# All Questions

**7**

votes

**1**answer

60 views

### On linear integer onequalities with infinitely many solutions

Suppose that a linear system of inequalities $Ax \le b$, where $A\in Z^{m\times n}$ and $b\in Z^m$, have integral coefficients, has an infinite number of integral solutions $x$.
Can one conclude ...

**0**

votes

**0**answers

15 views

### Prove the inequality, $\sqrt{n} \le (n!)^{\frac{1}{n}} \le \frac{n+1}{2}$ [on hold]

Prove the given inequality
$$\sqrt{n} \le (n!)^{\frac{1}{n}} \le \frac{n+1}{2}$$
$$\forall \ \ \ n \in \mathbb{N} $$

**12**

votes

**3**answers

374 views

### An inequality improvement on AMM 11145

I have asked the same question in math.stackexchange, I am reposting it here, looking for answers:
How to show that for $a_1,a_2,\cdots,a_n >0$ real numbers and for $n \ge 3$:
...

**-5**

votes

**0**answers

17 views

### How to Wacth The Live Game? [on hold]

Another weekend, another individual of your just about all highly-anticipated fights of any year. even though Klitschko will be the heavy favorite and few tend to be picking against him,
...

**4**

votes

**1**answer

223 views

### Improper integral $\int_0^1 \frac{\exp(ctx)}{\sqrt{(\exp(bt)-1)(1-\exp(atx))-(1-\exp(at))(\exp(btx)-1)}} dx$ with $-a$ and $b$ positive

Is the following function real analytic in $t>0$:
$$F(t)=\int_0^1\frac{\exp(ctx)}{\sqrt{(\exp(bt)-1)(1-\exp(atx))-(1-\exp(at))(\exp(btx)-1)}} dx,$$
where $-a$ and $b$ are positive, and $c\not=a$?
...

**22**

votes

**2**answers

410 views

### Uniform proof that a finite (irreducible real) reflection group is determined by its degrees?

Given a finite (irreducible real) group $G$ generated by reflections acting on euclidean $n$-space, it was shown by Chevalley in the 1950s that the algebra of invariants of $G$ in the associated ...

**0**

votes

**1**answer

94 views

### Time Hierarchy Theorem and P vs NP

One obvious strategy for proving P not equal to NP would be to show that there is some problem in NP which is hard for a time class strictly containing P (the origin of this question is the recent ...

**0**

votes

**1**answer

36 views

### schauder estimate for the heat equation on compact manifolds

I asked this question on math.stackexchange.com, however I didn't get any answers so I'll try it here.
Let $M$ be a compact manifold without boundary. Consider $Lu:=\partial_tu-\Delta u$. Let $f\in ...

**5**

votes

**1**answer

280 views

### Homogeneous metrics of given volume element, on the n-sphere.

Let $\omega$ be an $n$-form on $S^n$, nowhere vanishing.
Is there a Riemannian metric $g$ on $S^n$, so that its volume form is $\omega$, and $(S^n,g)$ is homogeneous? Is it unique, and if not, what ...

**-2**

votes

**0**answers

54 views

### A tricky 2d integral [on hold]

I tried to calculate such integral:
$$
\int d^2q \frac{\bf{q+q_2}}{(\mathbf{q}^2+m^2)((\mathbf{q-q_1})^2)^{1-i\eta}(\mathbf{q+q_2})^2}
$$
where $q$,$q_1$ and $q_2$ are two dimensional vectors. Can ...

**5**

votes

**2**answers

221 views

### A result of Sierpiński on non-atomic measures

There is a classical result commonly attributed to W. Sierpiński that reads as follows:
Theorem 1. If $f: \Sigma \to \bf R$ is a non-atomic (*) measure on a set $S$, then for every $X \in \Sigma$ ...

**1**

vote

**1**answer

36 views

### General solution to system of stochastic linear differential equations

Assume we are given the system of linear stochastic differential equations
$$dx_i = \sum_{j=1}^n a_{ij}(t) \cdot x_j \cdot dt + \sum_{j=1}^n \sigma_{ij}(t) \cdot x_j \cdot dB_{ij,t} + b_j(t)\cdot ...

