All Questions
150,236
questions
4
votes
0
answers
105
views
When does an iteration not add functions $\eta\to V$ at the final stage?
I am interested in better understanding the following property:
Let us say that an iteration of forcings $\langle\mathbb{P}_\alpha,\dot{\mathbb{Q}}_\beta\mid\alpha\leq\gamma,\beta<\gamma\rangle$ is ...
- 1,159
-4
votes
0
answers
31
views
Calculation problem for Fixing small box in big box [closed]
I have received 26 small boxes in big box with following dementions.
Each small box: 32.5 X 25 X 6.5
Big box: 65 X 50 X 53
All small boxes are well accomudated in big box but when i do the mathemetic ...
2
votes
1
answer
232
views
Simple proof for convexity of a real valued matrix function
I am looking for a simple and short proof showing that $X \to \|X X^\top\|_F^2$ is a convex function where $\|\cdot\|_F$ is the Frobenius norm. I have one proof by showing that the derivative is ...
- 395
4
votes
1
answer
358
views
Inequality of inclusion-exclusion term
This question was initially posted on math.stackexchange.com but did not receive any answers for half a week.
While analyzing the properties of an algorithm I am working on (I'm a computer scientist), ...
- 45
5
votes
1
answer
189
views
Modularity of the Drinfeld center of the category of G-graded vector spaces
Background: Let $G$ be a finite group, and $\mathrm{Vect}_G$ be the category of finite dimensional $G$-graded vector spaces over some algebraically closed field $k$ of char 0. It is well-known that $\...
- 53
1
vote
1
answer
69
views
Existence of a strongly regular vertex ordering on cubic graphs
Definition: Let $G=(V,E)$ be a cubic (i.e. $3$-regular) graph, and $<$ a total order on $V$. For $v\in V$ let $v^\downarrow$ denote the set of nodes $w\in V$ such that $w<v$, and let $\alpha(v) =...
- 191
3
votes
0
answers
51
views
Are two homotopic principal bundles isomorphic?
Let $E_1 \to B$ and $E_2 \to B$ be two principal $G$-bundles, where $E_1$ and $E_2$ are two simply-connected manifolds and $G$ is a compact Lie group.
Suppose there exists a $G$-equivariant continuous ...
- 687
0
votes
1
answer
272
views
How did Ramanujan come up with the Ramanujan summation and is it possible to extend it to higher number sets
How did Ramanujan come up with the Ramanujan summation and is it possible to extend it to higher sets (Everything circled in red is what I'm interested in (+ the Cauchy integral to make it Dedekind ...
- 11
4
votes
1
answer
160
views
Does a complex-oriented $E_1$ ring spectrum (not assumed to have graded-commutative homotopy groups) receive a map from $MU$?
It's well-known that complex cobordism $MU^\ast$ is universal among complex-oriented associative, graded-commutative cohomology theories $E$. This means that if $E$ is a multiplicative cohomology ...
- 58.7k
2
votes
0
answers
79
views
Self adjoint operators from energy functionals
It is known that the equation
$$
\Delta f = 0
$$
on some bounded domain $\Omega$ on $\mathbb{R}^n$ subjected to certain boundary conditions can be derived through the minimization of the Dirichlet ...
- 101
0
votes
0
answers
57
views
Meromorphic functions converging in measure
Let $f_1, f_2, \ldots$, and $g$ be measurable complex-valued functions on the open unit disk. We say that the sequence $f_1, f_2, \ldots$ converges in measure to $g$ if, for all $\epsilon, \mu >0$, ...
- 944
3
votes
1
answer
125
views
Does every graph admit an embedding such that identically-colored edges do not cross?
Given a graph, is it always possible to color the edges of the graph using two colors such that there exists an embedding of the graph in the plane where only opposite-colored edges cross?
Simple ...
- 133
3
votes
2
answers
150
views
Does $\mathsf{ZF}$ prove $\operatorname{Col}(\lambda,\kappa)$ preserves cardinals below $\lambda$?
