# All Questions

**0**

votes

**0**answers

3 views

### Differentiability of geodesics in Alexandrov subspaces of Riemannian manifolds

Let $M$ be a smooth Riemannian manifold. Let $X\subset M$ be a closed path connected subset which has curvature bounded below in the sense of Alexandrov with respect to the induced intrinsic metric. ...

**0**

votes

**0**answers

15 views

### Decomposable elements in cohomology ring

I feel this must be well known, but I don't have enough knowledge on the matter. So, if there is a literature on this, then please provide a reference.
Let $E$ be a ring spectrum, and $X$ a pointed ...

**1**

vote

**0**answers

28 views

### How many lines of exactly n points can be placed in a discrete, square grid of size m x m?

Per the title, I'm seeking the definition of a function $f(n, m)$ which evaluates to the number of lines made from exactly $n$ points which can be placed on a two-dimensional discrete, square grid of ...

**-7**

votes

**0**answers

14 views

### Student transcripts lost, you can apply for student academic qualifications

business type
Main items:
Diplomas, transcripts, embassy certification, certified by the Ministry of Education, student card - OFFER like.
Transact real embassy notarization (ie, returned overseas ...

**-4**

votes

**0**answers

19 views

### The transpose of a matrix times its transpose is the matrix's transpose times itself [on hold]

Somebody please help me to show the steps to prove this is true:
$R$ is a matrix and T is transpose:
$(R^TR)^T = R^TR^{TT} = R^TR$

**2**

votes

**0**answers

28 views

### Ideals of $L^1(G)$

I want to study closed ideals structure of $L^1(G)$. Is there a good paper or book which it characterized closed ideals and maximal ideals of $L^1(G)$?

**0**

votes

**0**answers

38 views

### An integral form of sum $\sum_{n\geq 0} \frac{f^{(n)}(0) g^{(n)}(0)}{(n!)^2}$ for two real analytic at 0 functions? Fourier|Taylor series parallels

Thinking of parallels between Fourier series and Taylor series, you might find out that the integral $\frac 1 {2 \pi}\int\limits_0^{2 \pi} f(e^{it})\,\overline{g(e^{it})} \,dt=\langle f,\, g\rangle$ ...

**5**

votes

**0**answers

105 views

### Errata on Rezk's paper

I am reading this paper of Rezk's http://arxiv.org/abs/0901.3602 A cartesian presentation of weak n-categories, and as it is pointed out in the introduction, it contained a wrong statement (2.19 in ...

**2**

votes

**0**answers

72 views

### étale cohomology of rings of integers of number fields and Shafarevich-Tate groups

Let $K$ be a number field, $A$ an abelian variety over $K$.
Let $\mathcal{O}$ be the ring of integers of $K$, $\mathcal{A}$ the Néron model abelian scheme of $A$ over $\text{Spec}(\mathcal{O})$.
For ...

**-1**

votes

**0**answers

37 views

### Positivity of holomorphic bisectional curvature and existence of rational curves

Let $X$ be a compact Kähler manifold such that $K_X$ is nef. When
there is no rational curve on $X$?
Motivation: Siu-Yau by the positive bisectional curvature assumption, produced a rational ...

**7**

votes

**0**answers

155 views

### How much mathematics has been formally verified?

That's a vague question so allow me to tighten it up a bit.
I recently noticed that there is a formal machine verified proof of the Central Limit Theorem (CLT) implemented with Isabelle. This ...

**5**

votes

**0**answers

47 views

### Multiplication in universal enveloping algebra in terms of PBW isomorphism

Let $\mathfrak g$ be a Lie algebra. Consider the multiplication map $m:\mathfrak g\otimes U(\mathfrak g)\to U(\mathfrak g)$ and $i:S(\mathfrak g)\to U(\mathfrak g)$ -- Poincare-Birkhoff-Witt ...

