# All Questions

**0**

votes

**0**answers

23 views

### Hodge-Tate weights of induced representation

Let $K$ be a finite extension of the field of $p$-adic numbers $\mathbb{Q}_p$ and let $E$ be another such extension, such that all the $\mathbb{Q}_p$ embeddings $K \to \bar{\mathbb{Q}}_p$ are ...

**0**

votes

**1**answer

34 views

### is there a global obstruction for a diffeomorphism to be an isometry?

Let $V$ be a finite dimensional vector space.
Let us call an automorphism $T:V\rightarrow V$ admissible if there exists an inner product $\langle , \rangle$ on $V$ making $T$ an isometry.
We know ...

**2**

votes

**0**answers

37 views

### How do we see the rank of the braid group?

The only presentation of the braid group that most people ever see is the standard Artin presentation
$$B_n=\langle σ_1,\cdots,σ_{n−1}|\ σ_iσ_j=σ_jσ_i\ \ (|i−j|>1),\ σ_iσ_{i+1}σ_i=σ_{i+1}σ_i ...

**0**

votes

**0**answers

21 views

### First order vs second order Markov Chain? [on hold]

I already built one first order discrete state Markov Chain model. It was build with R using the function 'markovchainFit()' in 'markovchain' package.
dat<-data.frame(replicate(20,sample(c("A", ...

**0**

votes

**1**answer

10 views

### product of two multivariate normal densities for the same vector, if one is only specified for a subset

A random vector x with n elements has a multivariate-normal density f(x).
Another distribution is known for m linear combinations of elements of x. The linear combinations are given in the form ...

**1**

vote

**0**answers

36 views

### If $f$ is separately holomorphic on $\Omega$ then $f\in\mathcal{C}^0(\bar\Omega)\Leftrightarrow f\in L^1(\Omega)$

Let $\Omega\subseteq\Bbb C^2$ be open bounded (and connected), $f:\Omega\to\Bbb C$ separately holomorphic (i.e. $f$ is holomorphic in each variable when the other is fixed).
Hartogs theorem is not ...

**3**

votes

**0**answers

46 views

### Existence of a measure-preserving bijection

Let $f, g \, \colon \mathbb{R}^n \rightarrow \mathbb{R}$ be two Borel-measurable functions such that $f$ is non negative and
g is radially symmetric,
the function $ (0, \infty )\ni t \mapsto g ...

**2**

votes

**0**answers

78 views

### “The Two Sheriffs” puzzle -2: threshold for security

I've already asked a question “The Two Sheriffs” puzzle with wrong assumption. Yoav Kallus in his amazing answer using Fano plane showed that the problem has a solution in the case of seven suspects.
...

**0**

votes

**0**answers

104 views

### Total degree of a polynomial

Let $\mathsf{F,G}\in\Bbb R[x_1,\dots,x_n]$ be minimum multivariate polynomials of least total degree $\mathsf{degF}$, $\mathsf{degG}$ respectively whose values are given at a set of points ...

**4**

votes

**1**answer

107 views

### Stabilisers of group actions

Let $G$ be an algebraic group acting on an irreducible algebraic variety $X$ over an algebraically closed field $k$ of characteristic $0$.
Suppose there exists some point $x \in X$ whose ...

**1**

vote

**0**answers

16 views

### Edge-disjoint path-systems in infinite digraphs

Let $ D=(V,A) $ be a directed graph without backward-infinite paths and let $ \{ s_i \}_{i<\lambda},U \subset V $ where $
\lambda $ is some cardinal. Assume that for all $ u\in U $ there is a ...

**1**

vote

**0**answers

66 views

### identity component of a formal group

Let $G=\operatorname{Spf} A$ be a formal group, the it is stated that the identity component $G^\circ$ (defined as $\operatorname{Spf} A_{\operatorname{fm}}$ for some open maximal ideal ...

