# All Questions

**0**

votes

**0**answers

45 views

### Variant of Holder's inequality [migrated]

So far I believed that only the reverse Holder inequality holds for $0<p<r<1,$ but then a student pointed out to me that
$$\|x\|_p \le n^{\frac{1}{p}- \frac{1}{r}} \|x\|_r.$$ A few numerical ...

**2**

votes

**0**answers

80 views

### Does attach-one-cell have a stable homotopy transfer?

Specifically, I am thinking of attaching one ordinary cell to an ordinary space in your favourite convenient category of spaces; so, given a cofiber sequence
$$ \mathbb{S}^k \to_c X \to_p X', $$
on ...

**5**

votes

**1**answer

322 views

### Renorming a Banach space to make projections contractive

Let $X$ be a Banach space and $P$ be a projection in $B(X)$. Then $X$ can be renormed so that $P$ has norm $1$.
Can the same be done for a family of projections? That is, given finitely many ...

**1**

vote

**0**answers

41 views

### Combination of certain linear-programming topics new?

Consider the combination of the following topics, aimed at a future book on Linear Programming:
Generalization of certain parts of the polyhedron theory and of the Simplex Algorithm to arbitrary ...

**-4**

votes

**0**answers

70 views

### four consecutive primes ending in 1,3,7, or 9 [on hold]

Examine the last four digits of four consecutive primes to seek 1,3,7,9 in any
order. You will find that they occur more than by chance. Do the same for the
frequency of two, three, four,.......

**10**

votes

**1**answer

249 views

### Polylogarithm sheaves

In many different places, I could find the notion on ''(poly)logarithm sheaves''. As is indicated in the name of it, I guess that it should have something to do with (poly)logarithm function: $\mathrm{...

**6**

votes

**4**answers

451 views

### Speed of convergence in Lebesgue's density theorem

Let $\lambda=\text{unif}([0,1])$ be uniform distribution on $[0,1]$ and $B$ be any Borel set. Lebesgue's density theorem states that for $\lambda$-almost all $x\in[0,1]$ the limit
$$\lim_{\epsilon\...

**9**

votes

**0**answers

102 views

### Existence of flat connections via characteristic classes, for nice groups

I have two questions about what I write below (which honestly seems pretty elementary).
Is it true (more or less)?
Is there a clean reference that I can cite.
Let $G$ be a compact Lie group, $M$ a ...

**0**

votes

**1**answer

48 views

### Bondy and Simonovits Proof for Small Graphs

In their paper, Cycles of Even Length in Graphs (http://renyi.hu/~miki/BondySimEven.pdf), Bondy and Simonovits prove that if a graph $G^n$ has $n$ vertices and at least $100kn^{1+1/k}$ edges then $G^n$...

**3**

votes

**0**answers

50 views

### Criterion for a equalizer to be a homotopy equalizer in spaces

Let $f,g\colon X\rightarrow Y$ be maps between spaces.
I am looking for criteria for the equalizer of $f$ and $g$ to be a homotopy equalizer and I am happy to get answers for whatever model category ...

**4**

votes

**2**answers

189 views

### Exceptional isomorphisms between finite simple Chevalley groups

Steinberg's "Lectures on Chevalley Groups"
https://math.depaul.edu/cdrupies/research/papers/chevalleygroups.pdf
contain ``a complete list of isomorphisms" among the various finite simple Chevalley ...

**4**

votes

**0**answers

73 views

### Cohomology operations on unoriented cobordism

In unoriented cobordism there exist stable cohomology operations looking similar to Steenrod squares (they were used by Quillen to compute the unoriented cobordism ring with its formal group law ...

**3**

votes

**0**answers

162 views

### Representability of the Weil restriction reference and proof

Proposition 2 of 7.6 of Néron Models [BLR] provides a sufficient condition for the representability of a Weil restriction $R_{S'/S}(X')$. The theorem is attributed to Grothendieck.
Is there an ...

**3**

votes

**1**answer

104 views

### Xi Function on Critical Strip - Mellin Transform

Story
I'm trying to prove following identity
$$\int_0^\infty \frac{\Xi(t)}{t^2 + \frac{1}{4}} \cos(xt) dt = \frac{1}{2} \pi (e^{\frac{1}{2}x} - 2e^{-\frac{1}{2}x} \psi(e^{-2x}))$$
where
$$\psi(x)=\...

**0**

votes

**0**answers

29 views

### The connection between the length of Fibonacci $p$-step numbers and it's limit values

One of the most important generalization of the classical Fibonacci numbers is the Fibonacci $p$-step numbers that is defined as follows
\begin{equation}\label{cp26}
F_n^{(p)}=F_{n-1}^{(p)}+F_{n-2}^...