Let $\lambda<\kappa$ be cardinals and consider the forcing $\operatorname{Col}(\lambda,\kappa)$ adding a generic surjection $\lambda\to\kappa$. More formally, $\operatorname{Col}(\lambda,\kappa)$ ...
- 2,462
14
votes
1
answer
895
views
Recognizing free groups
While I’m aware (and as it was pointed out in the comments) it is generally undecidable whether a given presentation represents a free group, I’m interested in criteria that nevertheless ensure that ...
- 1,055
-3
votes
0
answers
42
views
convergence of a numerical series using information about an entire series [migrated]
I'm on a problem that seems simple but turns out to be a bit twisted.
Let be $\sum_{n\epsilon N }^{}{u_nz^n}$ a power series with radius of convergence ρ = 1. Which of the following statements are ...
- 1
0
votes
1
answer
82
views
An example of module which is square-free, CS, NOT C3, and NOT nonsingular
Let $M$ be a right $R$-module ($R$ has unity). Recall that $M$ is called square-free if $M$ does not contain two nonzero isomorphic submodules with zero intersection. $M$ is called CS if every ...
- 175
2
votes
1
answer
180
views
Expected norm of a product of Gaussian matrices
Suppose $C_n$ is a product of $n$ $d\times d$ matrices with IID entries coming from standard normal. The following appears to be true. Is there an elementary proof?
$$E[\|C_n\|_F^2]=d^{n+1}$$
This ...
- 2,330
2
votes
0
answers
115
views
Do the nearby cycle and Beilinson's vanishing cycle functors commute?
Let $X$ be a complex algebraic variety with a pair of regular functions $f_1,f_2$. To these functions we can associate various functors: the nearby cycles functor $\Psi_{f_i}$, the vanishing cycles ...
- 961
2
votes
1
answer
157
views
Is this theorem true in the case of a general measure space?
I'd would like to confirm if the following proposition is indeed true in the case of an arbitrary measure space.
Theorem: Let $(X,\Sigma,\mu)$ be a measure space and $\{f_n\}_{n\in\mathbb{N}}\...
- 453
2
votes
0
answers
111
views
Existence of a hyper plane
I am very new to algebraic geometry, and self-studying varieties. I have the following question.
Suppose $Y$ is a variety of dimension $r$ and degree $d>1$ in $\mathbb{P}^n$. Let $P$ be a ...
- 321
-1
votes
0
answers
52
views
Prove that this equation for natural m and n doesnt have an answer [closed]
$19^(19)=m^3 + n^4$
from $19^(19)$ i mean 19 to the power of 19
i've tried m and n for mod k, k=1,2,...,11 but i haven't reached a solution
- 1
6
votes
2
answers
612
views
A conceptual proof that bounded index subgroups of a bounded torsion abelian group contain bounded index complemented subgroups
Call an abelian group $G = (G,+)$ $m$-torsion for some natural number $m$ if one has $m \cdot x = 0$ for all $x \in G$. A subgroup $H$ of $G$ is said to be complemented if one can write $G = H \oplus ...
- 106k
12
votes
1
answer
324
views
How exactly are realizability and the Curry-Howard correspondence related?
Consider, on the one hand:
the Curry-Howard correspondence between, on the one hand, types and terms (programs) in various flavors of typed $\lambda$-calculus, and on the other, propositions and ...
- 28.4k
0
votes
0
answers
40
views
The discrete orthogonal polynomials
I want a document or something that explains the following proposition:
The discrete orthogonal polynomials are the polynomial solutions of the given diference equation:
$$
\sigma(x)\Delta\nabla P_n(...
- 21
-4
votes
0
answers
52
views
Power summing function [closed]
f(x,p)=sum(n=1,n<=x,n^p) where p and x are integers. f(x,1)=(x^2+x)/2, and f(x,2)=x(x+1)(2x+1)/6, but what is f(x,p), where p is VERY BIG?