**2**

votes

**0**answers

28 views

### Expectation of Mahalanobis norm

Let $(g_i)_{i=1,...,d}$ sampled i.i.d. from a standard Gaussian, and $(\lambda_i)_{i=1,...,d}$ non-random s.t. $\max_i(\lambda_i)=1$ and $\lambda_i>0, \forall i$.
I am looking for the expectation ...

**1**

vote

**0**answers

30 views

### Zero divisors and boundary elements of $A^{-1}$

I need to understand basic properties of (a) zero divisors in Banach algebras or rings, and (b) spectral properties of elements of the boundary of the set of invertibles in a complex unital Banach ...

**3**

votes

**0**answers

80 views

### Nash's proof of De Giorgi-Nash-Moser theorem

I saw this question, but I think the answer didn't fully address what I want to know about it:
Nash's paper on parabolic equations.
It says almost everything developed later in elliptic and ...

**0**

votes

**0**answers

52 views

### $K_1(R)$ and splitting

Let $R$ be a commutative ring with unit. Under what conditions does the following exact sequence split?
$1\to E(R)\to Gl(R)\to K_1(R)\to 1$.

**3**

votes

**0**answers

40 views

### An identity of complicated combinations of gamma functions (related to hypergeometric functions)

Can somebody help me in proving the following equation?
\begin{align*}&\textstyle \sum _{d=0} ^{n} \frac{1}{d!(n-d)!} \frac{\Gamma (b+d) \Gamma (b+n-d) \Gamma (c-n+d) \Gamma (c-b+1-n + 2d) ...

**3**

votes

**0**answers

53 views

### Raising coefficients of a power series to some power

Suppose you are given a power series $P=\sum_{i=0}^\infty{a_nt^n}$. I am primarily concerned with those power series coming from rational functions of the form
$$ ...

**1**

vote

**0**answers

28 views

### Is this characterization of (-1)-eigenspaces of the Weyl group of $E_6$ known?

I recently needed to know which one-dimensional subspaces $\mathfrak s$ of the Lie algebra $\mathfrak t^6$ of a maximal torus $T^6$ of the compact exceptional group $E_6$, corresponding to circles $S$ ...

**-4**

votes

**0**answers

52 views

### What is this formula Name? Can anybody teach me guide me to understand this? [on hold]

Formula
If XT(t) at any time t relative to Timeframe T, then almost surely, there exists positive integers h and k such that every price belonging to the set [XT(t) – k , XT(t)+ k] is h(T) recurrent.
...

**2**

votes

**1**answer

29 views

### When is the direct product of two graph cores itself a core?

A graph homomorphism $f$ is a function $f : V(X) \to V(Y)$ such that if $uv \in E(X)$, then $f(u)f(v) \in E(Y)$. If such an $f$ exists, write $X \to Y$. $X$ and $Y$ are hom-equivalent if $X \to Y$ and ...

**4**

votes

**1**answer

196 views

### Primes isolated by large gaps to either side

Say that the $n$-th prime $p_n$ is isolated to degree $k$
(my notation) if
the prime gap to either side is larger than $\log p_n$ to the $k$-th power:
\begin{eqnarray*}
p_n - p_{n-1} & > & ...

**1**

vote

**0**answers

52 views

### Matchings in countably infinite geometric lattices of finite height

Let $L$ be a countably infinite geometric lattice of finite height $r\ge3$. (A geometric lattice of height $r$ is an atomistic semimodular lattice such that every maximal chain has $r+1$ elements.)
...

**1**

vote

**1**answer

92 views

### Generating finite groups using subgroups

For finite groups $L \leq K$ we define $d(L,K)$ to be the least $n \in \mathbb{N}$ for which there exist $a_1, \dots, a_n \in K$ such that $\langle L, a_1 \dots, a_n \rangle = K$.
Is there some $m ...

**3**

votes

**3**answers

167 views

### Reference request about the representations of the group $PSL_2(\mathbb{F}_q)$

Is there a review/exposition of the representation theory of $PSL_2(\mathbb{F}_q)$ ? Like an enumeration of its irreducible representations and their dimensions as a function of $q$?

