# All Questions

**-2**

votes

**0**answers

10 views

### Have there been attemps to manage the pool of worldwide mathematics students?

(Foreword: I am well aware that MO is not a blog, and not for argumentative questions. Therefore I have phrased my question in a rather specifically answerable form. If moderators still feel it is ...

**-1**

votes

**0**answers

14 views

### prove that the sequence a_n = [n((2)^(1/2))] + [n((3)^(1/2))] contains infinitely many even and odd integers

im not sure how to proceed.i have done a few problems similar to this but i can't solve this one. thanks for any help.( by the way this is a problem from croatia team selection test )

**0**

votes

**0**answers

6 views

### Proof of the measure representation lemma, used by P. L. Lions in the proof of the concentration-compactness

Please can someone tel me where i can find the proof of this :
Thank you

**-3**

votes

**0**answers

18 views

### Caledonian college level2 [on hold]

assume we have a stick of one meter length. we put 999 ants on the stick, at arbitrary positions and arbitrarily facing either left or right. At a certain time, all ants start moving with the same ...

**1**

vote

**0**answers

10 views

### A tensor equation related to an invariant of a diffeomorphism

Let $M$ be an $n$-dimensional differentiable manifold, $f : U
\rightarrow V$ a diffeomorphism between open neighbourhoods $U$, $V$
of $M$ with $f(x)=x$ for some $x \in U$, and let $R$, $S$, $T$ be
...

**1**

vote

**0**answers

9 views

### random odes adapted solution

Let $\{\omega_t\}$ be a Levy process (like Brownian Motion, stable process). Consider the following random ode
$$x_t=x_0+\int_0^tb(x_s+\omega_s)ds$$
Where $b$ is a bounded continuous function (not ...

**2**

votes

**0**answers

27 views

### Permutation-invariant matrix representation

The question guide says that Mathoverflow is for research level mathematics. While I do not perform research in mathematics (I study quantum chemistry), I believe this question is research-level ...

**3**

votes

**1**answer

45 views

### Singularities of the moduli stack of polarized hyperkahler varieties

Inspired by the recent question on singularities of the moduli stack of Calabi-Yau threefolds (Singularities of the moduli stack of Calabi-Yau threefolds) I'd like to ask the following question.
Is ...

**-4**

votes

**0**answers

23 views

### Something about iterated logarithm [on hold]

that's my first question there.
So, can you explain, why iterated log well-defined with base more than e^(1/e).
I considered a f = w^(1/w), and prove that f(max) = e^(1/e), so if I prove that log* ...

**-2**

votes

**0**answers

64 views

### Why are algebraic cycles rational?

Let $X_{/\mathbb{C}}$ be a projective non-singular variety of dimension $n$ and $Z \subset X$ be an irreductible subvariety of dimension $p$.
Denote by $\mathrm{H}_{\mathrm{dR}}^i(X,\mathbb{C})$ the ...

**2**

votes

**2**answers

38 views

### How does one calculate/estimate/guarantee the girth of a non-Abelian Cayley graph?

This question is in reference to this other question,
Can someone point out references (or explain!) which give techniques of being able to prove for any Cayley graph this property of having a girth ...

**8**

votes

**2**answers

251 views

### For what real $t$ is $\{n^t : n \geq 1\}$ linearly independent over $\mathbb{Q}$?

It's straightforward that $t$ must be irrational. I have googled many variations of this question and browsed through some books on transcendental number theory. There is much that is said about when ...

**1**

vote

**0**answers

52 views

### Complexity :: Integer Programming :: Non-Poly Example

When learning about computational complexity I find that when discussing the NP-Complete problems authors always give examples of such problems that can in fact be solved in poly time.
I understand ...

**0**

votes

**0**answers

11 views

### Non-discrete modularity measure in graph analysis [on hold]

I work in neuroimaging, and right now graph theory is all the rage. Most graph analyses that parcel brain regions into modules do so in a discrete fashion. This might ignore the idea that one brain ...

**-5**

votes

**0**answers

40 views

### limit exercise which requires ingenuity1 [on hold]

Hello im an eleventh grader in the best mathematics high school in my country. I wanted to see if any of you guys can help me solve a limit without integrals and L'Hospital, as i havent learnt them ...

**1**

vote

**1**answer

94 views

### Is there a nonzero sheaf with all cohomologies vanish?

Is there a topological space $X$ with a nonzero sheaf $\mathcal{F}$ of abelian groups such that $H^i(X,\mathcal{F})=0$ for all $i=0,1,2...$?

**2**

votes

**0**answers

140 views

### Intuition behind the definition of quantum groups

Being far from the field of quantum groups, I have nevertheless made in the past several (unsuccessful) attempts to understand their definition and basic properties. The goal of this post is to try to ...

**1**

vote

**0**answers

36 views

### Twisting stable maps to C* equivariant space by a line bundle

Let $X$ be a $\mathbb{C}^*$-equivariant algebraic variety. Then there is a notion of a map to $X$ twisted by a line bundle. Namely, let $B$ be a variety and $L/B$ a line bundle. Let $P_L=L\setminus ...