**4**

votes

**1**answer

251 views

### Geometric and arithmetic Frobenius

I read in Serre's "Lectures on $N_X(p)$" that when $X$ is a scheme defined over $\mathbb{F}_q$ (a finite field), the geometric Frobenius $F: X \mapsto X$ is defined by fixing every element of the ...

**1**

vote

**0**answers

11 views

### The isotropy group for the Euler-Lagrange vector-fields

Let $Q$ be a manifold, and let $X_{EL}$ be a second order vector-field on $TQ$ derived from the Euler-Lagrange equation,
$$ \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q} } \right) - \frac{ \...

**0**

votes

**1**answer

80 views

### Is the following set closed with respect to the Hausdorff metric? [on hold]

Let $(X,d)$ be a non-empty complete metric space, let
M be the set of all non-empty compact subsets equipped
with the Hausdorff metric, and $N$ be a positive integer.
Is
$$
\{A\subset X : 1\le \# A \...

**0**

votes

**0**answers

58 views

### why $\varphi''\in L^{2}(R)$ [on hold]

I have the following question: Let $T_{c}$ be an unbounded operator with domain $D(T_{c})=\{u\in L^{2}(R), T_{c}(u)\in L^{2}(R)\}$.
If $\forall \varphi \in \mathcal{C}^{\infty}_{0}(R): \|\varphi''\...

**6**

votes

**1**answer

80 views

### Involutions and Little Adjoint Representations of Simple Algebras

In what follows I'm going to use $V_{\theta_s}$ for the little adjoint representation af a Lie algebra i.e. the representation associated with the highest short rooth $\theta_s$.
Is easy to see that ...

**5**

votes

**0**answers

33 views

### Coarse embeddability into Hilbert space of residually finite groups

By definition a finitely generated group G is coarsely embedded into Hilbert space if there is a function $F: G\to \ell_2$, such that $\|F(g_n)-F(h_n)\|\to\infty$ iff $d(g_n,h_n)\to\infty$, where $d$ ...

**-3**

votes

**0**answers

25 views

### A question about linear operator [on hold]

Let V be a finite-dimensional vector space over field R. Let $A$ be a linear operator on V. And let $A^3$+ $A$ = $0$. Prove that $tr(A) = 0$.

**5**

votes

**2**answers

210 views

### Alternative construction of the first Chern class map

Let $X$ be a compact Kähler manifold. Consider the exponential sequence $0 \to \mathbf Z \to \mathscr O_X \to \mathscr O_X^* \to 0$. The boundary map gives a map $H^1(X, \mathscr O_X^*) \to H^2(X, \...

**6**

votes

**1**answer

152 views

### Can the Hochschild cochain complex be given the structure of a “homotopy BV algebra”?

In a 1993 letter, Deligne posed the following (paraphrased from a paper of Gerstenhaber and Voronov's):
Conjecture (Deligne). The Hochschild cochain complex $CC^*(A)$ of an associative ...

**3**

votes

**1**answer

112 views

### $2M = M$ and its subset

I have some question concerning arithmetic of cardinal in ZF.
Write $ X = Y$ if there is a bijection between them.
Let $M$ be a set such that $2M = M$.
Can I show, in ZF, that any infinite subset $X$ ...

**0**

votes

**1**answer

79 views

### A map between direct limits

Let $C$ be a category which has all small colimits.
I have the following situation:
$\{A_i\}_{i \in I}$ and $\{B_j\}_{j \in J}$ are two directed systems in $C$,
with transition maps $\alpha_{i_1,i_2}...

**5**

votes

**1**answer

204 views

### Why relative consistency results by forcing arguments are provable in finitistic metatheory

It is claimed in many textbooks that relative consistency results, such as $\text{Con}(\text{ZFC})\rightarrow\text{Con}(\text{ZFC}+2^{\aleph_0}\geq\aleph_2)$, are provable in the finitistic metatheory....

**7**

votes

**0**answers

114 views

### Winding number of a random walk on the square lattice before hitting the origin

Let us consider a simple random walk on $\mathbb{Z}^2$ started at $(x,0)$ and killed upon hitting the origin. Define the total winding number $w_x$ around the origin to be the (signed) number of ...

**2**

votes

**0**answers

47 views

+50

### How are Polynomials of Toric ideals Studied with Exponents as ST-cuts?

Topic: Toric ideals on Expected value of Structure Functions in Random Graphs
Goal: to understand the toric ideal where the exponents $h_i$ and $s_j$ are st-vertex-cuts of a digraph
\begin{equation}
...

**3**

votes

**1**answer

42 views

### When is a limit cycle generated by a Hamiltonian oval stable?

Consider a real polynomial $H$ of degree $n+1$ in the plane. A closed, connected component of a level curve $H=t$ is denoted by $\gamma(t)$ and called an oval of $H$. Let $\omega$ be a real 1-form ...