**-5**

votes

**0**answers

105 views

### Can the following expressions be regarded as general formula of prime numbers? [on hold]

Commonly accepted opinion is that there is no general formula for prime numbers. But we propose expressions for two pairs of 2-dimensional arrays which contain indexes $p$ in the sequences $6p + 5= 5, ...

**6**

votes

**1**answer

148 views

### Does the normal ordered product on differential operators lift to $U\left(\mathfrak{gl}_n\right)$ ?

Let $n\in\mathbb N$. Let $k$ be a commutative ring. Let $\Omega$ denote the $k$-algebra of polynomial differential operators on $n$ variables $x_1$, $x_2$, ..., $x_n$ over $k$. (The multiplication in ...

**14**

votes

**3**answers

1k views

### Example of a variety with $K_X$ $\mathbb Q$-Cartier but not Cartier

I know the definition of $K_X$ on a normal, singular variety, but I don't have a good set of examples in my mind. What's an example of a variety where $K_X$ is $\mathbb Q$-Cartier but not Cartier? ...

**10**

votes

**0**answers

403 views

### Quaternions: ellipse effect

I would be interested in an explanation of the "six ellipse effect" produced by the pseudocode below (I also wonder how close are these to being actual ellipses). Note the code is somewhat similar to ...

**0**

votes

**0**answers

37 views

### Is this theory decidable?

It is well-known that both Presburger arithmetic (by contrast with Peano arithmetic) and Tarski geometry are decidable. I was in the shower this morning and wondered whether there exists an elegant ...

**6**

votes

**2**answers

152 views

### non commutative polynomial which is zero for all matrix evaluation

I want to work on $K$ an algebraic closed (commutative) field of characteristic zero (even if it seems to be more general).
We can define the free K-algebra of polynomials in non commutative ...

**2**

votes

**0**answers

67 views

### Defining Inertia Stack

Let $X$ be a topos and $F: \zeta \rightarrow X$ a stack on $X$. Now in the paper http://arxiv.org/pdf/math/0411337v2.pdf ( Definitions 2.1.1.5 and 2.1.1.1) of Lieblich, he describes the inertia stack ...

**-1**

votes

**0**answers

17 views

### Consecutive numbers with three numbers using the measure of an Isoceles triangle [on hold]

I asked this question because the application I'm using to measure the length and angle and won't let me use fraction of angle C and base of c of an isosceles triangle..
...

**0**

votes

**1**answer

121 views

### about the horizontal lift in a principal bundle

I'm currently studying Fibre Bundle by Nakahara's book, and I'm a bit confused about the following:
Imagine we have a Principal Bundle $P(M,G)$ with open chart {$U_i$} and a local section ...

**1**

vote

**1**answer

122 views

### Is it true that $ \mathcal{H}^{n-1} (\operatorname{spt} \mu _E \setminus \partial ^{*}E)=0$?

In Federer's Theorem, $ \mathcal{H}^{n-1} (\partial ^{m}E \setminus \partial ^{*}E)=0 $, where $E$ is a set of finite perimeter in $ \mathbb R^n $, $\partial ^{e}E$ is the essential boundary of E, and ...

**6**

votes

**0**answers

198 views

+100

### “The” natural double complex associated to a principal $G$-bundle?

Let $\pi: P \to M$ be a principal $G$-bundle. We have the associated adjoint bundle $ad(P)= P \times_{ad} \mathfrak g$ whose sections correspond to infinitesimal guage trasformations.
Consider the ...

**8**

votes

**0**answers

51 views

### Are all sneaky groups products of Frobenius and 2-Frobenius groups?

I've been stuck thinking about this for a while.
Def. Let $G$ be a finite solvable group whose order is divisible by only three primes: $p,q,$ and $r$. Suppose that $G$ has cyclic subgroups of ...

