# All Questions

152,108
questions

0
votes

0
answers

26
views

### What is the Y^n-space? [closed]

What is so special about Y^n-space?
How can you explain Y^n-space to a second-grade student?
Is the concept of a Y^n-space important to quantum mechanics and astronomy?

0
votes

0
answers

49
views

### What is transcendental Cantor set? an example, please? [closed]

What is the transcendental Cantor set? an example, please?
Do transcendental Cantor sets have the same properties as regular ones?
Can we construct a transcendental Cantor function? How?

0
votes

0
answers

16
views

### Names for product-like algebras involving a "duo of directed pseudoforests"

I am looking for the names (and/or for any information regarding) two algebras, one "free" and one "restricted" by an equivalence class.
In both cases, there is an (infix) binary ...

1
vote

1
answer

47
views

### Decompose a function into a bounded part and a Lipschitz part

Let $f: \mathbb R^d \to \mathbb R^d$ be a measurable function such that
$$
\sup_{x,y \in \mathbb R^d} \frac{|f(x) - f(y)|}{\max \{1, |x-y| \}} < \infty.
$$
Are there functions $g,h: \mathbb R^d \...

1
vote

0
answers

27
views

### Question on the geometric lemma in $p$-adic representation theory

$\DeclareMathOperator\GL{GL} \DeclareMathOperator\Sp{Sp} \DeclareMathOperator\Ind{Ind}\DeclareMathOperator\B{B} $
Let $F$ be a $p$-adic field and $\Sp_{2n}$ the symplectic group over a $2n$-...

0
votes

0
answers

19
views

### Estimates on number of observations and iterations depending on number of states, when applying the Baum-Welch algorithm to HMMs

Are there papers estimating how many observations $\mathcal{O}$ and how many random initializations $\ell$ one needs, to get an arbitrary good agreement between the model $\lambda = (\pi,A,B)$ that ...

1
vote

0
answers

11
views

### How to modeling continuous batching in large-scale inference with queuing theory approach?

I want to model continuous batching in large model inference problems, but my knowledge in data theory is insufficient, and I haven't found an appropriate queuing theory model to use for modeling. So, ...

0
votes

1
answer

65
views

### Finding automorphism groups of regular graphs

Can some body help me with some source code for finding automorphism groups of regular maps?. For example: the type of graph is denoted as {p, q}, which means that they are tessellations of the plane ...

1
vote

0
answers

150
views

### Can we cite two pre-prints on Arxiv in one another? [closed]

I have two pre-prints posted on Arxiv. 2nd uses some definitions from first so I cited it. But if a reviewer raises some questions in first which have answer in second, can I cross cite them? Is it ...

2
votes

0
answers

81
views

### A 4th-order linear PDE

I am interested in the following type of 4-th order linear PDE with 2 variables (x, t):
$x^3 f_{xxxt}+ f =0$
Does anyone know if this type of PDE already appeared in the literature? It looks quite ...

-6
votes

0
answers

45
views

### Are Iterative approaches to intricate Number Theory problems, more likely to yield positive results than say divisibility approaches? [closed]

Below please see educational based paper based upon infinite factors of 2, in one of the 3 variables A, B or C.
Please comment on the iterative core SGC1 loop analysis. Relatively easy read.
http:\www....

2
votes

0
answers

36
views

### Generalized Puiseux series for diagonal reflections of the curves $y = \frac{x}{(1-ax)(1-bx)^m}$

Reflection of the curve $y = f_m(x) = \frac{x}{(1-ax)(1-bx)^m}$ through the diagonal line $y=x$ in the $xy$-plane can be regarded as local compositional inversion of the curve $y=f_m(x)$. ($x,y,a,b$ ...

2
votes

0
answers

27
views

### Perturbation method for time-periodic singular system of ODEs

I am studying a problem arising in physics, and I managed to simplify it to a differential system (initial value problem) of the form:
$$
\begin{cases}
\dot{x} = \epsilon f_1(x,y,t) + \epsilon^2 f_2(...

2
votes

0
answers

64
views

### Grassmannian containing tangent variety of a curve

We work over $k=\mathbb{C}$. We consider the
the Grassmanian $G(2,4)$ of lines in $\mathbb P^3$ which we embed
by Plücker into $\mathbb P^5$. It is basic that under this embedding
$G(2,4)$ is ...

3
votes

0
answers

30
views

### Finite dimensional distribution of a stochastic process Lipschitz on every relatively compact set

Let $X_t$ be a Markovian Itô diffusion process, defined by an SDE
\begin{equation}
dX_t = \mu(X_t)dt + \sigma(X_t)dW_t\,.
\end{equation}
Let $f(x,t;x_0,0)$ denote its transition density function. ...

3
votes

1
answer

52
views

### Interpreting a diagram in Borceux-Quinteiro's paper on enriched sheaves

I am somewhat new to working with enriched categories, and have a question about how to interpret Definition 1.2 in Borceux-Quinteiro's paper A theory of enriched sheaves.
The authors consider a ...

-2
votes

0
answers

49
views

### Area and perimeter of a race track [closed]

A dirt track is set up for amateur auto racing. It consists of a rectangle with half circles on the ends. The diameter of the half circles are both 35 yards. The length of the rectangle is 150 yards. ...