**1**

vote

**0**answers

45 views

### Runs of consecutive numbers all of which are rebel numbers [migrated]

A positive integer is said to be a rebel number if it is the product of numbers none of which share any of the original number´s digits. Thus 10 = 2 x 5 is a rebel number, while none of the primes is. ...

**5**

votes

**1**answer

77 views

### Reference request: Riesz potential $I_\alpha : L^{d/\alpha} \to \rm{BMO}$?

Let us denote the Riesz potential in $\mathbb R^d$ by
$$
I_\alpha (f)(x) := c_{d, \alpha} \int_{\mathbb R^d} \frac{f(y)}{|x-y|^{d-\alpha}}
\, dy.$$
By the classical Hardy-Littlewood-Sobolev theorem ...

**2**

votes

**0**answers

82 views

### A homomorphism in the long exact sequence of a fibration for a homogeneous space of a Lie group

Let $G$ be a connected Lie group, and let $H\subset G$ be a (closed) Lie subgroup, not necessarily connected. Set $X=G/H$.
The fibration $j\colon G\to X$ with fiber $H$ induces an exact sequence
$$
...

**0**

votes

**0**answers

39 views

### Generalization of a class of sets [on hold]

In topological space, we start with open set, which serves as fundamental set. We know that union of finite disjoint open sets is the smallest set amongst any kind of unions of open sets, so we have a ...

**-2**

votes

**0**answers

34 views

### Decomposition of ball in Banach Tarski paradox and covering a soccer ball [on hold]

These are 2 separate questions but both related to ball. In both parts, let's use the unit ball (radius = 1) for simplification.
Banach Tarski paradox says that it's possible to decompose a ball in ...

**0**

votes

**0**answers

26 views

### An upper bound on the number of sets of parallel lines covering points in a finite plane?

Let $\mathbb{F}$ be a finite field of characteristic $2$. Let $L_m$ denote the set of lines in $\mathbb{F}^2$ with slope $m\in\mathbb{F}$, that is, all parallel lines of the form $y=mx+b$. Consider a ...

**-2**

votes

**0**answers

25 views

### MatLab loop which stops after X iterations [on hold]

sorry this is a bit of a simple question but I can't find the answer.
I'm trying to halt a loop after 25 iterations like this:
...

**-1**

votes

**1**answer

26 views

### Can Singular Value Decomposition Optimal Newman Modularity? [on hold]

I face some problem on the way home.
I want to optimize Newman Modularity Q , Can I use SVD to do that?
Thanks!

**2**

votes

**3**answers

192 views

### When a homeomorphism is a diffeomorphism w.r.t to a suitable smooth structure?

Assume we have a homeomoprhism $\phi:M\rightarrow M$, where $M$ is a topological manifold which admits at least one smooth structure.
Is it always possible to construct a smooth structure on $M$ ...

**3**

votes

**0**answers

50 views

### When are principal bundles preserved by colimits?

Let $G$ be a topological group and consider a family $$G\rightarrow E_i\rightarrow B_i$$ of $G$-principal bundles indexed over the natural numbers. Suppose we have $G$-bundle morphisms ...

**-1**

votes

**0**answers

20 views

### Estimation VS detection [on hold]

I would like to know what is the difference exactly between estimation (parametric or not) and detection in the statistic signal process.
Thanks in advance and have a good day

**36**

votes

**3**answers

1k views

### Is the set AA+A always at least as large as A+A?

Let $A$ be a finite set of real numbers. Is it always the case that $|AA+A| \geq |A+A|$?
My first instinct is that this is obviously true, and there is a one-line proof which I am foolishly ...

**2**

votes

**1**answer

152 views

### The topology of Fano schemes of lines

Is there any references concerning the computation of the fundamental groups and Hodge numbers of Fano schemes of lines in a smooth hypersurface in $\mathbb{P}^n$?

**0**

votes

**0**answers

67 views

### Is it possible to find an explicit definition of the “universal” (co)tangent bundle?

Let $H_{0,1}(\mathbb{P}^2, d)$ be the space of holomorphic degree $d$
maps (that are not multiply covered) from $\mathbb{P}^1$ to $\mathbb{P}^2$ with one marked point
$y \in \mathbb{P^1} $ ...

**-2**

votes

**0**answers

29 views

### Green`s function [on hold]

Find the Green's function $G(x,y, x',y')$ for Laplace's equation in
$0<x'<a$, $0<y'<b$; with $G=0$, $x'=0$, $G_{x'}=0$, $x'=a$, $G_{y'}=0$, $y'=0$, $G=0$, $y'=b$,
and $0<y'<b$, ...

**0**

votes

**0**answers

41 views

### On covering by smooth numbers

Denote $P(y)=\mathsf{greatest}\mbox{ }\mathsf{prime}\mbox{ }\mathsf{factor}\mbox{ }\mathsf{of}\mbox{ }y$.
Denote $S(x,y)=\{n<x: P(n)<y\}$.
Denote $S_t(x,y)=\sum_{i=1}^tS(x,y)$ as $t$-fold ...

