0
votes
0answers
13 views

Outer measure preserving bijection

Suppose X is a Sierpinski set (So X is uncountable and every null subset of X is countable). Let f be a bijection on X. Must/Does there exist a non null subset Y of X such that for every subset W of ...
-1
votes
0answers
14 views

Independent and Dependent Variables [on hold]

Hi guys i have a question regarding independent and dependent variables. Provide an example that shows the variance of the sum of two random variables is not necessarily equal to the sum of their ...
0
votes
0answers
43 views

Self-contained book on Ricci Flow/Geometric Analysis

Can someone please tell me whether there is any self-contained book on Geometric Analysis/Ricci Flow/analytic techniques used in Riemannian Geometry? By self-contained I mean it does not assume that ...
0
votes
2answers
21 views

Integrability at $z$ of the 2-form $ d\omega=\frac{\partial_{\bar{\zeta}}g(\zeta)}{\zeta-z}d\zeta\wedge d\bar{\zeta} $

Given $g\in\mathcal{C}^1(\bar\Delta)$, and $z\in\Delta$, how can i prove that the 2-form $$ d\omega=\frac{\partial_{\bar{\zeta}}g(\zeta)}{\zeta-z}d\zeta\wedge d\bar{\zeta} $$ is integrable in $z$? At ...
0
votes
0answers
2 views

Global and local maxima in a weighted sum of logarithms of linear functionals?

Initially posted on math.stackexchange, was recommended that this is a more relevant forum: Is is possible to describe, and locate efficiently, the maxima of the function below in the parameters ...
0
votes
0answers
61 views

An (open?) problem about a sequence of nested sub-matrices and their determinant

I prefer to start with an example. Consider the matrix $$ A = \left[ \begin{array}{ccc} 1 & 1 & 0 \\ 1 & 1 & 1 \\ 1 & 0 & 1 \end{array} \right] $$ It is invertible, since its ...
0
votes
0answers
22 views

Calculating age with decreasing year values [migrated]

This is my first question on mathoverflow.net, with everything this entails. This question is about the perceived duration of every year as one ages. We will call $Y_0$ the perceived duration of our ...
0
votes
0answers
17 views

Good covering of a (singular) curve

Let $W$ be a $2$-dimensional complex manifold and $C\subset W$ a compact complex curve (possibly singular). I would like to know a reference for the following fact: there exists a collection ...
2
votes
1answer
45 views

Obtain 4-manifolds by repeating surgeries of submanifolds in $S^4$

In his paper QFT and Jones Polynomials, Witten states: "It is a not too deep result that every 3-manifold can be obtained from or reduced to $S^3$ (or any other desired 3-manifold) by repeated ...
1
vote
0answers
13 views

Biggest volume parallelotope inside the union of two parallelotopes

Given a parallelotope $P$ symmetric around the origin, and a vector $v$, such that $(P+v)∩(P−v)$ is not empty, is there a simple way to obtain a parallelotope $Q⊂(P+v)∪(P−v)$, symmetric around the ...
1
vote
0answers
8 views

Mappings between adaptive networks and Markov processes

Are there any known mappings between adaptive networks models (i.e. graph model representations of networks where the internal vertex dynamics and connectivity topology can change subject to specific ...
1
vote
0answers
23 views

boundedness of a sequence $ \in L^{\infty}(I,H^1(M))\cap Lip(I,L^2(M))$ implies that its temporal derivative is bounded as well

Hi I have the next claim which I would like to find a proof of it. I have a sequence of functions $u_\epsilon(t,x) \in H^1(M)$ where $M$ is a compact manifold, and $u_\epsilon \in ...
1
vote
0answers
56 views

A moment problem

Suppose $X, Y$ are two positive random variables such that $\mathbb{E}[X^\alpha] = \mathbb{E}[Y^\alpha]$ for all $\alpha \in (0, 1/2)$. It is also known that the first moment exists for each of them, ...
-4
votes
4answers
180 views

Studying topology: which first, algebraic or differential? [on hold]

I have recently studying the basics of topology (ideas in point set, connectedness compactness) and I want to continue my studies but i'm interested in both differential and algebraic topology. which ...
0
votes
0answers
9 views

Prefactor of a bounded differences inequality

I have a question concerning the prefactor of a bounded difference inequality. In Corollary 1, see p.7 there is the inequality $\text{Var}[Z]\leq\frac{1}{2}\sum\limits_{i=1}^n c_i^2$. On the other ...
0
votes
0answers
54 views

Are all minimal zero-dimensional spaces compact?