2
votes

0
answers

41
views

### How is the $k$-times iterative frame bundle $FF\cdots FM$ associated to the higher order frame bundle $F^k M$?

$\DeclareMathOperator\Gl{Gl}$As I understand it a natural bundle is one for which a diffeomorphism on the base space lifts to an automorphism on the total space of the bundle. It is my understanding ...

5
votes

1
answer

642
views

### Are there mutually independent undecidable statements

In a recursively axiomatized theory such as PA, are there undecidable statements that are arithmetically true but mutually independent (i.e., are there two statements A and B that are each undecidable ...

-1
votes

0
answers

29
views

### Does domination of stochastic processes imply the domination can always be realized by the coupling temporally/incrementally?

Suppose we have two stochastic processes $X=(X_t)_{t\in[0,\infty)}$ and $Y=(Y_t)_{t\in[0,\infty)}$. Assume they have the same state space $S$ with a partial ordering "$\leq$", i.e. for $x,y\...

-1
votes

0
answers

56
views

### Minimal metatheory for Gödel's first incompleteness theorem [duplicate]

When studying the complete proof of Gödel's first incompleteness theorem, I started to harbor a metamathematical worry of circularity. For reference, I am studying the proof in A Concise Introduction ...

1
vote

0
answers

43
views

### Does the local family index theorem hold for compact manifolds with corners?

Let $\pi:X\to B$ be a submersion with closed, oriented and spin fibers of even dimension. Suppose $X$ and $B$ are compact, and let $E\to X$ be a complex vector bundle over with a Hermitian metric $g^E$...

1
vote

0
answers

53
views

### Are coherent modules with integrable log-connections locally free?

Let $X$ be a smooth Noetherian scheme over a field $K$. It is known that every coherent module with integrable connection on $X$ is locally free.
Is the same true for coherent modules with log-...

7
votes

1
answer

357
views

### Powers of $3$ close to powers of $2$

The musical scale of $5$ fifths has good temperament because $3^5$ is quite close to a power of $2$, namely $2^8-3^5=13$, and I suspect that in the subsequent powers of $3$ none is so close to a power ...

3
votes

1
answer

85
views

### Reference request for log-differential forms

I read in a paper of Kato about log-differential forms, that if $X$ is a smooth locally Noetherian log-scheme, and $D$ is a reduced normal crossing divisor, then there is a definition of a sheaf on $X$...

1
vote

1
answer

72
views

### About Čech cohomology in transformation groups

I'm starting a study about theory of transformation groups and equivariant cohomology, in what I read several times that Čech cohomology is the most compatible with this theory, but until now I haven'...

2
votes

2
answers

130
views

### $L^p$ domination of mixed partial derivatives by the unmixed ones?

Is it true that for each real $p\ge1$ there is some real $C_p$ such that for all smooth real-valued functions $u$ compactly supported on $S:=(0,1)^2$ one has
$$\|D_1D_2u\|_p\le C_p(\|D_1^2u\|_p+\|D_2^...

4
votes

0
answers

109
views

### Exponential trigonometric integral

I want to compute the normalization constant of some probability density on SO(3). After some simplification, I arrive at the following double integral:
$$ \tag{1}\label{eq:1}
\int_0^{2 \pi} \int_0^{\...

2
votes

0
answers

28
views

### Explicit example of drift $F$ so that the law of $F+B$ is not absolutely continuous with respect to $B$

Let $\mu_0$ be the law of Brownian motion on the space of continuous functions. If $\mu\sim\mu_0$ agrees on null sets then there is some progressively measurable $F\in W_0^{1,2}$ a.s. so that $\mu$ is ...

1
vote

1
answer

177
views

### On shortest vector problem

Assume we have an oracle which gives the length of the shortest vector in a lattice. Given this oracle can we find the shortest vector in polynomial time?

0
votes

1
answer

222
views

### A basic conjecture/observation on the Riemann $\xi$-function

Based on computations I have made the following mini-conjecture: For any zeta zero $s_0$ with $|s_0|\geq|1-s_0|$ and for $0<\tau<1$ define $M_\tau=|s_0|(1+(1-\tau)^2)$. Let
$\xi$ stand for the ...

1
vote

0
answers

74
views

### Namba forcing, one Cardinal up

The classical Namba forcing collapses $\omega_2$ to have cofinality $\omega$ while preserving the cardinal $\omega_1$. Higher analogs were constructed to (under some additional hypotheses) give a ...

1
vote

1
answer

97
views

### Zeroes of entire function on $\mathbb C^n$

Let $n\ge 2$ be an integer and let $f$ be an entire function on $\mathbb C^n$. Let $A$ be a subset of $\mathbb R^n$ with positive $n$-dimensional Lebesgue measure. Then if $f$ vanishes at $A$, this ...

1
vote

0
answers

36
views

### Infinite radical ideal cubed equals zero for tame hereditary Artin algebras

Let $A$ be a tame hereditary Artin algbera and mod$A$ the category of finitely generated (left) $A$-modules. Further, let rad$_A$ be the radical ideal of mod$A$, which is the smallest ideal containing ...

