0
votes
0answers
27 views

How to put together a set of modified conditional distributions to a joint distribution? [on hold]

I am abstracting my original problem to a simple scenario.Consider a bi-variate multi-modal mixture of gaussian distribution, P(x,y). When we slice through x or y we get a univariate multi-modal ...
3
votes
0answers
142 views

Quasi-disjoint subsets of an infinite set and $\neg \mathsf{AC}$

Is it consistent with $\mathsf{ZF}$ (without $\mathsf{AC}$) that there is an infinite set $X$ and a subset $S\subseteq\mathcal P(X)$ of the same cardinality as $\mathcal P(X)$ with the property that ...
0
votes
0answers
38 views

A Problem on Fixed Point Theory [on hold]

Let $T:\mathbb{R}\rightarrow\mathbb{R}$ be a function satisfying the following conditions: (a) $T$ is continuous, (b) $T(n)=2015n+1$, $\forall{n}\in\mathbb{Z}$, and (c) $|T(x)-T(y)|\geq 2015|x-y|, ...
4
votes
0answers
67 views

When does the canonical model structure on $\mathcal V$-$\mathbf{Cat}$ give a structure of monoidal model category?

Let $\mathcal V$ be a closed symmetric monoidal model category. It is well known that the category $\mathcal V$-$\mathbf{Cat}$ of $\mathcal V$-enriched categories is itself a closed symmetric monoidal ...
1
vote
0answers
135 views

Primes in integral domains

Let $\mathcal O_{\mathbb K}$ be the ring of integers in a number field $\mathbb K$. It is easy to prove that the number of (non-associated) primes in $\mathcal O_{\mathbb K}$ is infinite. On the other ...
1
vote
0answers
42 views

how to find coordinate of unknown point given the distance against N known points [migrated]

I am meeting with a problem, say I have already know the coordinates of N points (a1,a2,a3....) in 3D space. And I have a new point, say x. I only know the distances from x to the known N points. Is ...
6
votes
2answers
622 views

Publication in proceedings

Why and how publishing a paper in proceedings? What are the difference with a "classical" journal? What's the list of the main proceedings in which one can publish? Do proceedings papers (never, ...
1
vote
0answers
129 views

How rigid can a rigid object be in GR?

Consider a cubic lattice of space probes, with rocket motors and lasers to measure distance, and a clock to measure time. As they more from free space to the vicinity of some black hole, they try to ...
4
votes
0answers
95 views

Infinite simple p-groups with only trivial irreps in characteristic p

Is there a prime $p$ and an infinite simple $p$-group $G$ such that for any field $K$ of characteristic $p$ the only irreducible $KG$-module, whether finite or infinite dimensional, is trivial (that ...
1
vote
0answers
96 views

Characterization of the Riemann curvature tensor

Let $(M^n,g)$ be a Riemannian manifold, $a\in M$ be a fixed point. It it well known that there exists a coordinate system near $a$ (e.g. the normal one) such that $$g_{ij}(x)=\delta_{ij}+O(|x|^2).$$ ...
2
votes
1answer
64 views

Relationship of clique, independence, and chromatic numbers

For any graph $G=(V,E)$ let $\bar{G}$ be the complement graph. Is $$\text{inf}\big\{\frac{\omega(G)+\omega(\bar{G})}{\chi(G)} : G \text{ is a finite graph}\big\}$$ known? If not, what lower bounds are ...
0
votes
0answers
15 views

Probe permutationally matrix extreme properties-II

Call $S_{r}$, collection of $0/1$ matrices of rank atmost $r$ that increase rank if any $1$ is changed to $0$. Given $M\in\{0,1\}^{n\times n}$ of rank $r$, what is probability that $M$ could be ...
1
vote
0answers
71 views

Strichartz estimates for the wave equation

Strichartz estimates for the wave equation $\Box u=F $ with $u(0)=g_0$ and $\partial_t g(0)=g_1$ can be stated as $$\Vert u\Vert_{L^q_tL^r_x}+\Vert u\Vert_{C^0_t\dot{H}_x^s}+\Vert\partial_t ...
1
vote
1answer
145 views

Zeta functions versus Cramer's conjecture

A mathematics professor today asked me if Cramer's conjecture on prime gaps has anything to do with Riemann Zeta function. I did not know but my guess was somehow Cramer's conjecture captures local ...
7
votes
2answers
205 views

Definition of internal field objects

Let $\mathcal{C}$ be a category with finite limits and a strictly initial object $\mathbf{0}$. The final object is denoted by $\mathbf{1}$. I propose the following definition of a field object ...
3
votes
1answer
142 views

For a cross section $\sigma\colon G/N\to G$, how is $\sigma(y)^{-1}\sigma(x)^{-1}\sigma(xy)$ called?

