0
votes
2answers
78 views

Expected summation of dropped intervals?

For each $n\in\mathbb{N}$, let $I_n$ be an interval of length $1/2^{n}$. We drop each $I_n$ onto the interval $[0,1]$ uniformly at random (so that there is "wraparound" if need be). What is the ...
2
votes
1answer
101 views

Determining whether $k(x + x^{-1})$ is post-critically finite for $0 < |k| < 1$

My REU partner and I are working on a problem involving iterations of quadratic rational maps over an algebraically closed field $K$ that is complete with respect to a non-trivial non-archimedean ...
18
votes
1answer
487 views

Is there a generalization of homotopy groups to fractional dimensions

Does there exist a reasonable candidate for such an object as $\pi_{\frac12}(X)$?
0
votes
0answers
65 views

Showing that a sequence of random variables with increasing expected value converges to a Poisson random variable

Consider a sequence $\{X_n\}_{n \geq 1}$ of nonnegative, integer-valued random variables. For any random variable $Y$ and $k \geq 1$, let $(Y)_k = Y(Y-1)(Y-2)\dots(Y-k+1)$ be the $k^\mathrm{th}$ ...
0
votes
1answer
119 views

Stacks with representable morphisms to algebraic stacks

If $Y$ is an algebraic stack over a scheme $S$ and $X$ is a stack such that there exists an $S$-morphism $X\to Y$ representable by algebraic spaces, then is $X$ an algebraic stack (in the sense that ...
14
votes
0answers
223 views

An algebraic strengthening of the Saturation Conjecture

The Saturation Conjecture (proved by Knutson-Tao) asserts that $c_{n\mu,n\nu}^{n\lambda}\neq 0\Rightarrow c_{\mu,\nu}^{\lambda} \neq 0$, where $c$ denotes a Littlewood-Richardson coefficient and $n$ ...
2
votes
0answers
152 views

Is the twisted symmetric fifth power $L$-function holomorphic?

Let $\pi$ be a Maass cusp form for SL($2,\mathbb Z$). Let $\omega$ be a primitive Dirichlet character. Let us consider the $L-$ function $$L(s,Sym^5 \pi \times \omega)$$ or $L(s,Sym^6 \pi \times ...
4
votes
1answer
157 views

Check symplectomorphism property on infinitesimal generators

I stumbled over the following question: First, let me give the basic definition of a symplectic group action: Let $(M, \omega)$ be a symplectic manifold and $G$ a Lie group. A smooth action $\Phi:G ...
11
votes
1answer
241 views

On the global structure of the Gromov-Hausdorff metric space

This is a purely idle question, which emerged during a conversation with a friend about what is (not) known about the space of compact metric spaces. I originally asked this question at ...
-5
votes
0answers
33 views

Intersection Question of set theory [closed]

At an institute where students can opt more than one subject, of 300 students, 55 did not choose any of Mathematics, Physics or Social. 110 choose Mathematics, 130 choose Physics and 140 choose ...
14
votes
0answers
151 views

Minimal number of intersections in a convex $n$-gon?

For a convex polygon $P$, draw all the diagonals of $P$ and consider the intersection points made by those diagonals. Let $f(n)$ be the minimal number of such intersections where $P$ ranges over all ...
6
votes
1answer
373 views

Pure motives and compatible systems of $\ell$-adic representations

I am trying to understand the statement of the conjectures of Deligne on special values of certain $L$-functions, from his article titled, "Valuers de Fonctions L et periodes d'integrales" which ...
0
votes
1answer
196 views

A question on permutations

Given integers $1$ through $n$, let $S$ be set of ordering of integers that respect even alternating or reverse alternating permutations (https://en.wikipedia.org/wiki/Alternating_permutation) up to ...
4
votes
2answers
136 views

Are periodic billiard trajectories stable on a manifold with strictly convex boundary?

Let $(M,g)$ be a compact Riemannian manifold with strictly convex boundary. Let $\gamma:S^1\to M$ be a periodic billiard trajectory (geodesic in the interior and reclects specularly at the boundary). ...
-1
votes
1answer
203 views

Class forcings and elementary embeddings

In the Hamkins-Kirmayer-Perlmutter paper "Generalizations Of The Kunen Inconsistency", they prove the following theorem: "Theorem 7: In any set forcing extension $V[G]$, there is no nontrivial ...
5
votes
1answer
222 views

Transcendental distance sets

Define a set $S \subset \mathbb{R}^d$ as a transcendental distance set if the distance between any pair of distinct points of $S$ is transcendental. For example, $S = \{ k \, \pi \;\mid\; k=1,2,\ldots ...
1
vote
0answers
47 views

Extending an homotopy, knowing the two base functions extend

Let $A\subset B$ be paracompact spaces, and let $C$ be a paracompact space. Let $f_0,f_1:A\rightarrow C$ be continuous functions. $F:A\times[0,1]\rightarrow C$ a homotopy from $f_0$ to $f_1$. Suppose ...
0
votes
3answers
117 views