2
votes

1
answer

89
views

### Example of pseudo $3$-manifold without any shape structure

I'm reading Andersen and Kashaev's A TQFT from quantum Teichmüller theory and the following condition in their definition of admissible oriented triangulated pseudo $3$-manifold confused me:
...

0
votes

0
answers

21
views

### Estimate the gradient (with respect to local coordinates) of a partition of unity on a manifold

Suppose $\{U_\alpha\}$ is an atlas of coordinate patches of a (noncompact) smooth manifold $M$ of dimension $n$, with coordinates $(x_\alpha^1,\dots,x_\alpha^n)$ on $U_\alpha$. Furthermore we assume ...

3
votes

0
answers

80
views

### Representations of $\mathrm{GL}_n(\mathcal{O})$ in functions on Grassmannians

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\Gr{Gr}$Let $\mathbb{F}$ be a non-Archimedean local field. Let $\mathcal{O}$ be its ring of integers.
The natural representation of the group $\GL_n(\...

3
votes

0
answers

93
views

### Is a derived scheme determined by classical + formal points?

Say we have a derived scheme over an algebraically closed field $X/k$, viewed as a functor $X : \operatorname{Aff}_k^{\operatorname{op}} \to \infty\operatorname{-Grpd}$ and we know its formal ...

1
vote

0
answers

37
views

### Fractional powers of Dirichlet-to-Neumann map to derive estimate for PDE

Assume $\Omega$ is an open, bounded subset of $\mathbb R^3$ with smooth boundary $\partial \Omega= \Gamma$. For $u \in
H^{1/2}(\Gamma)$, let $U \in H^1(\Omega)$ denote the weak solution of
the ...

2
votes

0
answers

39
views

### Constructing spaces of analytic sections. Silva spaces

This is a follow up on this question Representing geodesic compactifications of $S^1\times \Bbb R$ as analytic sections over base (analytic) foliations to add more details.
In the linked question I ...

4
votes

1
answer

115
views

### Class numbers in the unramified biquadratic extensions of number fields

Let $K/k$ be an unramified biquadratic extension of number fields (i.e., $\operatorname{Gal}(K/k)\simeq V_4$), and $k_1$, $k_2$ and $k_3$ its three intermediate fields. I know, in general, we can ...

5
votes

0
answers

82
views

### How short can the axioms of propositional logic be?

There are a number of axiom systems for classical propositional calculus. Here, I focus on those which use negation ($\neg$) and implication ($\to$) as the connectives, with Modus Ponens and ...

6
votes

1
answer

170
views

### Is the dual of a Fréchet space weakly* separable?

It is known that if $X$ is a separable Banach space with dual $X^\ast$, then $B_{X^\ast}$, the closed the unit ball in $X^\ast$, is compact and metrizable in the weak* or $\sigma(X^\ast, X)$-...

1
vote

0
answers

40
views

### Etale local systems and proper base change

I am looking for a reference, or a proof, of the following statement:
Let $f:Y\longrightarrow X$ be a smooth proper map of quasiprojective $K$ schemes, and let $\overline{f}:\overline{Y}\...

4
votes

1
answer

114
views

### Infinite sequences/ordered tuples of proper classes in NBG

The question is originally from math stack exchange here.
Basically, what I am asking is if we can define ordered tuples of proper classes in NBG. My idea, for finite tuples of proper classes, was to ...

1
vote

0
answers

40
views

### Are 1-Wasserstein and 2-Wasserstein distances between multivariate normal distributions equivalent?

The $p$-Wasserstein between two measures $\nu_1$ and $\nu_2$ on $X$ is given by
$$W^p_p(\nu_{1},\nu_{2})=\underset{\pi\in\Gamma(\nu_{1},\nu_{2})}{\inf}\int_{\mathbf{\mathcal{X}}^{2}}d(x,y)^p\pi(dx,dy)$...

1
vote

0
answers

103
views

### What is the possible reminders modulo 4 of an "odd part" of a polynomial?

Let $f(x)$ be a polynomial with integer coefficients. Let $f(x) = 2^k \cdot m$ where $m$ is odd. The questions are
What are the possible values of $m \mod 4$ (1, 3 or both)? I want the algorithm ...

0
votes

0
answers

59
views

### Alternative proof of a theorem of Meshulam

A duplicate of this: I am reading the following paper https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=1e3f28b90e3802bc90052cb6ce3cf6b7fd02fa66.
Theorem 1 says: Let $C$ be a ...

2
votes

1
answer

69
views

### Coupling small and large injectivity radii

I'd like to know whether a manifold of constant curvature, which has large injectivity radius at many points, can have points of arbitrary small injectivity radius.
More precisely, for a point $x$ in ...

2
votes

1
answer

135
views

### Are these two norms on localized versions of $L^p_q$ equivalent?

$\newcommand{\RR}{\mathbb R}\newcommand{\diff}{\, \mathrm d}$ We fix $T \in (0, \infty)$ and $p, q \in [1, \infty)$. Let $\mathbb T$ be the interval $[0, T]$.
Let $E$ be the space of all real-valued ...