**2**

votes

**1**answer

79 views

### Misere nim variant

Is there a name (and strategy) for this nim variant?
There are $n$ lists of objects, say $L_1,\ldots,L_n$ where $L_i = \{a_{i,1},a_{i,2},\ldots,a_{i,n_i}\}$. Players take turns choosing a list and ...

**2**

votes

**0**answers

50 views

### Is stable map space $\overline{M_{0,n}}(\mathbb{P}^n,d)$ is irreducible for all n,d?

I read a paper 'Notes On Stable Maps And Quantum Cohomology, W.Fulton and R.Pandharipande'. And I think that $\overline{M_{0,n}}(\mathbb{P}^n,d)$ is irreducible. But I cannot find an exact statement ...

**2**

votes

**0**answers

48 views

### Structure of $C^k$ ($k<\infty$)Riemannian metrics on a manifold

$M$ is a smooth manifold. It's known that if $M$ is compact, then the space of smooth Riemannian metrics has a Frechet manifold structure. For the space of $C^k$($k<\infty$) Riemannian metrics, ...

**1**

vote

**1**answer

68 views

### Uniqueness of $\partial_t u -u\Delta u=0$ with $u(0,\cdot)=1$

Is there anything known about uniqueness of classical solutions to
$$
\partial_t u -u\Delta u=0\quad u(0,\cdot)=1
$$
on smooth domains $[0,T]\times D$ without boundary conditions? I know that ...

**-2**

votes

**0**answers

69 views

### exponential tail bound for conditional probability

I am aware of exponential tail probabilities for unconditional probability (for ex: Normal). Are there any similar results available for conditional probability (w.r.t to a sigma field) in literature ...

**3**

votes

**0**answers

113 views

### Integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of varieties of general type is a rational numbers?

It is known that the integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of Calabi-Yau varieties is a rational numbers
My question is on moduli space of varieties of ...

**0**

votes

**1**answer

68 views

### Undergrad : decomposition of an integer as sum, with constraints [on hold]

I need to know if there is a way to determine in how many ways one can write n as $ n= x_1 + x_2 + \cdots + x_k$ with each $x_j \in \mathbb{N}$, and with the extra restriction that $x_j \leqslant ...

**26**

votes

**0**answers

310 views

### Are there $n$ groups of order $n$ for some $n>1$?

Denote $N(n)$ : number of groups of order $n$
Does $N(n)=n$ hold for some $n>1$ ?
I checked the OEIS-sequence https://oeis.org/A000001 as well as the squarefree numbers in the range ...

**2**

votes

**0**answers

102 views

### How close to being well-orderable does this make my powerset?

Let's work in a set theory without assuming AC (for instance, but not necessarily, ZF). Fix a set $k$ satisfying $k\times k \simeq k$, and consider its powerset $X = 2^k$. I have a technical condition ...

**0**

votes

**1**answer

233 views

### Reverse optimization of a minimum cost flow network

Given an undirected graph $(V,E)$, with $W$ as the weight of each edge, and a convex cost function $F(X)$, such as $|X|^k$ ($k>1$).
The cost to send $x$ unit of flow through edge $e_i$ is defined ...

**-1**

votes

**0**answers

32 views

### Multisets and set cardinality [on hold]

Consider $0<\lambda<1$, and let $A$ be a multiset of positive integers. Let $A_n=\{a\in A: a\leq n\}$. Assume that for every $n\in\mathbb{N}$, the set $A_n$ contains at most $n\lambda$ numbers. ...

**3**

votes

**0**answers

35 views

### Traces of fractional Sobolev spaces $W^{s,p}$ with $0<s<1/p$

I've stumbled upon a problem involving the trace of a function in a fractional Sobolev space of the form $W^{s,2}(H)$, where $H$ is a half-plane in $\mathbb{R}^2$. Would it be possible to define a ...

**15**

votes

**3**answers

1k views

### Good reference for studying operads?

Can you, please, recommend a good text about algebraic operads?
I know the main one, namely, Loday-Vallette "Algebraic operads". But it is very big and there is no way you can read it fast. Also ...