**-1**

votes

**0**answers

55 views

### A question on complexity notation

I am considering writing ''$\Pi^{n}_{i_{0},...,i_{n-1}}$-comprehension'' as abbreviation for ''$\Pi^{0}_{i_{0}}$-comprehension plus ... plus $\Pi^{n-1}_{i_{n-1}}$-comprehension'' in the context of an ...

**1**

vote

**0**answers

46 views

### Outer measure preserving bijection

Suppose X is a Sierpinski set (So X is uncountable and every null subset of X is countable). Let f be a bijection on X. Must/Does there exist a non null subset Y of X such that for every subset W of ...

**-2**

votes

**0**answers

27 views

### Independent and Dependent Variables [on hold]

Hi guys i have a question regarding independent and dependent variables.
Provide an example that shows the variance of the sum of two random variables is not
necessarily equal to the sum of their ...

**3**

votes

**1**answer

164 views

### Self-contained book on Ricci Flow/Geometric Analysis

Can someone please tell me whether there is any self-contained book on Geometric Analysis/Ricci Flow/analytic techniques used in Riemannian Geometry? By self-contained I mean it does not assume that ...

**1**

vote

**2**answers

67 views

### Integrability at $z$ of the 2-form $ d\omega=\frac{\partial_{\bar{\zeta}}g(\zeta)}{\zeta-z}d\zeta\wedge d\bar{\zeta} $

Given $g\in\mathcal{C}^1(\bar\Delta)$, and $z\in\Delta$, how can i prove that the 2-form
$$
d\omega=\frac{\partial_{\bar{\zeta}}g(\zeta)}{\zeta-z}d\zeta\wedge d\bar{\zeta}
$$
is integrable in $z$?
At ...

**0**

votes

**0**answers

14 views

### Global and local maxima in a weighted sum of logarithms of linear functionals?

Initially posted on math.stackexchange, was recommended that this is a more relevant forum:
Is is possible to describe, and locate efficiently, the maxima of the function below in the parameters ...

**2**

votes

**0**answers

131 views

### An (open?) problem about a sequence of nested principal sub-matrices and their determinants

Problem: Let $A$ be a $n \times n$ integer matrix, $\det(A) = \pm 1$. Under which conditions there exist a nested sequence of principal submatrices of size $n$ such that they all have determinant $\pm ...

**0**

votes

**0**answers

22 views

### Calculating age with decreasing year values [migrated]

This is my first question on mathoverflow.net, with everything this entails.
This question is about the perceived duration of every year as one ages. We will call
$Y_0$
the perceived duration of our ...

**0**

votes

**0**answers

44 views

### Good covering of a (singular) curve in a complex surface

Let $W$ be a $2$-dimensional complex manifold and $C\subset W$ a compact complex curve (possibly singular). I would like to know a reference for the following fact: there exists a collection ...

**3**

votes

**1**answer

103 views

### Obtain 4-manifolds by repeating surgeries of submanifolds in $S^4$

In his paper QFT and Jones Polynomials, Witten states: "It is a not too deep result that every 3-manifold can be obtained from or reduced to $S^3$ (or any other desired 3-manifold) by repeated ...

**1**

vote

**0**answers

21 views

### Biggest volume parallelotope inside the union of two parallelotopes

Given a parallelotope $P$ symmetric around the origin, and a vector $v$, such that $(P+v)∩(P−v)$ is not empty, is there a simple way to obtain a parallelotope $Q⊂(P+v)∪(P−v)$, symmetric around the ...

**1**

vote

**0**answers

19 views

### Mappings between adaptive networks and Markov processes

Are there any known mappings between adaptive networks models (i.e. graph model representations of networks where the internal vertex dynamics and connectivity topology can change subject to specific ...

**1**

vote

**0**answers

36 views

### boundedness of a sequence $ \in L^{\infty}(I,H^1(M))\cap Lip(I,L^2(M))$ implies that its temporal derivative is bounded as well [on hold]

Hi I have the next claim which I would like to find a proof of it.
I have a sequence of functions $u_\epsilon(t,x) \in H^1(M)$ where $M$ is a compact manifold, and $u_\epsilon \in ...