Fundamental solution for a parabolic PDE with constant coefficents

[Cross posting http://math.stackexchange.com/questions/1374384/fundamental-solution-for-a-parabolic-pde-with-costant-coefficents ] I don't know if this question is more appropriate in Mathematics and ...
-2
votes
0answers
75 views

Singular cohomology groups [closed]

I have a question concerning inclusion of singular cohomology groups with different coefficients. To be more precise, we know that the inclusion $i:\mathbb{Z}\hookrightarrow\mathbb{R}$ naturally ...
-5
votes
0answers
56 views

Exponent value of a negative number [closed]

What is the value of (-x)^0 ? (Here x is a variable)
10
votes
0answers
363 views

Which journals publish applied mathematics with mostly pure mathematics content?

In the spirit of Which journals publish expository work? please advise: What consistently high quality journals$^1$ today publish results that would otherwise go to a pure mathematics journal if ...
2
votes
1answer
118 views

Is the top interval of a finite distributive lattice an hypercube lattice?

Let $(L,\wedge,\vee)$ be a finite distributive lattice. Let $M$ be the (unique) maximum element. An element $a \in L$ is called maximal if $a \le a' < M$ implies $a = a'$. Let $b = ...
0
votes
0answers
31 views

Why a cone/parabolic set for the nontangential maximal function?

Suppose $f\in L^p(\mathbb{R}^d)$. Then the Dirichlet BVP for the Laplace equation $\Delta u = 0$ in the upper-half plane $\mathbb{R}^d\times\mathbb{R}_{>0}$ with boundary value $f$ can be solved by ...
2
votes
0answers
96 views

Vector inequation problem [closed]

$${A_i} = \left( {\begin{array}{*{20}{c}}{{A_{i1}}}\\{{A_{i2}}}\\ \vdots \\{{A_{in}}}\end{array}} \right),{B_i} = \left( {\begin{array}{*{20}{c}}{{B_{i1}}}\\{{B_{i2}}}\\ \vdots ...
5
votes
0answers
79 views

Characteristic Cycles and Nearby Cycles

Let $Y$ be a smooth algebraic variety over $\mathbb{C}$, let $X = Y \times \mathbb{C}$ and let $f: X \to \mathbb{C}$ be the projection. Let $M$ be a (not necessarily regular) holonomic $D_X$-module ...
0
votes
0answers
105 views

Is any blow-up of smooth subvarieties always an extremal contraction?

Let $X$ be a smooth complex projective variety and $Z$ be a smooth subvariety of $X$. Take the blow-up $\pi: Y \to X$ of $X$ along $Z$. Then I want to know whether $\pi$ is the contraction of an ...
1
vote
0answers
24 views

What is the minimum number of filled cells in a partial Latin rectangle with autotopism group $\cong C_2$ and autoparatopism group $\cong S_3$?

Definitions: a partial Latin rectangle is an $r \times s$ matrix containing symbols from $[n] \cup \{\cdot\}$ such that each row and each column contains at most one copy of any symbol in $[n]$. The ...
1
vote
1answer
65 views

Essential surfaces in the Exterior of Montesinos knots

Hatcher and Oertel computed the boundary slopes of essential surfaces of Montesinos knots in this paper. But they do not consider surfaces that do not intersect the boundary of the exterior. An ...
-1
votes
0answers
38 views

optimization of quadratic over linear function [closed]

I'm a computer science student. Please I need a help in solving a constrained normalized quadratic function. I'm familiar with solving quadratic constrained optimization function with matlab by ...
1
vote
0answers
95 views

Randomly partitioning the unit interval with continuous functions

I want to construct a family of continuous functions $H$ in order to randomly partition the unit interval. That is, consider a partition $\lambda$ of the unit interval into $n$ subintervals: $\lambda ...
0
votes
0answers
73 views

Finite-index subgroups of the ideles

Let $k$ be a number field and denote by $J_k$ the idele group of $k$. Recall that the finite-index open subgroups of $J_k$ which contain $k^*$ are very important in class field theory. My question ...
0
votes
0answers
111 views

Existence of a map between curves

Given two algebraic curves defined over the rationals, is there a method for determining whether there exists a surjective map from one curve to the other? For instance, suppose X and Y are affine ...
0
votes
1answer
63 views

Bohr compactification and “discretization”

Let $G$ is a compact group. We can form the Pontriagin dual $\widehat{G}$ of $G$: it is then discrete space. One can consider the Bohr compactification $b\widehat{G}$ of $\widehat{G}$ which is compact ...
0
votes
0answers
16 views

Tangent vectors to coadjoint orbits [migrated]