**6**

votes

**1**answer

107 views

### Main term in the number of sign changes of $\psi(x) - x$

Define $N_\Delta(T)$ to be the number of sign changes of $\psi(x) - x$ in the interval $[1, T]$.
Landau's Theorem says $N_\Delta(T)$ is $\Omega(\log T)$ [1].
But perhaps that estimate is too crude. ...

**8**

votes

**0**answers

78 views

### Does the ring $R = \mathbb{Z}[X^{\pm1}]$ of Laurent polynomials over $\mathbb{Z}$ satisfy $SL_2(R) = E_2(R)$?

Let $R = \mathbb{Z}[X^{\pm1}]$ be the ring of Laurent polynomials on one indeterminate over $\mathbb{Z}$. Let $E_2(R)$ be the subgroup of $GL_2(R)$ generated by the matrices that differ from the ...

**2**

votes

**0**answers

55 views

### Gaussian Integrals and Pseudo-Anosov Maps

The hep-th section of arXiv if often filled with beautiful semi-rigorous computations on Mathematics. However sometimes it is very difficult to understand what is being stated.
Here I take from: ...

**2**

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**0**answers

28 views

### Is the class of commutative generalized Euclidean rings stable under quotient and localization?

Let $R$ be an associative ring with indentity and let $E_n(R)$ be the subgroup of $GL_n(R)$ generated by matrices obtained from the identity matrix by replacing an off-diagonal entry by some $r∈R$. ...

**2**

votes

**0**answers

72 views

### An elementary question about metrics on the real plane [on hold]

Given the metric $d_p$ on the real plane,
i.e.
$$ d_p(x,y) = d_p((x_1, y_1), (x_2, y_2)) = [|x_1 - x_2|^p+ |y_1 - y_2|^p]^{1/p} $$
for which values of $p$ ($\geq 1$) is it true that the following ...

**1**

vote

**0**answers

47 views

### Irreducible binary quartic form with prescribed $I$ and $J$-invariants

Let $F(x,y) = ax^4 + bx^3y + cx^2y^2 + dxy^3 + ey^4$ be a binary quartic form with integer coefficients. It is well-known that $F$ has two algebraically independent invariants under the action of ...

**0**

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**0**answers

139 views

### Learning roadmap for algebraic number theory

I have read some elementary number theory from David Burton's text and I know groups and rings from Herstein's book Topics in Algebra and some field theory from different sources online. I am ...

**5**

votes

**0**answers

42 views

### What is the precise relationship between primitive Hida families and the connected components of the ordinary locus of the eigencurve?

In the references I've found discussing this question, I have not found any statements that I can understand and that are as precise as I would like. I'm more familiar with Hida families than with the ...

**1**

vote

**0**answers

44 views

### A non-surjective coboundary map induced by a central extension

Let $k$ be a number field and
$$ 1\to A \to B \to C \to 1$$ be a central extension of finite groups over $\mathcal{O}_k$ (the ring of integers of $k$), with $B$ non-commutative. Consider the induced ...

**3**

votes

**0**answers

39 views

### $p$-forms acting on spinors

I'm trying to understand the paper by Atiyah, Hitchin and Singer called: ''Self-duality in four dimensional Riemannian geometry", available here.
I'm stuck at the point where it explains how the ...

**3**

votes

**1**answer

128 views

### Breaking the RSA encryption based on a $(e,N)$ given an integer $w \neq 0$ such that $e^w = 1 \mod(N)$?

In his book 'Forcing with Random Variables and Proof Complexity' Jan Krajíček claims (p.154) that it is possible to break the RSA encryption with public key $(e,N)$ if one has has an integer $w \neq ...

**0**

votes

**0**answers

40 views

### Addition Operations in Complete Lattices

Given a complete bounded lattice $L$, what do we know about the possibility of defining an addition operation $+$ that, broadly speaking, behaves like arithmetical addition? By this, I mean that as ...

**0**

votes

**0**answers

27 views

### Expression for Joint-PDF of Langevin equation?

How to derive exact or approximate analytical expression for time-dependent joint-PDF (velocity-coordinate PDF) for Langevin equations of Brownian motion?
Langevin equations is:
$\dot{x}=v$
...