**3**

votes

**1**answer

69 views

### Saturated classes and cofibrantly generated model structures

There seem to be two definitions of what a saturated class should be:
A class of morphisms closed under retracts, pushouts and transfinite composition.
A class of monomorphisms containing all ...

**0**

votes

**1**answer

117 views

### An example of ``all non-torsion rational points on an elliptic curve are integral points''?

For an elliptic curve $E$ over $\mathbb{Q}$, it is well-known that the torsion points on $E$ are integral points.
Then, is it possible that there exists an example whose all of non-torsion rational ...

**0**

votes

**0**answers

65 views

### On semi-complete ring K[X_1,X_2,…,X_∞]] and Popescu theorem

Let $P_n \colon= K[X_1,...,X_n]$ be a $n$-variables polynomial ring. We define 'semi-complete' polynomial ring $P_{\infty}$ by the following$\colon$
$P_{\infty} = K[X_1,...,X_\infty]] \colon = \...

**2**

votes

**1**answer

134 views

### Criteria for the surjectivity of the reduction map of the $SL_n$-group scheme

Let $R$ be a commutative ring and let $I\subseteq R$ be an ideal. We have a natural projection map
$$
\pi:SL_n(R)\rightarrow SL_n(R/I)
$$
(In the original question I had put $GL_n$ instead of $SL_n$ ...

**1**

vote

**0**answers

63 views

### Law of large numbers for random functions?

Is there a version of the law of large numbers for random functions of the type: $h(X_j,\hat{\theta}_n)$, where $X_1,\dots,X_n$ are i.i.d. random variables, with distribution $F$, and $\hat{\theta}_n =...

**-3**

votes

**0**answers

23 views

### calculus question related to derivative of an integral [on hold]

let g be differentiable function at [-1,1], such that g(0) = 0 and g'(0) = 1
does the next limit exists? and if so, what is it?
https://i.imgsafe.org/b9fe48f29b.png
I understand I need to use l'...

**4**

votes

**1**answer

206 views

### Hilbert modular forms twist-equivalent to their conjugates

Let $L / K$ be a solvable (or cyclic) Galois extension of totally real fields, and let $f$ be a Hilbert modular newform over $L$.
Suppose that, for every $\sigma \in Gal(L / K)$, the conjugate ...

**0**

votes

**2**answers

40 views

### Make multiple batches of maximum size, different sized objects

I am a software developer with a rather simple problem. I don't really know how to express it in mathematical terms - I'll just try to write it down:
I have multiple different files... let's say 20 ...

**6**

votes

**1**answer

145 views

### Does every cocompact lattice admit a homomorphism (with infinite image) into a compact Lie group?

Let $\Gamma$ be a cocompact arithmetic lattice in a semisimple algebraic group. Does it admit a homomorphism $\Gamma \to K$ with infinite image into a compact real Lie group $K$?

**2**

votes

**0**answers

75 views

### Decay of the Fourier transform of a surface area measure

Let $\mu$ be a surface area measure of a manifold $M\hookrightarrow\mathbb{R}^{n+1}$. If $M$ is the unit sphere $S^n$, it's known that surprisingly the Fourier transform of $\mu$ decays: $$|\hat\mu(\...

**1**

vote

**0**answers

34 views

### Basis for a set of polynomials in Sage? [on hold]

I have a large set of polynomials in the coordinates $x,y,z$ in Sage, (e.g. $x^5y-3x^2y^2+2xy^3+x^2yz-y^2z$). I want to know, for example, if $x^5y$ is in the span of my set. Is there a Sage command ...

**1**

vote

**0**answers

19 views

### Reference Request: $M_t/M_t/1/K$ queue length distributions

I am investigating functionals defined over sequences of discrete probability distributions related to dynamical/stochastic system performance. As an initial step, I am searching for references that ...

**5**

votes

**1**answer

220 views

### Intuitive descriptions of some large cardinals

I was trying to formulate intuitive descriptions of some large cardinals.
Roughly something equivalent to "A manifold is an object which looks like patches of $R^n$ glued together". Not perfectly ...

**7**

votes

**1**answer

154 views

### Lexicographic distribution of irreducible polynomials

Let $A = {\mathbb F}_2[X]$, though the following can be adapted to $p \neq 2$ too. Order the elements of $A$ lexicographically. Equivalently, take a polynomial such as $P = X^4 + X + 1$, write its ...

**1**

vote

**0**answers

99 views

### Combinatorial splitting in number rings

The goal of this problem is to see if there is a structured way to factor numbers constructed from a set of distinct odd primes $p_1$ through $p_n$ in a number ring.
Take an arbitrary non empty ...