**7**

votes

**2**answers

165 views

### A moment problem

Suppose $X, Y$ are two positive random variables such that $\mathbb{E}[X^\alpha] = \mathbb{E}[Y^\alpha]$ for all $\alpha \in (0, 1/2)$.
It is also known that the first moment exists for each of them, ...

**-3**

votes

**4**answers

219 views

### Studying topology: which first, algebraic or differential? [on hold]

I have recently studying the basics of topology (ideas in point set, connectedness compactness) and I want to continue my studies but i'm interested in both differential and algebraic topology. which ...

**2**

votes

**0**answers

92 views

### Are all minimal totally separated spaces compact?

Let us call a space $(X,\tau)$ totally separated if for every two distinct points there is a clopen set containing one, but not the other. If for every topology $\sigma\subseteq\tau$ with $\sigma\neq ...

**1**

vote

**1**answer

93 views

### Minimal totally separated spaces

Let us call a space $(X,\tau)$ totally separated (ts) if for every two distinct points there is a clopen set containing one, but not the other. If for every topology $\sigma\subseteq\tau$ with ...

**-1**

votes

**0**answers

32 views

### Is there any theorem which guarantees the existence of an eigenvalue for a non-normal matrix in the vicinity of its perturbed matrix? [on hold]

Let $A=(a_{ij})$ be a non-normal square matrix of order $n$ such that $a_{ji}=1/a_{ij}$ if
$a_{ij}\neq 0$ and $0$ otherwise. If $B$ is the perturbed matrix obtained from $A$ such that $B$ also ...

**1**

vote

**0**answers

48 views

### Why is the polynomial relating the invariants of a binary polyhedral group fixed by an overgroup?

Let $G$ be a finite subgroup of $\mathrm{SL}(2,\mathbb{C})$ and $N \triangleleft G$ a normal subgroup. Let $x, y, z$ be the fundamental invariants for the standard action of $N$ on $\mathbb{C}^2$, ...

**4**

votes

**1**answer

142 views

### A variant of random walk

Standard random walk assumes a sequence of iid RVs $\{X_i\}_{i\geq 0}$ and studied the distribution of $S_n=\sum_{i=0}^n X_i$.
Here, I am wondering whether there is some work on
$T_n=\sum_{i=0}^n ...

**-4**

votes

**0**answers

35 views

### Two easy questions of propositional logic [on hold]

if M1VM2 is unsatisfiable can we say M1|=¬M2;
if M|=ψ then does ¬ψ|=¬Μ;
Please help

**-2**

votes

**0**answers

35 views

### The Gherkin - equation for the curve inoder to calculate the surface area of revolution [on hold]

I am trying to calculate the surface area of revolution for The Gherkin. not sure about how to obtain the equation of the curve but i have the data points that allowed me to graph it in excel but the ...

**2**

votes

**2**answers

260 views

### The free group of a group and the kernel of a canonical morphism

Let $G$ be a group and $F_G$ the free group on the set $G$. Then there exists a canonical surjective morphism ${\rm can}: F_G \to G \to 1$ constructed as follows: let $(e_x)_{x \in G}$ be a copy as a ...

**2**

votes

**0**answers

99 views

### (co)limits in the category of diffeological spaces vs. category of smooth manifolds

I am wondering which (co)limits that exist in the category of smooth manifolds are preserved by the inclusion into the category of diffeological spaces? Are there any results that allow us to ...

**-2**

votes

**0**answers

47 views

### Riemann-Stieltjes integrable? [on hold]

Let f and alpha be functions defined by
$$
f(x) =
\begin{cases}
x & 0 \leq x < 1\\
2x & 1 \leq x \leq 2
\end{cases}
$$
$$
\alpha(x) =
\begin{cases}
1 & 0 \leq x \leq 1\\
2 ...