2
votes
1
answer
136
views
On spectral calculus and commutation of operators
Let $\mathcal{H}$ be a Hilbert space, $B\in\mathcal{B}(\mathcal{H})$ be bounded and self-adjoint and $A:\mathcal{D}(A)\to\mathcal{H}$ closed (but not necessarily self-adjoint or bounded). The ...
- 833
1
vote
0
answers
143
views
Deformations over $A_{\inf}$
Setup:
Let $K$ be a perfectoid field of characteristic $0$ with tilt $K^{\flat}$.
Let $A_{\inf}=W(\mathcal{O}_{K^{\flat}})$ be the infinitesimal period ring.
Let $\mathcal{X}$ be a flat, projective $\...
- 282
2
votes
0
answers
50
views
Can the Weyl algebra be free over its invariant subalgebra?
Let $k$ be an algebraically closed field of zero characteristic, let $P_n$ denote the polynomial algebra in $n$ indeterminates, and let $G$ be a finite group of linear automorphisms. Then, by ...
- 2,525
14
votes
1
answer
629
views
Euler's proof of $\frac{\pi}{6}=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\cdots$
Euler proved
$$\frac{\pi}{6}=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\cdots$$
where the reasoning of the signs thus is prepared, so that of the second may be had as $-$, prime ...
- 303
-1
votes
1
answer
92
views
How to prove that increasing the number of constant symbols of a first-order logic by the number of formulas keeps the number of formulas the same [closed]
Let $S$ be a set of theory symbols for a first-order logic, and let $C$ be a set of constant symbols in $S$ such that $|C| = |L(S)|$, where $L(S)$ is the set of all formulas generated by $S$ in the ...
- 3
-1
votes
0
answers
23
views
Vertex expansion or vertex isoperimetric number of the cartesian product of cycles [closed]
Vertex expansion or vertex isoperimetric number of the cartesian product of cycles when all cycles are the same, C_m.
Exact value or any upper or lower bound?
- 1
2
votes
0
answers
172
views
Are there integers $x,y,z$ such that $1 + x - x^3 + x^2 y^2 + z + z^2 = 0$?
In my previous question Can you solve the listed smallest open Diophantine equations? I discuss the smallest equations (in some well-defined sense) for which it is not known whether they have any ...
- 4,813
1
vote
1
answer
116
views
Is this constraint convex?
I have an optimization problem where the following constraint causes DCP Rule Error.
$$e^{x_n} \leq B \log _2\left(1+\frac{e^{\rho_n} g_n^2}{\sum_{i=1}^{n-1} \exp \...
- 11
4
votes
0
answers
55
views
Pfaffian elements and anomalies
If $X$ is a compact even dimensional spin manifold, then we have a family of chiral Dirac operators parametrized by $Met(X)$, the (infinite dimensional) manifold of Riemannian metrics on $X$. This is ...
- 6,679
-1
votes
0
answers
50
views
Measuring to exact decimal places with ruler and compass exclusively [closed]
Do you know any way to construct a segment given its length in decimals, using only a ruler and compass, in an exact way?
For example:
a) 0.54896753
b) 12 decimals of acos(20°)
1
vote
0
answers
78
views
Orthogonal representation of free products of two groups
Suppose $A$ and $B$ are two countable, discrete, amenable groups. One definition of amenability tells us that there is a sequence of finitely supported, positive definite functions that converges to 1 ...
- 131
0
votes
0
answers
134
views
Research directions related to the Hilbert-Smith conjecture
The Hilbert-Smith Conjecture (HSC) is a famous open problem in geometric group theory stating "for every prime $p$ there are no faithful continuous action of the $p$-adic group of integers $A_p$ ...
- 121
6
votes
1
answer
328
views
When are the chirp signals orthogonal?
Assume that we have two bounded-time chirp signals,
\begin{align}
x(t)&=\exp\Big(j\pi(\alpha t^2+\beta t+\gamma)\Big),\quad 0\leq t\leq T,\\
y(t)&=\exp\Big(j\pi(\alpha' t^2+\beta' t+\gamma')\...