**1**

vote

**0**answers

93 views

### Bockstein cohomology

There is a notion of Bockstein homomorphism $\beta$. I am interested precisly in the case of sequence $$0 \rightarrow \mathbb{Z}/p \mathbb{Z} \rightarrow \mathbb{Z}/p^2 \mathbb{Z} \rightarrow ...

**3**

votes

**0**answers

65 views

### realizing uniform boundedness of Galois representations associated to elliptic curves

This is less of a question and more of an argument that I've been worried about for a while and want to check (apologies for the length and if my writing is unclear).
Suppose I have an elliptic curve ...

**0**

votes

**0**answers

29 views

### Weighted maximal number of disjoint chains in the integer divisibility poset for $\{1,2,\ldots,n\}$

In the mathoverflow question here the asymptotic growth of antichains in the divisibility poset ${\cal P}_n$ of the set of natural numbers $\{1,\ldots,n\}$ is considered. I have a somewhat dual ...

**7**

votes

**1**answer

349 views

### Number of matrices with given Smith normal form

Denote with $\mathcal{M}$ the set of $(m \times n)$-matrices with integer coefficients bounded by some $K$. Given a matrix $B \in \mathcal{M}$ that is in Smith normal form, is anything known about the ...

**0**

votes

**0**answers

61 views

### Proving a functional inequality [on hold]

Consider two monotonically decreasing functions $f_0(x)$ and $f_1(x)$ for which the following holds:
\begin{equation}
1-t\leq f_0(t)\leq f_1(t)\leq1.
\end{equation}
Let $n,m\in\mathbb{N}$ and $m\leq ...

**1**

vote

**1**answer

138 views

### Reference for holder estimate on parabolic equation with neumann boundary condition

I saw a type of holder estimate in Friedman's book: partial differential equations of parabolic type(page 200 3.24) as following:
Suppose we have a uniformly parabolic equation with holder ...

**5**

votes

**1**answer

321 views

### Grothendieck's paper on principal bundles, reduction to a torus step

In Grothendieck's paper "Sur la Classification des Fibres Holomorphes sur la Sphere de Riemann", there is a step I don't understand in section 4, where he proves reduction to a torus. He states (lemma ...

**-4**

votes

**0**answers

25 views

### Curve with Matlab [on hold]

I have posted this question:
http://math.stackexchange.com/questions/1547373/curve-with-matlab
but I have not answers. Can you help me?

**-1**

votes

**1**answer

31 views

### Convex Optimization in an Ellipsoid

Suppose we want to minimize a linear objective inside an ellipsoid that is,
$\min _x l^Tx$
such that $(x - \mu)^TA(x - \mu) \leq \beta ^2$.
Here, A is PSD and $\mu$ is a fixed vector. Can this be ...

**43**

votes

**3**answers

2k views

### Operations via Morse Theory

I am interested in seeing if and how Morse Theory can "do everything". Some core things are handle decomposition, Bott periodicity, and Euler characteristic. But what do the normal (co)homology ...

**3**

votes

**0**answers

71 views

### Obtaining the metric from the mixed Ricci tensor $R^i{}_j$

In chapter 5 of the book "Einstein Manifolds", Arthur Besse discusses the possibility to find the metric $g$ when knowing the Ricci curvature tensor $Ric(g)$ ($=R_{ij}$).
But what do we know about ...

**21**

votes

**0**answers

261 views

+50

### Isometric embeddings of finite subsets of $\ell_2$ into infinite-dimensional Banach spaces

Question: Does there exist a finite subset $F$ of $\ell_2$ and an infinite-dimensional Banach space $X$ such that $F$ does not admit an isometric embedding into $X$?
There are some results of the ...

**7**

votes

**2**answers

454 views

### Can all the sporadic groups be expressed as permutation groups based on a single big cycle?

Working on M11, I came up with that it can be generated using the following permutations:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
[[2, 0, 1, 7], [3, 4, 5, 6]]
[[4, 0, 6, 7], [2, 3, 1, 5]]
[[0, 7], [4, 6], ...