Let us call a space $(X,\tau)$ totally separated if for every two distinct points there is a clopen set containing one, but not the other. If for every topology $\sigma\subseteq\tau$ with $\sigma\neq ...
0
votes
1answer
62 views

Minimal zero-dimensional spaces

Let us call a space $(X,\tau)$ zero-dimensional (0d) if for every two distinct points there is a clopen set containing one, but not the other. If for every topology $\sigma\subseteq\tau$ with ...
-1
votes
0answers
31 views

Is there any theorem which guarantees the existence of an eigenvalue for a non-normal matrix in the vicinity of its perturbed matrix? [on hold]

Let $A=(a_{ij})$ be a non-normal square matrix of order $n$ such that $a_{ji}=1/a_{ij}$ if $a_{ij}\neq 0$ and $0$ otherwise. If $B$ is the perturbed matrix obtained from $A$ such that $B$ also ...
0
votes
0answers
38 views

Why is the polynomial relating the invariants of a binary polyhedral group fixed by an overgroup?

Let $G$ be a finite subgroup of $\mathrm{SL}(2,\mathbb{C})$ and $N \triangleleft G$ a normal subgroup. Let $x, y, z$ be the fundamental invariants for the standard action of $N$ on $\mathbb{C}^2$, ...
3
votes
1answer
126 views

A variant of random walk

Standard random walk assumes a sequence of iid RVs $\{X_i\}_{i\geq 0}$ and studied the distribution of $S_n=\sum_{i=0}^n X_i$. Here, I am wondering whether there is some work on $T_n=\sum_{i=0}^n ...
-4
votes
0answers
31 views

Two easy questions of propositional logic [on hold]

if M1VM2 is unsatisfiable can we say M1|=¬M2; if M|=ψ then does ¬ψ|=¬Μ; Please help
-2
votes
0answers
30 views

The Gherkin - equation for the curve inoder to calculate the surface area of revolution [on hold]

I am trying to calculate the surface area of revolution for The Gherkin. not sure about how to obtain the equation of the curve but i have the data points that allowed me to graph it in excel but the ...
1
vote
2answers
157 views

The free group of a group and the kernel of a canonical morphism

Let $G$ be a group and $F_G$ the free group on the set $G$. Then there exists a canonical surjective morphism ${\rm can}: F_G \to G \to 1$ constructed as follows: let $(e_x)_{x \in G}$ be a copy as a ...
2
votes
0answers
78 views

(co)limits in the category of diffeological spaces vs. category of smooth manifolds

I am wondering which (co)limits that exist in the category of smooth manifolds are preserved by the inclusion into the category of diffeological spaces? Are there any results that allow us to ...
-2
votes
0answers
38 views

Riemann-Stieltjes integrable? [on hold]

Let f and alpha be functions defined by $$ f(x) = \begin{cases} x & 0 \leq x < 1\\ 2x & 1 \leq x \leq 2 \end{cases} $$ $$ \alpha(x) = \begin{cases} 1 & 0 \leq x \leq 1\\ 2 ...
9
votes
0answers
106 views

What are explicit obstructions to realizability of formal group laws as complex-oriented ring spectra?

Recall that a complex-oriented spectrum is a ring spectrum E with a map $MU \to E$. Analogously, a ring with a (1-d commutative) formal group law is (represented by) a ring $R$ with a map $L \to R$ ...
1
vote
1answer
86 views

Contraction semigroup

Let $(X, \mu)$ be a finite measure space and let $A$ be a non-negative self-adjoint operator which generates a contraction semigroup $e^{tA}$ on $L^2(X, \mu)$. If additionally, we have that $e^{tA}$ ...
1
vote
1answer
101 views

Fourier coefficients of real analytic functions on an n-dimension torus

Let $(\mathbf{R}^n,\langle\;,\; \rangle)$ be the n-dimensional euclidean space endowed with the standard inner product. For a lattice $L\subseteq \mathbf{R}^n$ we let $cov(L)$ denote the covolume of ...
7
votes
0answers
67 views

Self-avoiding random walks that always turn

I am wondering if the statistics of self-avoiding random lattice-walks on $\mathbb{Z}^2$ that turn left or right at each step (i.e., they cannot continue the direction of the preceding step) have been ...
0
votes
0answers
21 views

Proving Unboundedness of a Martingale [on hold]

Suppose I have a submartingale $X_k$, what results/theorems can be useful if I want to show that $X_k$ is unbounded in the limit. There are results (basically bounding $\mathbb{E}X_k$) for convergence ...
0
votes
0answers
31 views

Looking for an example of a contour integral with matrix entries [on hold]

Let $A$ be a matrix (if needed assume it to be the adjacency matrix of graph). Let one be given two functions $P(z)$ and $Q(z,A)$ such that both are polynomials in $z$ and $A$, where $z$ is some ...
7
votes
0answers
85 views

Identifying a Hopf algebra cohomology theory

Here is a cohomology theory for a Hopf algebra, which I am sure has appeared elsewhere. I met it in the van Est spectral sequence for Hopf algebras. Apologies for my being stupid here, but it would be ...
0
votes
0answers
16 views

density function time series

I have a time series of density functions, say A1-A5. Each density function is defined as $f(x)=\Sigma_{i=1}^{N} \beta(x-a_i)$, where $\beta$ is a smoothing function (e.g., gaussian or delta), and N ...
6
votes
1answer
233 views

What's the difference between Euler systems and Kolyvagin systems?