- 261
0
votes
0
answers
130
views
Proof that a specific cubic equation has three real roots [migrated]
I'm trying to prove that the cubic equation
$a_3 \lambda^{3} + a_2 \lambda^{2} + a_1 \lambda + a_0 = 0$
has three real roots. The coefficients are
$a_3 = - 1 - \sigma - \tau - \chi$
$a_2 = -2 (\sigma +...
0
votes
0
answers
33
views
Amenability of $\textrm{w}_0(A)$ for a $C^*$-algebra $A$
Let $A$ be a $C^*$-algebra with only finite dimensional irreducible representations. As in a previous question, let $\textrm{w}_0(A)$ denote the subspace of $\ell^{\infty}(A)$ consisting of all weakly ...
- 2,118
2
votes
0
answers
24
views
Is anything known about the equivariant homotopy theory of surfaces with the action of a finite subgroup of the mapping class group?
The Nielson realization theorem for a surface says that every finite subgroup of the mapping class group is realized by a finite subgroup of homeomorphisms on the surface. Furthermore, for a genus $g \...
- 51
-1
votes
0
answers
43
views
Measurable Function and Inverse Maps [migrated]
Every text I read about random variables starts by introducing the concept of measurable functions. It goes something like this:
Suppose you have 2 measurable spaces $(\Omega, \Gamma)$ and $(\Omega', \...
- 1
4
votes
0
answers
231
views
Does there exist research about equation like $u_{tt}=\det(D_{x}^{2}u)+\dots$?
I have asked this question on Mathematics Stack Exchange yesterday, but there still is no reply.
Does there exist research about equation like $$u_{tt}=\det(D_x^2 u)+\cdots\text{?}$$ That is to say, ...
0
votes
0
answers
46
views
Primal optimal attained implies dual optimal attained
Given some optimization problem $\min_{x \in S \subset \mathbb{R}^n} f_0(x)$ $\text{s.t.}$ $f_i(x) \leq 0, 1\leq i\leq m$. We can find the dual problem $\max_{\lambda\in\mathbb{R}^m} g(\lambda)$ $\...
- 123
3
votes
0
answers
33
views
When does Morita equivalence between two Hopf-von Neumann algebras imply also equivalence of their categories of comodules?
Let $A$ and $B$ be two Hopf-von Neumann (bi)algebras. Furthermore, let us assume that we know that they are Morita equivalent as von Neumann algebras (i.e. their categories of appropriate ...
- 31
2
votes
0
answers
50
views
Exponential of Liouville Numbers
By Mahler classification of Transcendental real numbers (into the sets of $S$-, $T$- and $U$-numbers), we know that
Any Liouville number is a $U$-number.
$\log \alpha$ is either an $S$- or a $T$-...
- 505
2
votes
0
answers
62
views
Complemented C* Algebras
let $A$ and $B$ be unital separable commutative $C^*$ algebras, with $A\subset B$. Is it true that $A$ is complemented in $B$?
- 151
2
votes
0
answers
65
views
How to define the Sobolev quotient space $H^s(Γ)/{\mathbb R}$
Let $\Gamma$ be the boundary of a Lipschitz domain $\Omega\subset \mathbb R^3$. Denote by $H^s(\Gamma)$ the usual scalar Sobolev space for $s\in\mathbb R$. I want to know the definition of the ...
- 63
5
votes
1
answer
250
views
Does the oriental inject into the cube?
For every $n \geq 0$ there is an inclusion of the ordered set $\{0<1<\dots<n\}$ into the product
$\{0<1\}^{\times n}$ sending $i$ to the increasing sequence $(0 < \dots<0<1<\...
- 421
2
votes
0
answers
59
views
Can the set of parafinite congruences be descriptive-set-theoretically complicated?
Fix an algebra $\mathfrak{A}$ with underlying set $\mathbb{N}$ and finite language $\Sigma$. The set of congruences on $\mathfrak{A}$ is a closed subset $C_\mathfrak{A}$ of $2^\mathbb{N}$ (with the ...
- 19.1k