Let $O_x:=\{Ad^*_g (x); g \in G\}$ be the orbit of $x \in \mathfrak{g}^*$ and $Ad$ the adjoint map. Now take $\xi \in \mathfrak{g}$ then $g(t):=Ad^*_{e^{t \xi}}(x)$ defines a map $g: I \rightarrow ...
6
votes
2answers
234 views

Non strictly-singular operators and complemented subspaces

If $T$ is a bounded operator which is not strictly singular, acting on a separable Banach space $X$, can one always find an infinite dimensional, closed and complemented, subspace $Y$ such that $T$ ...
0
votes
0answers
36 views

Counting the k-factors of the complete graph on n vertices [closed]

I was originally trying to solve the following problem: 10 people are in a room, and you give them a task. Their task is for each person to shake hands with exactly 3 other people in the room. How ...
3
votes
0answers
79 views

What does “control of a deformation problem” mean?

Is the expression "control of a deformation problem' ever defined? There are of course many examples relating a dg-Lie or L-infty algebra to a deformation problem, and the phrase is evocative. Is it ...
-3
votes
0answers
82 views

What are the problems with Logicism? [closed]

"Maybe" logicism is a ("philosophical") stand, posture in mathematics. My questions are: Why logicism is not a "absolute" posture in mathematics (what are your problems)? Are there some evidence for ...
5
votes
2answers
209 views

Baire Category Theorem for complete uniform spaces

The version of the Baire Category Theorem I have in mind is the statement that a countable intersection of dense open subsets of a complete metric space is dense. The question is: is it likewise ...
26
votes
4answers
2k views

Computer calculations in a paper

I think I can improve the current upper bound concerning an open problem. The ideas are purely combinatorial, but in the end I have to calculate the maximum of a really ugly, non elementary function ...
0
votes
0answers
24 views

Time-stepping numerical scheme for the advection dispersion equation

I am facing a simple (at first glance) problem. I need to implement a numerical scheme for the solution of the first order wave propagation equation with chromatic dispersion included. My original ...
1
vote
0answers
58 views

Motivic Pfister type varieties and norm varieties

Due to results of Rost it is known that the Grothendieck-Chow motiv of a Pfister quadric $X$ belonging to a pure $\alpha \in H^n(k,\mu_2)$ is decomposable in the following way $M(X) = ...
5
votes
1answer
186 views

Hahn Banach type extension of a Lipschitz map

The problem that I posted was a much generalized form of what I had in my mind. All I want to know the literature of Hahn-Banach type extension of Lipschitz map. I know only about the result by ...
11
votes
2answers
382 views

Relationship between étale and topological $K(\pi,1)$s

I was trying to find a proof, or a counterexample to the claim that if $X/\mathbb{C}$ is connected smooth projective, then $X$ is a $K(\pi^{\mathrm{\acute{e}t}},1)$ if and only if $X^\mathrm{an}$ is a ...
0
votes
0answers
94 views

Degrees of generators of radical ideals

Let $I \subseteq \mathbb{C}[x_1,\ldots,x_n]$ be an ideal generated by polynomials $f_1,\ldots,f_r$ of degree at most $d$. Is it possible to generate the radical $\sqrt{I}$ of this ideal with ...
13
votes
1answer
543 views

Elementary Proof of Infinitely many primes $\mathfrak{p} \in \mathbb{Z}[i]$ in the sector $\theta < \arg \mathfrak{p} <\phi $

A quick look at the primes in $\mathbb{Z}[i]$ suggests they might be evenly distributed by angle if we zoom out on a coarse enough scale. I would like ask about the much weaker statement forgetting ...
2
votes
0answers
52 views

A question on the behavior of intersections of certain block design

Let $[d]$ be a universe and $S_1, \dots, S_m$ be an $(\ell, a)$-design over $[d]$ which means that: $\forall i \in [m], S_i \subseteq [d], |S_i|=\ell$. $\forall i \neq j \in [m]$, $|S_i \cap S_j| ...
0
votes
0answers
118 views

Is the complex structure on a del-Pezzo surface a regular complex structure?

Let $(X, \omega, J)$ be a compact symplectic manifold with an almost complex structure. Fix some homology class $\beta \in H_2(X, \mathbb{Z})$. An almost complex structure $J$ is said to be ...
3
votes
0answers
21 views

Characterization of complete lattices with join-incomplete lattice endomorphisms

Let $L$ be an complete lattice. A lattice homomorphism $f: L\to L$ is said to be join-incomplete if there is an infinite set $S \subseteq L$ such that $f(\bigvee_L S) > \bigvee_L f(S).$ How can ...
1
vote
0answers
158 views

(Reference request) Unwinding the notion of local non-constancy in constructive analysis

In constructive mathematics, several authors, including Bishop himself, use the term "locally non-constant" function. That is: A function $f: [a, b] \longrightarrow \mathbb{R}$ is called locally ...

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