**4**

votes

**1**answer

281 views

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

This is less of a direct 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 ...

**2**

votes

**0**answers

62 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 ...

**32**

votes

**1**answer

498 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 ...

**-4**

votes

**0**answers

28 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?

**6**

votes

**2**answers

212 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 ...

**0**

votes

**0**answers

69 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 ...

**3**

votes

**0**answers

91 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 ...

**0**

votes

**1**answer

69 views

### Simple question about notation: formulas starting with a quantification [on hold]

Let $C\subset\mathbb{R}$ and suppose that $f:C\to2^C$ is a point to set map. Suppose that $f(x)$ is a set containing only negative real numbers for every $x\in C$. Are there any problems with the ...

**8**

votes

**1**answer

104 views

### On linear integer inequalities 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 that ...

**2**

votes

**0**answers

26 views

### How does a permutation $P$ affect the singular value $\sigma_{\text{max}}(Q^\top P^\top Q)$ for orthogonal $Q$?

Let $q_i$ for $i=1,\ldots,m$ be the columns of the matrix $Q\in\mathbb{R}^{n\times m}$, $n>m$, which are pairwise orthonormal ( i.e.
$q_i^\top q_j = \begin{cases} 1 & \text{if}\quad i=j \\ 0 ...

**13**

votes

**3**answers

535 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 $n \ge 3$:
...

**3**

votes

**0**answers

37 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 ...

**4**

votes

**0**answers

98 views

### Wreath product of an abelian group with a nilpotent group

By work of Coulbois, the wreath product of two finitely generated free abelian group is $LERF$; i.e, every finitely generated group of this wreath product is closed in the profinite topology.
Is there ...

**1**

vote

**1**answer

109 views

### Linear forms that avoid numbers with lot of factors

Is following true?
For every given $c>0$ there is an $n_c>0$ such that for every $n>n_c$ there are integers $n<a,b<2n$ such that there are two positive integers $\frac{n}{2(\log ...

**-7**

votes

**0**answers

84 views

### Show that $G$ a group? [on hold]

Suppose that $G$ is a semigroup , and for every $a$ in $G$ there is unique $a^*$ in $G$ that
$aa^*a=a$
Prove that $G$ is a group.

**-6**

votes

**0**answers

133 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, ...

**0**

votes

**0**answers

29 views

### Compact factors of Lie groups; possibly varying definitions [migrated]

Let $G$ be a real connected semisimple Lie group. Are the following equivalent?:
(1) $G$ has no proper cocompact Normal subgroups.
(2) $G$ has no proper cocompact connected Normal subgroups.
In ...

**6**

votes

**1**answer

117 views

### Inequality for the maximum of Gaussian variables

Let $X=(X_1,\dots,X_n)$ and $Y=(Y_1,\dots,Y_n)$ be centered Gaussian vectors
with variance matrix $\Gamma_X$ and $\Gamma_Y$. We assume that the matrix
$\Gamma_Y-\Gamma_X$ is positive definite. Is it ...

**0**

votes

**0**answers

47 views

### Solution of the system of differential equations [on hold]

Consider that we are working in the polynomial ring $\mathbb{C}[x]$.
Suppose we have the following system of linear differential equations:
$$\left\{\begin{matrix}
L_1(y)=f_1\\
L_2(y)=f_2
...

**3**

votes

**1**answer

146 views

### When can you canonically extend an ultrafilter after forcing?

Suppose that $V$ is a model of $\sf ZFC$, and fix some regular $\kappa$, say $\omega_1$ for practical purposes.
Let $\cal U$ be an ultrafilter on $\omega_1$ in $V$ which is non-principal and even ...

**-2**

votes

**0**answers

76 views

### exponential tail bound for conditional probability [on hold]

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

**1**answer

255 views

### Hypothesis test beyond simple hypotheses (mathematical statistics)

In mathematical statistics, the following problem (simple hypothesis test) is considered: given a data sample, test the hypothesis $H_0$ stating that all sampled values are values of a random variable ...

**0**

votes

**1**answer

134 views

### about the horizontal lift in a principal bundle [on hold]

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 ...

**0**

votes

**0**answers

61 views

### Advanced use of commutation matrices [on hold]

I am aware of matrix operators vec and kronecker product, commutation matrices and various related identities like stated in ...

**0**

votes

**1**answer

50 views

### Maximal chromatic number with a fixed number of edges

Given a graph $G$ with $m$ edges, what is the maximum chromatic number $\chi(G)$ that the graph can have?
My guess is that $\chi(G) \leq r(m)$ where $r(m) := \max\{k\in \mathbb{N}:
\frac{k(k-1)}{2} ...

**2**

votes

**0**answers

135 views

### Was “arithmetical translation” (coding in the Goedel sense) ever a part of Hilbert's Program?

Was "arithmetical translation" (that is, coding in the Goedel sense) ever a part of Hilbert's Program? I ask this question for several reasons:
i) it gives the numerals |, ||, |||,.... an ersatz ...

**-1**

votes

**0**answers

33 views

### conformal deformation with fixed boundaries

For a flat plane with certain boundary, e.g., a rectangular patch, is it possible to conformally displace or deform such patch to a curved bump with exact same boundary? In this thesis, Dr. Keenan ...

**5**

votes

**1**answer

161 views

### Definition of a normed ring

A normed ring "should" be a monoid object in the monoidal category of normed abelian groups. There are (at least) two choices of morphisms of normed groups, namely bounded or short homomorphisms, ...

**1**

vote

**0**answers

81 views

+50

### Shape-related vector fields

Assume that $M$ is a surface in $\mathbb{R}^{3}$. We denote its shape operator by $S$. A vector field $X$ is shape related to $Y$ if $S(X)=Y$.
(of course it is not an equivalent relation).
...