**-1**

votes

**0**answers

10 views

### Compute Faber polynomials in Matlab [on hold]

I want to compute some faber polynomials associated to an ellipse centered at a point (u,v) (in the complex plane: u+iv) in Matlab.
Say the ellipse has minor axis a along the x coordinates (real part) ...

**1**

vote

**1**answer

46 views

### Sobolev multiplication $\otimes$ of $H^1=W^{1,2}$ in vector bundles

Let $E\to X$ be a vector bundle with an inner product and fix a reference connection $A_0$ on $E$. Then for $1\leq p < \infty$ and $k\geq 0$ we can define the Sobolev space $W^{k,p}(E)$ as the ...

**8**

votes

**1**answer

94 views

### Best Hölder exponents of surjective maps from the unit square to the unit cube

The Peano's square-filling curve $p:I\to I^2$ turn's out to be Hölder continuous with exponent $1/2$ on the unit interval $I$ (a quick way to see it, is to note that $p$ is a fixed point of a ...

**5**

votes

**3**answers

262 views

### Introductory texts to mathematics [on hold]

I am interested in texts recomendations for a 14 years old boy who wants to study more mathematics than he does at school. He seems quite talented, but his knowledge of maths is rather low. I would ...

**11**

votes

**2**answers

478 views

### Mysterious identity between numbers of odd/even meander systems

Definitions:
An upper arch system of order $n$ is a subset of the plane consisting of $n$ non-intersecting closed semicircles in the upper half-plane whose endpoints belong to the set $\{(k,0)\mid ...

**0**

votes

**0**answers

36 views

### Proof for existence of isoperimetric minimizer by compactness theorem

Let $X$ be an $n$-dim closed Riemannian manifold, then given a number $0 <v < vol(X)$, there exists a Borel subset $A\subset X$ attaining $I(v)$, $I$ is the isoperimetric profile.
The existence ...

**2**

votes

**1**answer

46 views

### Approximating the norm of an operator-valued linear function with operator inputs via a matrix-valued linear function

Let $\mathcal{H}$ and $\mathcal{K}$ be infinite-dimensional Hilbert spaces.
Let $B_1, \ldots, B_k \in B(\mathcal{H}).$
Define $L: B(\mathcal{K})^k \rightarrow B(\mathcal{H}\otimes \mathcal{K})$ via ...

**1**

vote

**3**answers

138 views

### ideals of polynomial ring with complex number coefficients

Let $\mathbb{C}[x,y]$ be the polynomial ring with variables $x,y$ and coefficient in $\mathbb{C}$.
Let $f,g\in \mathbb{C}[x,y]$.
Let $(f,g)$ be the ideal of $\mathbb{C}[x,y]$ generated by $f,g$.
...

**2**

votes

**0**answers

54 views

### first chern class versus compactifying divisor in Ramanujam's surface

I have an elementary question about Ramanujam's surface. Ramanujam's surface is naturally the complement of a singular divisor $D$ in the one point blow up of $CP^2$, $\mathbb{F}_1$. One can resolve ...

**-4**

votes

**0**answers

29 views

### Can anybody help me for this counting question? [on hold]

Peter has 12 pairs of socks and 6 pairs of gloves in different
colors. His socks are in green, yellow, black, and grey (3 pairs each). Peter's gloves are either blue, black, or red (2 pairs each). ...

**1**

vote

**0**answers

55 views

### Lower bound on class number of binary quadratic forms of discriminant of the form n^2+4

While searching for a use for the "sum invariant" of indefinite binary quadratic forms of discriminant $D = n^2 + 4$ (see https://cs.uwaterloo.ca/journals/JIS/VOL17/Smith/smith5.html), I believe I ...

**8**

votes

**4**answers

423 views

### Random Diophantine polynomials: Percent solvable?

Suppose one generates a random polynomial
of degree $d$ with integer coefficients
uniformly distributed within $[-c_\max,c_\max]$.
For example, for
$d=8$, $|c_\max|=100$, here is one random ...

**1**

vote

**1**answer

75 views

### Inner product spaces without symmetry/hermitian axiom

Consider a vector space $X$ over $\mathbb R$ and a bilinear form
$ \langle \cdot, \cdot \rangle : X \times X \rightarrow \mathbb R$.
We assume furthermore that for any $x \in X$ there exists $y \in ...

**2**

votes

**1**answer

105 views

### Could we extend the exact sequence $K^0(X)\to K_0(X)\to K_0(D_{sg}(X))\to 0$ to the left?

Let $X$ be a variety over a field $k$. We have the bounded derived category of coherent sheaves $D^b_{coh}(X)$ and the derived category of perfect complex $Perf(X)$. It is clear that $Perf(X)$ is a ...

**4**

votes

**0**answers

108 views

### Koopman representation, weakly compact action, Ozawa Popa

Given a weakly compact action (Ozawa-Popa) of a discrete group $\Gamma$ on p.m space $X$, consider the Koopman representation $\pi$ on $L^2(X)$. Compose this representation with the Calkin projection. ...

**4**

votes

**0**answers

214 views

### Order theory as a foundation of mathematics?

I know the followings kinds of formalization of mathematics:
based on set theory (e.g. ZFC)
based on type theory (e.g. the formalism of Coq proof assistant, as an advanced example)
based on category ...