-topos?

My question is :
Is there a classifying $\infty$-topos for $\infty$-connected objects ? Does this $\infty$-topos has a nice description (as an $\infty$-category ) ?
What I mean by $\infty$-connected ...

**3**

votes

**0**answers

80 views

### Rings that are $K_0$ of finite groups

Is there a simple characterisation of all rings which appear as $K_0$ of finite groups? By $K_0$ of a finite group $G$ I mean $K_0(\mathbb C[G])$ which in the same as a ring of virtual characters of ...

**5**

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**0**answers

143 views

### Is an irreducible ideal in $R$ also irreducible in $R[x]$?

Let $R$ be a commutative Noetherian ring and $I\subset R$ an ideal that is irreducible in the sense that if $I = J_1 \cap J_2$, then $I=J_1$ or $I=J_2$. Is (the ideal generated by) $I$ irreducible in ...

**3**

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**0**answers

90 views

### Does the Bombieri-Lang conjecture imply severe restrictions on rational points on twists of hyperelliptic curves?

According to Silverman, the Bombieri-Lang conjecture implies
that the rational points of surface on general type lie on
finite set of curves, except for a finite set of points.
Let $f$ be univariate ...

**-4**

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**0**answers

63 views

### Non-standard numbers and exponential form of Zeta function

Basic idea
For a long time I was looking for a numerical system that would allow to compare infinite sets. In contrast to Cantor's approach that empathizes the possibility of on-to-one correspondence ...

**-4**

votes

**0**answers

42 views

### Are all derivatives of sinc function bounded on real axis? [on hold]

It seems that all derivatives of sinc function (sinc(x)=sin(x)/x) are bounded on real axis. Is it true or no? Thanks in advance.

**1**

vote

**1**answer

43 views

### Does order-preserving equal continuous? [on hold]

Let $P,Q$ be posets and endow them with the interval topology $\tau_i(P)$ and $\tau_i(Q)$ respectively. Is it true that if $f: P\to Q$ is order-preserving, then it is continuous, and vice versa?

**3**

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26 views

### Path-connected Hausdorff interval topologies

Let $(P,\leq)$ be a poset with more than $1$ point such that the interval topology $\tau_i(P)$ is path-connected and $T_2$. Does this imply that $[0,1]$ order-embeds into $P$?
(This is a follow-up ...

**1**

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**0**answers

32 views

### Minkowski spacetime in Newman Penrose formalism

I have a rather basic question for which (surprisingly!) I cannot find a short and clear answer anywhere:
I'm currently looking at the Newman Penrose (NP) formalism (I use primarily Chandrasekhar's ...

**5**

votes

**0**answers

92 views

### Indecomposable representations of a wreath product

If $G$ is a finite group, we know the irreducible representations of $G ≀ S_n$ (over $\mathbb Q$) are classified by partitions of $n$ 'decorated' by an irrep of $G$.
I'm wondering to what extent the ...

**4**

votes

**0**answers

53 views

### “Edge Density” of Infinite Planar Graphs

Given an infinite planar graph $G$, let's denote by $\{H_1,H_2,\dots,H_m\}$ all the labeled graphs on $n$ vertices that appear as subgraphs of $G$. Also let
$$d_n=\frac{\sum_{i=1}^m \#E(H_i)}{nm}$$
...

**3**

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**0**answers

87 views

### Elementary examples on sheaf extension

Let $V\subset\mathbb{P}^n$ be a projective variety and $C_V$ its conormal subvariety in $T^\ast\mathbb{P}^n$. Denote by $\mathscr{O}_{C_V}$ its structure sheaf, then when will the condition
...

**3**

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**0**answers

66 views

### Representing rational homotopy class by geometric objects

Given a smooth manifold $M$, we can study its rational homotopy type by looking at differential forms. I am wondering if there is a way to represent each $rational$ homotopy class by geometric ...

**3**

votes

**1**answer

54 views

### convex hull of the set of permutations with one cycle

is there a way to describe the convex hull of the set of permutation matrices with exactly one non-trivial cycle?
or maybe I should ask for the convex hull of cycle matrices :
let $(i_{1},..,i_{k})$ ...

**3**

votes

**1**answer

90 views

### Kernel of the natural map between group $C^*$-algebras

Let $\Gamma$ be a discrete group. We can form two $C^*$-algebras: the universal (or full) and reduced, to be denoted by $C^*_u(\Gamma)$ and $C^*_r(\Gamma)$ (respectively). Both of them are completions ...

**12**

votes

**2**answers

699 views

### Why should we care about “higher infinities” outside of set theory?

Let's say you are a prospective mathematician with some addled ideas about cardinality.
If you assumed that the natural numbers were finite, you'd quickly vanish in a puff of logic. :)
If you ...

**6**

votes

**2**answers

342 views

### Geodesics on SO(3)

I have two 3D rotations about the origin, represented as
$3 \times 3$ orthogonal matrices $M_1$ and $M_2$
(specified by numerical entries),
and I would like to interpolate (and compute)
a continuous ...

**1**

vote

**0**answers

32 views

### C^1 Sard related question

Let $X$ be a $k+1$ rectifiable set with finite $k+1$ Hausdorff measure in $\mathbb{R}^{n+1}$ and set $Z=\{x\in X;\;\ \textrm{s.t} \;\; e_{n+1}\perp T_xX \}$, where $T_xX$ is the approximate tangent ...

**2**

votes

**0**answers

31 views

### Coupling Marginals of Distributions on the Sphere

Given a distribution $P_X$ on $\mathbb{R}$, when does there exist a coupling (i.e. joint distribution) $P_{X^n}$ of $X_1,...,X_n$, each distributed according to $P_X$, such that $\sum X_i^2 = n$ ...

**2**

votes

**0**answers

52 views

### Listing all Lattice Points in a Box

Let $B := [-1,1]^n$ be an $n$-dimensional box. Moreover, let $v_1,\ldots,v_n \in \mathbb{R}^n$ form a basis of $\mathbb{R}^n$, where the entries of the $v_i$ are explicitly irrational. We can assume ...

**1**

vote

**0**answers

28 views

### About the partial expectation polynomials in the Interlacing-I paper and perfect matchings

I am thinking of the polynomials $f_{s_1,s_2,..,s_k}$ as in the definition 4.3 in this paper http://annals.math.princeton.edu/wp-content/uploads/annals-v182-n1-p07-p.pdf
In the use of these ...