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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?
user523904's user avatar
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?
user523904's user avatar
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 ...
user1661473's user avatar
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 \...
Akira's user avatar
  • 667
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 $2n$-...
Andrew's user avatar
  • 835
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 ...
Ben123's user avatar
  • 143
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, ...
oleotiger's user avatar
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 ...
Zahid Malik's user avatar
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 ...
user523880's user avatar
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 ...
Math2024's user avatar
-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....
D. Ross Randolph's user avatar
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 $y=f_m(x)$. ($x,y,a,b$ ...
Tom Copeland's user avatar
  • 9,817
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(...
squille's user avatar
  • 121
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 ...
JackYo's user avatar
  • 541
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. ...
Luís Ferreira's user avatar
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 ...
memento morison's user avatar
-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. ...
Mathidiot's user avatar
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 ...
R. Rankin's user avatar
  • 230
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 ...
Jacques Sentier's user avatar
-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\...
jdods's user avatar
  • 213
-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 ...
God bless's user avatar
  • 107
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 $g^E$...
Ho Man-Ho's user avatar
  • 1,087
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-...
kindasorta's user avatar
  • 1,167
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 ...
Juan A. Navarro's user avatar
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 $X$...
kindasorta's user avatar
  • 1,167
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'...
Ludwik's user avatar
  • 235
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^...
Iosif Pinelis's user avatar
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^{\...
Peter Johnson's user avatar
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 ...
user479223's user avatar
  • 1,247
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?
Turbo's user avatar
  • 13.6k
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 ...
Alexis's user avatar
  • 31
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 ...
Hannes Jakob's user avatar
  • 1,500
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 ...
Bazin's user avatar
  • 15k
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 ...
kevkev1695's user avatar
  • 1,013
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: ...
Shana's user avatar
  • 235
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 ...
Anar C's user avatar
  • 21
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(\...
asv's user avatar
  • 20.9k
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 ...
E. KOW's user avatar
  • 732
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 ...
BBB's user avatar
  • 21
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 ...
53Demonslayer's user avatar
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 ...
ayoub-chess's user avatar
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 ...
Joel's user avatar
  • 51
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 $\sigma(X^\ast, X)$-...
Liviu Nicolaescu's user avatar
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}\...
kindasorta's user avatar
  • 1,167
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 ...
Shthephathord23's user avatar
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)$...
Vladimir Zolotov's user avatar
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 ...
Denis Shatrov's user avatar
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 ...
JBuck's user avatar
  • 173
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 ...
Nandor's user avatar
  • 247
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 ...
Akira's user avatar
  • 667

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