**-6**

votes

**0**answers

24 views

### Center of Gravity Question [on hold]

What's the value of x?
G is the center of the gravity of this triangle.

**3**

votes

**0**answers

64 views

### Partial formality of A-infinity structure implies formality

Let $A$ be a (finite dimensional, unital, associative) $k$-algebra, where $k$ is a (algebraically closed) field. Let $M$ be a (finite dimensional) $A$-module. Then, it is known that ...

**-4**

votes

**0**answers

36 views

### Prove that OB^2 + PC^2 = OP^2 [on hold]

Suppose you have A,B,C,D four points in harmonic range and O, P are the midpoints of AB and CD respectively. Prove that Prove that $OP^2=PC^2+OB^2.$
I would guess that this is a sort of corollary to ...

**-2**

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**0**answers

39 views

### Ideal of Operators [on hold]

If H is infinite dimensional Hilbert space, $A,B\in B(H)$ and $A+B=1$, then either rang $A$ or rang $B$ contains a subspace with the same dimension as $H$ ? (this is the Lemma 17.3 of A Course in ...

**0**

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**0**answers

42 views

### GI-hard problems that would benefit from efficient algorithm for GI

The exponential time hypothesis (ETH) states that 3SAT can not be solved in subexponential time. As far as I know, it is not known whether an efficient algorithm for graph isomorphism problem (GI) ...

**5**

votes

**0**answers

107 views

### horocycle flow and the prime number theorem

Looking at Zagier's Eisenstein Series and the Riemann Zeta Function, we get a proof of the prime number theorem using horocycles. I would really love it if there were a geometric proof like this.
...

**-2**

votes

**0**answers

66 views

### Turning $\{0<\dots<n\}$ into a measure space [on hold]

I'm looking for references who define interesting (i.e. nontrivial, i.e. not the Borel subsets of the order topology on $\{0<\dots < n\}$, which is discrete) $\sigma$-algebras on finite ...

**4**

votes

**0**answers

86 views

### How can a sequence of functions become a basis of L^2

Let $\{\varphi_n(x)\}_{n=1}^\infty$ be an orthonormal basis of $L^2(\Omega)$, where $\Omega$ is a bounded domain in $\mathbb R^d$ with sufficiently smooth boundary. I want to find the assumption on a ...

**4**

votes

**0**answers

114 views

### A metric on $Homeo([0,1])$

One can define a metric on the set $Homeo([0,1])$ by setting $dist(f,g) =$ measure of support of $f^{-1}g$, that is the measure of the set of points $x$ where $f(x)\ne g(x)$. Was this metric studied ...

**-1**

votes

**1**answer

159 views

### Is there a proof (maybe formulated by Feferman) which says that a proof about the (in)consistency of ZFC is unachievable? [on hold]

Is there a proof (maybe formulated by Feferman) which says that a proof about the (in)consistency of ZFC is unachievable?
A professor said it to me a long time ago, but I don't have any references.
...

**0**

votes

**0**answers

56 views

### $\mathbb{Z}/4\mathbb{Z}$ is indecomposable in the homotopy category of chain complexes of abelian groups [on hold]

I want to understand the accepted answer to this question. The answer is supposed to work for the homotopy category of chain complexes of abelian groups too. (i.e. it shows that that category is not ...

**1**

vote

**0**answers

25 views

### A question about Fourier transform of function of the type $(1+P(x))^{z}$

Let $$f= (1+P(x))^{z},$$
where $P(x)\ge 0$ is a real polynomial in $\mathbb{R}^n$ of degree $2m>0$, and $z=a+ib$ with $a<0$. I want to study the behavior near the origin of the Fourier ...

**0**

votes

**0**answers

34 views

### Dual space of vector fields with null divergence

Let us consider $\mathscr D(\mathbb R^3;\mathbb R^3)$ the space of smooth compactly supported vector fields in $\mathbb R^3$ and let us define
$\widetilde{\mathscr D}=\mathscr D(\mathbb R^3;\mathbb ...