**-1**

votes

**1**answer

37 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 ...

**-1**

votes

**0**answers

38 views

### Alternative Geometries [migrated]

In our world, the distance between two points (in 2d) is defined as $\sqrt{(\Delta x)^2 + (\Delta y)^2}$. Suppose that in an alternative geometry, it was defined as $\sqrt[p]{|\Delta x|^p + |\Delta ...

**1**

vote

**0**answers

88 views

### Algebraic independence criterion

Is there any criterion for checking algebraic independence of a set of polynomials in $n$ variables in terms of the leading monomials with respect to some monomial order ? The Jacobian criterion is ...

**1**

vote

**1**answer

83 views

### Tight binomial left tail bound

Let $X \sim \text{Bin}(n,p)$. Wikipedia claims
$$\mathbf P[X \leq (p-\epsilon)n ] \leq e^{ - 2 \epsilon^2 n}.$$
This follows from Hoeffding's inequality ...

**0**

votes

**0**answers

114 views

### Is the positive existential theory undecidable?

Could you tell if the positive existential theory of $\mathbb{C}[e^{\mu x} \mid \mu \in \mathbb{C}]$ is undecidable in the language $\{+, \cdot , \frac{d}{dx} , 0, 1, e^x\}$ ?
How can we prove the ...

**12**

votes

**0**answers

299 views

### If $k$ is an algebraically closed field of any characteristic, then the fundamental group of $A$ is abelian

This is a followup to my earlier question, see here. I reproduce it as follows.
Let $A$ be an abelian variety over a field $k$ of characteristic $0$. How do I prove, without using transcendental ...

**0**

votes

**0**answers

49 views

### Simplicial approximation diagram [on hold]

Let $K$ and $L$ be simplicial complexes as given, and let $\phi:|K|\to|L|$ be the continuous map, where $A=\phi(a)$, $B=\phi(b)$, and so on.
Check whether the map $\phi$ has a simplicial ...

**5**

votes

**0**answers

172 views

### all subsets borel

Assume Martin's axiom plus $\neg CH$. It is well known, via almost disjoint forcing, that every set of reals of size less than continuum is an example of a metric space whose subsets are all ...

**2**

votes

**1**answer

74 views

### F-points of product of closed subgroups vs. product of F-points, F a local field, reference?

Let $F$ be a finite extension of $\mathbb Q_p$, where p is an odd prime. Let $G$ be a connected reductive group defined over $F$. Let $M, H$ be closed $F$-subgroups of $G$ (in particular, I'm ...

**9**

votes

**3**answers

187 views

### What characterizations of relative information are known?

Given two probability distributions $p,q$ on a finite set $X$, the quantity variously known as relative information, relative entropy, information gain or Kullback–Leibler divergence is defined ...

**6**

votes

**0**answers

108 views

### Improving Baumgartner's result?

Q1: Is it consistent with the failure of CH to have an $\aleph_1$-dense subset $A \subseteq \mathbb{R}$ such that for every $X \subseteq \mathbb{R}$ of size $\aleph_1$, there is a $C^{\infty}$ map $F: ...

**7**

votes

**2**answers

475 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], ...

**12**

votes

**2**answers

234 views

### Factorization of a matrix as a product of a symmetric and a skew-symmetric matrix

When can an $n\times n$ matrix $M$ be written as a product $M=AB$, where $A^T=A$ and $B^T=-B$?
For example, a necessary condition is that the trace of $M$ vanishes. In this case, it is easy ...

**-4**

votes

**1**answer

174 views

### The difference between Hilbert Scheme and Chow Scheme

I am confused by Hilbert Scheme and Chow Scheme. Whenever you have a point in hilbert scheme, take its fiber in the universal family and take its fumdamental class, we get a point in Chow Scheme; and ...

**0**

votes

**0**answers

135 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 ...

**5**

votes

**1**answer

500 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 ...

**2**

votes

**0**answers

59 views

### When is $\left[\begin{smallmatrix} D_1 & B \\\\ -B^T & D_2 \end{smallmatrix} \right]$ $\mathbb{R}$-diagonalizable?

Is there some block-wise characterization of $\mathbb{R}$-diagonalizability (by similarities) of
$$\begin{bmatrix} D_1 & B \\\\ -B^T & D_2 \end{bmatrix},$$
where $D_1$ and $D_2$ are real ...

**7**

votes

**1**answer

122 views

### Equalizing Geometric means of Graph Cycles

Consider a strongly connected directed graph $G$. I have been stuck on the following question: can you assign real numbers in $[0,1]$ to each edge of $G$ so that the geometric mean of all cycles are ...

**0**

votes

**0**answers

18 views

### Fractal Dimension Estimate from Hurst Paramater using Higuchi's Algorithm [on hold]

I am using R Stats package to calculate the Hurst parameter of my Center of Pressure Data set. I am using Higuchi's Algorithm to calculate it. I went and read his paper and saw that "index H is ...

**5**

votes

**1**answer

183 views

### What is known about the large cardinal strength of Shelah's categoricity conjecture?

Shelah's categoricity conjecture states that for every Abstract Elementary Class $\mathcal{K}$ there is a cardinal $\mu$ depending only on $\operatorname{LS}(K)$ (i.e. the Löwenheim–Skolem number of ...

**-1**

votes

**0**answers

68 views

### A statistical conundrum [on hold]

I have a statistical problem in a domain that I can not talk about due to a NDA. However, I have worked out how to describe an exactly analogous problem as follows.
You are in charge of record ...