Let $G$ be a locally compact group, let $N$ be a closed normal subgroup of $G$, and let $\sigma\colon G/N\to G$ be a cross section. Let us define $\alpha\colon G/N\times G/N \to N$ by the formula $$ ...
3
votes
2answers
73 views

regular polyhedra (and polytopes) in hyperbolic geometry, and generalisations

While there exist regular tesselations of the hyperbolic plane with arbitrary regular polygons, there are no new regular polyhedra in hyperbolic (3D) space. This being quite trivial, it is probably ...
1
vote
0answers
35 views

Isolated singularities of harmonic mappings

Can a homeomorphic harmonic mapping $f=(u,v,w):\Omega\to \Omega'$ have isolated singular points. Here $\Delta f =0$, and singular point is a point with zero Jacobian. This will extend Lewy theorem for ...
2
votes
0answers
135 views

A lower-dimensional algebraic topology problem between homology group and fundamental group

Let \begin{equation} A\stackrel{\alpha}{\longrightarrow}B\stackrel{\beta}{\longrightarrow}C\quad\quad (1) \end{equation} be a short sequence of abelian groups and homomorphisms. We say that the ...
11
votes
2answers
1k views

Do the real numbers “know” that they are countable in a larger model?

(This was first posted to math.stackexchange but had no answers there after several days): Let ${\mathbb R}$ be the set of real numbers in whatever is your favorite model of $ZFC$. Then (by Levy ...
0
votes
0answers
13 views

Whats the difference between math.SE and mathoverflow? [migrated]

i wanted to know that : Whats the difference between math.SE and mathoverflow ? Are they of SE community or different ?
-3
votes
0answers
38 views

How to solve this using trig idenities [on hold]

(sin(x) + sin(-x))(cos(x) + cos(-x)) I am confused how you get 0 for the answer, can someone explain how my book go to that answer. Like the steps you did. Thanks :)
-1
votes
0answers
43 views

Zeros of a Real Analytic Function [on hold]

Let $f:[0,1] \rightarrow \mathbb{R}$ be a non-zero real analytic function. Consider $Z(f) \subseteq [0,1]$ as the set where $f$ vanishes. What can we say about $Z(f)$? This is (i) finite, (ii) ...
0
votes
0answers
29 views

Journals on stochastic approximation/control theory [on hold]

What are some good journals on stochastic approximation/control theory? Thanks
2
votes
0answers
49 views

Uniqueness of solution of elliptic equation with exponential nonlinearity

Consider the following equation $$\Delta v + p(r)e^v = 0$$ on $\mathbb{R}^n$ where $p(r)$ is a polynomial in $r = |(x_1,..., x_n)|$. I want to understand when equations like these have unique ...
1
vote
0answers
83 views

Does the ring of invariants inherit normality?

Let $A$ be a normal ring (in the sense that its localizations at prime ideals are normal domains), and suppose that a finite group $G$ acts on $A$ by ring automorphisms. Form the subring $A^G \subset ...
3
votes
2answers
215 views

Etale local fibrations in the Grothendieck ring of varieties

Let $k$ be a field and $K_0(Var_k)$ the Grothendieck ring of varieties over $k$. This is the ring generated by isomorphism classes of varieties over $k$ with multiplication given by $$ [X \times_k Y] ...
0
votes
0answers
15 views

Finding the bound of a mixture model percentile [on hold]

I could do with some help on the following issue. I'm trying to obtain $\alpha$ from: $\beta = \int_{\alpha}^{\infty} \sum_{i=1}^{n} p_i f_i(x) dx$ I have that: $0 \leq p_i \leq 1$, $\sum_{i=1}^{n} ...
2
votes
0answers
58 views

degenerate points in the moduli space of flat principal $G$-bundle with respect to a linear representation on a complex

Let $(A^\bullet,\partial)$ be a complexe of $\mathbb{C}$-vector spaces. We suppose that this complex is of finite length, and all $A^\bullet$ are finite dimensional. Let $H^\bullet$ be the cohomology ...
1
vote
0answers
33 views

Select n vectors from k vectors (in 3D) such that each component of the resultant vector >= each component of a given vector M

this was left unanswered for 1 week on MStackExchange, so I thought MOverflow would be more appropriate. Thanks :) Let $R = (R_x, R_y, R_z)$ be the resultant vector of the n vectors and $M = (M_x, ...
0
votes
1answer
81 views

generalization of highest weight theorem for semisimple lie algebras

Let $\mathfrak g$ be a real semisimple Lie algebra (without compact factors) with Iwasawa decomposition $\mathfrak g=\mathfrak k\oplus \mathfrak a\oplus \mathfrak u$. Let $\mathfrak p$ be a ...
6
votes
0answers
56 views

Vanishing of Dolbeault cohomologies and Steinness

That Stein manifolds have all $(p,q), p \geq 0, q \geq 1$ vanishing Dolbeault cohomology groups is more or less standard. I am a little bit confused about the reverse implication: whether the ...
1
vote
2answers
69 views

Ascending chain condition on radical ideals

There is a basic theorem in the geometry of schemes saying that the Spec of a Noetherian ring is a Noetherian topological space. It can be formulated as the ACC condition implies the ACCR condition ...
4
votes
0answers
146 views

Is there a citeable reference for star-shaped open subsets of R^n being diffeomorphic to R^n?