**5**

votes

**0**answers

122 views

### Is there an explicit construction of Tate-Beilinson residue?

Background: Tate's construction of abstract residues is generalized in Beilinson's constructon as follows:
Let $E$ be a unital, cubically decomposed $k$-algebra, i.e., (a) there are two sided ideals ...

**0**

votes

**0**answers

35 views

### Explicit solution of recursive function for $F(n,a)=F(n-1,a)+F(n-(1+a),a), F(b,a)=1, b={1,2,3…,a+1}$ [on hold]

For the most common cases, $a=0$ and $a=1$, the explicit solutions are generally known as:
$$F(n,0)=2^{n-1}$$
$$F(n,1)=\dfrac{\phi^n-(-\phi)^{-n}}{\sqrt{5}}$$
Is it possible to derive similar ...

**3**

votes

**1**answer

199 views

### Irreducible polynomial $p_{n}(x)=\sum_{k=0}^{n}\dfrac{x^k}{k!}$ for all positive integers $n$

Let $n$ be a positive integer greater than $1$, and define the polynomial $$p_{n}(x)=\sum_{k=0}^{n}\dfrac{x^k}{k!}$$
Is $p_{n}(x)$ irreducible in $\mathbf{Q}[x]$?
I can show it when $n$ is a ...

**5**

votes

**1**answer

126 views

### Regular minimal model of $X_0(p^2)$

Consider the compactified modular curve $X_0(p^2)$ and the corresponding algebraic curve over $\mathbb{Q}$. My questions are the following:
Where do the cusps of $X_0(p^2)_{\mathbb{Q}}$ live? That ...

**1**

vote

**1**answer

85 views

### Basis for the Orlicz Space

Does the Orlicz space (https://en.wikipedia.org/wiki/Birnbaum-Orlicz_space) has unconditional Schauder basis? Can we find such a orthonormal basis like the Hermitian polynomials in $L^2$?

**3**

votes

**3**answers

133 views

### A question about intuition of fluid limit in queuing system

This is a question about intuition in understanding the fluid limit queuing system.
Assume we have a sequence of queuing systems $\{S^N\}_{N=1}^{\infty}$ with N servers and each server has unit ...

**12**

votes

**2**answers

390 views

### 1-st cohomology of multiplicative group in a vector space

Let $\mathbb k$ be a field of characteristic $p$ and let $\mathbb k_n$ be a 1-dimensional representation of $\mathbb k^\times$, where the action is given by $t\circ v= t^n v$. Is it known what are the ...

**0**

votes

**0**answers

139 views

### exactness of induction functor [on hold]

I am studying induction functor of algebraic groups. In particular, let $G$ be a reductive group scheme defined over an algebraically closed field $k$ of prime characteristic and $T$ a maximal torus ...

**3**

votes

**0**answers

168 views

### the origin of the differential of Spectral Sequence? [on hold]

I'm wondering why the differential in homological Spectral Sequences $(E^*_{p,q},d^r)$ is defined as;
$d^r_{p,q}: E^{r}_{p,q} \rightarrow E^{r}_{p-r,q+r-1}$ .
From Weibel's homological algebra(p122), ...

**-3**

votes

**0**answers

77 views

### Finding Bijection between Permutation Set [on hold]

$\beta$ is a subset of symmetric group $S_n$ which acts on $n$ elements of set $X$. Permutations of
$\beta$ acts on $k $ elements of $X$ only.
Set $L$ is a set of $n$ labels which labels ...

**3**

votes

**0**answers

49 views

### Lattice points in regular simplex

Suppose we are given a regular (closed) simplex $S$ in a vector space $V$ of dimension $n$, whose vertices have integer values. Then for a lattice $L$, is there a sufficient criterion, for $S$ to ...

**10**

votes

**2**answers

657 views

### Witness to a failure of Fubini/Tonelli

Is it provable in ZFC that there is a subset of the plane all of whose vertical cross sections have Lebesgue measure zero and all of whose horizontal cross sections are complements of sets of Lebesgue ...