Is there a difference between Euler systems and Kolyvagin systems - or do they refer to the same thing? For example there is the Heegner point Euler system, but you don't really see a Heegner point ...
-3
votes
0answers
25 views

Calculus II Function Construction [on hold]

I need help please! Construct a function that is continuous and non-negative [0,1], with the property that the area under the function on [0,1] is finite yet the arc length on [0,1] is infinite.
2
votes
0answers
111 views

Fiber bundle in smooth category and topological category

Let $M$ be a smooth manifold and $G$ be a Lie group. Denote by $Bun(M,G)$ the set of all equivalent smooth Principal bundles on $M$ with structural group $G$ in smooth category. And denote by ...
3
votes
0answers
44 views

When is a $2$-Calabi–Yau triangulated category the cluster category of a QP?

Keller–Reiten's main theorem in Acyclic Calabi–Yau categories implies that if $\mathcal{C}$ is a $2$-Calabi–Yau (algebraic) triangulated category admitting a cluster-tilting object $T$ such that the ...
0
votes
0answers
48 views

Existence of a Lie algebra element orthogonal to the adjoint orbit of another element

Consider a compact, semi-simple, connected Lie group $G$ and its Lie algebra $\mathfrak{g}$. Denote the Killing form by $K$. Given a single $A \in \mathfrak{g}$ when (i.e. which groups and which $A$) ...
5
votes
0answers
55 views

Descriptive Complexity of Knot Equivalence

I was reading a little about knots (in a popular math book that wasn't very good) and the book put forth several knot invariants like the Alexander and Jones polynomials. But these are not complete ...
0
votes
0answers
34 views

Is there an action functional for the s-dependent Floer equation?

The usual Floer equation (in local coordinates) \begin{equation*} \partial_su+J(t,u)(\partial_tu-X_{H_t}(u))=0 \end{equation*} is derived as the gradient flow of the symplectic action functional ...
2
votes
1answer
68 views

Renorming into contraction

In Pazy's book on semigroups he mentions (page 18) that when you have a commuting family of operators $B(t)$, such that $$ \sup \| B(t_1) .. B(t_n) \| \le M $$ for all finite choices $t_1, .. t_n$ ...
-2
votes
0answers
45 views

Are universally catenary equidimensional local rings Cohen-Macaulay? [on hold]

Cohen-Macaulay rings are universally catenary, I do not choose catenary rings because we can find catenary but not universally catenary rings at wiki Catenary ring. Cohen-Macaulay local rings are ...
4
votes
2answers
129 views

Counterexample on completely distributive lattices

I would like to see an example of a complete lattice $C$ which is both a frame and a dual-frame, i.e. finite meets distribute over arbitrary joins and finite joins distribute over arbitrary meets ...
-2
votes
0answers
64 views

Integer solution to the equation [migrated]

Does there exists an integer solution (for every integer $m\geq 1$) for the following equation? $$x_1x_2...x_n+(2y+1)z+y=4m+3$$ where, $1\leq x_1\leq x_2\leq...\leq x_n\leq l$,$0\leq y \leq ...
2
votes
0answers
68 views

Dominating affine varieties over $k$ with affine smooth varieties over $k$

Given a geometrically integral affine variety $X:=\mathrm{Spec}(K[X_1,\ldots, X_n])/(f_1,\ldots, f_m)$ over a possibly imperfect field $K$, does there always exist an affine variety $\tilde{X}$ ...
4
votes
0answers
65 views

Arithmetic quotients of Bruhat-Tits buildings for groups over local fields of positive characteristic

I have been led to believe that there is a result giving a description of the quotient of a Bruhat-Tits building $\Delta(G,k)$, for a semisimple algebraic group $G$ over a non-archimedean local field ...
-3
votes
0answers
41 views

Compactly generated semi-simple Lie groups [on hold]

Let $G$ be a connected semi-simple Lie group with finite center and no compact factors. Is $G$ necessarily compactly generated? What if it also has $\mathbb{R}$-rank at least 2?
6
votes
3answers
270 views

Exact sequences of groups and Tannakian formalism

By work of Deligne and others (I am following Deligne-Milne's notes which I just began to read: http://www.jmilne.org/math/xnotes/tc.pdf) we know that a given affine group scheme G can be recovered ...
11
votes
1answer
550 views

“The Two Sheriffs” puzzle

This puzzle is taken from the book Mathematical puzzles: a connoisseur's collection by P. Winkler. Two sheriffs in neighboring towns are on the track of a killer, in a case involving eight ...
0
votes
1answer
231 views

Reference for a lemma on étale maps

The Stacks Project has the following really nice Lemma concerning étale maps of rings: Let $A\rightarrow B$ be a finitely presented, étale morphism of rings. Then there exists a presentation $$ ...

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