A folk theorem says that star-shaped open subsets of R^n are diffeomorphic to R^n. Is there a citeable reference for this result? For the sake of being definite, let's say that “citeable” means ...
1
vote
1answer
42 views

Division methods for divergent continued fractions

I hadn't even noticed before entering the subject above the parellel with the title of an earlier question posted here titled Summation methods for divergent series. And it's just mutatis mutandis as ...
3
votes
0answers
100 views

Frequency of a representation of SO(3)

When generalizing the basic tenets of Fourier Theory to the symmetric group $S_n$, we can define a notion of the frequency of a basis function (i.e. an irreducible representation of $S_n$). In ...
5
votes
2answers
164 views

A balls and urns model for a hashing problem

Fix $N \in \mathbb{N}$. Suppose we throw $N$ numbered balls into $N$ numbered urns, so that for each $b \in \{1,\ldots,N\}$, ball $b$ lands in urn $j$ with equal probability $1/N$. Choose a number $c ...
4
votes
0answers
62 views

Approximation of convex body by polytopes

In a recent survey paper, Approximation of convex sets by polytopes, Bronstein claims that under Hausdorff distance $\rho_H$, for every convex body $U$, $$\rho_H(U,\mathcal{P}_n)\leq c(U) ...
1
vote
0answers
22 views

Can we give efficiently the solution of a bilinear system of equations over a finite field?

Consider a finite field $F$ and suppose we have a system of equations $$h_1(\alpha,\beta)=0,h_2(\alpha,\beta)=0,...,h_t(\alpha,\beta)=0$$ where $\alpha=(\alpha_1,...,\alpha_s)$ and ...
4
votes
1answer
174 views

Decomposing $(\mathbb C^n)^{\otimes m}$ as a representation of $S_n\times S_m$

$V=\mathbb C^n$ is a $\mathbb CS_n$-module, where $S_n$ is the symmetric group of degree $n$, via the representation sending a permutation to the corresponding permutation matrix. The tensor power ...
0
votes
1answer
105 views

$u_n$ bounded in $L^\infty(0,T;H) \cap L^2(0,T;V)$ implies $u_n \to u$ strongly in $L^2(0,T;H)$?

Let $V \subset H$ be a dense and compact embedding. Let $$\lVert u_n\rVert_{L^\infty(0,T;H)} + \lVert u_n \rVert_{L^2(0,T;V)} < C$$ where $C$ is independent of $n$. It follows that eg. $u_n ...
3
votes
1answer
132 views

The Jordan Plane and Enveloping Algebras

Let $k$ denote a field of characteristic $0$ (assume algebraically closed for convenience). Define $J=k\langle x,y|[x,y]=y^{2}\rangle$. This noncommutative algebra (which can be viewed as a derivation ...
1
vote
0answers
108 views

Density of numbers whose prime factors all come from a fixed congruence class

Let $q$ be a positive integer greater than one, and let $a$ be an integer such that $\gcd(a,q) = 1$. Define $$D(a,q) = \{n \in \mathbb{N} : p | n \Rightarrow p \equiv a \pmod{q} \}.$$ Do we know the ...
-4
votes
0answers
54 views

The Birthday Paradox [on hold]

I was looking at the birthday paradox, and the many solutions. One of them that came up was the Poisson Distribution. The website I was looking at detailed the process to solve ...
0
votes
0answers
35 views

Property of summations [on hold]

Suppose to have the following identity: $$ \sum_{i=i_0}^{i_1}\sum_{j=j_0}^{j_1} f(i,j) = \sum_{i=i_0}^{i_1}\sum_{j=j_0}^{j_1} f(i,j)g(i,j), $$ for 'good' indexes $i,j$ and some functions $f,g$. What ...
1
vote
2answers
137 views

Bertini theorem for big divisors and klt pairs

Let $X$ be a smooth projective variety and let $D$ be a big $\mathbb Q$-divisor on $X$. Assume that for $m$ large $|mD|$ has no fixed components. Is there a $\mathbb Q$-divisor $D'\equiv D$ so that ...
8
votes
0answers
118 views

History of preservation theorems in forcing theory

For my honours thesis, I am studying a general preservation theorem using a framework provided by Shelah. I am mainly concerned about revised countable support iteration of $\dot{S}$-semiproper ...
1
vote
1answer
51 views

Multinomial proxy variables: Bound on probability of their sums

Suppose $(X_1,X_2,..X_i,..,X_b)$ as multinomial vector of random variables with $N=\sum_{i=1}^b X_i$ and probabilities $p_i$ to parametrize the $X_i$. Let us take the following imagination to ...
2
votes
1answer
74 views

Coarsely trivial Borel cross section for $G\to G/N$

Let $G$ be a locally compact group, and let $N$ be a closed, normal subgroup, and let $\pi\colon G\to G/N$ be the quotient homomorphism. It is known that there exists a Borel cross section, i.e., a ...
0
votes
1answer
62 views

Are Zariski connected and closed semisimple subgroups of semisimple and simply connected algebraic groups again simply connected? [on hold]

Let $G$ be a semisimple and simply connected linear algebraic group over $\mathbb{C}$. Let $H$ be a connected, Zariski closed and semisimple linear algebraic $\mathbb{Q}$-subgroup of $G$. Is $H$ a ...

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