# All Questions

**2**

votes

**0**answers

46 views

### Regularity of finite variation kernels in the (intersection) of the semimartingale spaces $H^p$

Suppose you have a continuous semimartingale $S_t=M_t + A_t$ where $A_t$ is the continuous finite variation part which has the form $A_t = \int_0^t b_s \, \mathrm{d} s$, where $\int_0^{\infty} |b_s| ...

**5**

votes

**3**answers

218 views

### Invertible operator with countable spectrum

Let $H$ be a separable Hilbert space and $A$ is an invertible bounded operator on $H$. Can we approximate $A$ with an invertible operator $B$ such that $sp(B)$ is a countable set?
Motivation:
...

**0**

votes

**0**answers

27 views

### Solution of ODE related to normal density

This question below is from mathse. I reqeustioned here because very limited respond there.
Let $\phi:\mathbb{R}\mapsto\mathbb{R}$ be the standard normal density, ...

**0**

votes

**0**answers

21 views

### fit a parametrized function to data [on hold]

Is there a mathematical aprouch to find known function from given datapoints:
Y = CK10^(-x)/(K+10^(-x))^2
I need to find C and K.

**1**

vote

**0**answers

32 views

### Transferring locally uniformly convex norm by bounded linear operator from one Banach space to another

I'm trying to find a simple proof this theorem
Let $Y$ be a locally uniformly convex Banach space and $X$ be a Banach space and let $T$ be a bunded linear operator from $X$ into $Y$ such that for ...

**8**

votes

**0**answers

166 views

### Ideas behind Gitik's solution of PCF conjecture

Recently Moti Gitik has refuted Shelah's PCF conjecture (see Short extenders forcings II ) by proving the following theorem:
Theorem. Assuming the consistency of infinitely many strong cardinals, one ...

**14**

votes

**2**answers

2k views

### Is there an algebraic number that cannot be expressed using only elementary functions?

(this is basically a repost of a question I asked at M.SE last year)
Is there an explicit real algebraic number (such that we can write its minimal polynomial and a rational isolating interval) that ...

**1**

vote

**2**answers

96 views

### Caratheodory equations

Ok, I am reading Fillipov book on discontinuous right hand side differential equations (the red book).
He states the next lemma:
"
Let the function $f(t,x)$ satisfy the Caratheodory conditions and ...

**-2**

votes

**0**answers

41 views

### Expected value when rolling multiple k-sided dice and keeping the highest score and 1s cancelling higest remaining values [on hold]

sorry for the long title. I think the question is explained there, but I will go a bit further. I know how to calculate the expected value of n k-sided dice and keeping the highest score. If I am not ...

**0**

votes

**1**answer

422 views

### Maximal score for the 2048 game [duplicate]

t's been weeks (months?) since the 2048 game--by Gabriele Cirulli--took Internet by storm. I have an explicit integer $X$ which is greater or equal than any score of this game. Possibly my $X$ is the ...

**1**

vote

**0**answers

81 views

### Families of curves with “almost-general” moduli

The Brill-Noether theorem says that, if $\rho(d, g, r) := (r + 1)d - rg - r(r + 1) \geq 0$, then there exists a unique component of the Hilbert scheme of curves of degree $d$ and genus $g$ in ...

**0**

votes

**0**answers

6 views

### Recursively calculate Tikhonov regularizer in b-spline objective function

I'm trying to write a program to calculate cubic b-spline based on set of inputs. But I can't figure out how to calculate value of Tikhonov regularizer.
My b-spline function is this:
I have ...

**3**

votes

**0**answers

36 views

### Stochastic integration by parts to obtain Kailath Segall identity for iterated stochastic integrals?

If $(M_t)_{t \geq 0}$ is a continuous local martingale, one can define the iterated integrals $I_0=1$, $I_1(t)=M_t$ and for $n \geq 2$ $$I_{n}(t) = \int_0^t I_{n-1} (s) \mathrm{d} M_s.$$ By noting ...

**4**

votes

**1**answer

217 views

### Lower bound on the irrationality measure of $\pi$

There seems to be a lot of work on the upper bound for the irrationality measure of $\pi$, but I could not find anything on a lower bound except the general $\mu(\pi)\geq2$. Looks like it is the best ...

**1**

vote

**0**answers

49 views

### coxeter element of a reflection group (reference request)

I am reading reflection groups and coxeter groups book by Humphreys. now I want to learn more about "coxeter element" of a reflection group. Can any body suggests me some good books to read more about ...

**1**

vote

**0**answers

101 views

### Continuous dependence of the roots of a polynomial on its coefficients

In their article "The roots of a polynomial vary continuously as a function of the coefficients" Garry Harris and Clyde Martin give a topological proof of the well-known theorem that the roots of a ...

**3**

votes

**0**answers

44 views

### Is the absolute of a compact space the projective limit of the Stone-Čech compactifications of its open dense subsets?

Is the following statement true, and if it is, does someone have a reference?
Let $X$ be a compact (i.e., compact and Hausdorff) topological space. Then the Gleason space (=Iliadis absolute, ...

**2**

votes

**1**answer

77 views

### Fractional Brownian motion via Hilbert space

The Brownian motion has the following (Levy-Ciesielski?) construction via Hilbert space isomorphisms:
Let $\{ Z_i \}_{i \in \mathbb{Z}}$ be i.i.d. $N(0,1)$ random variables defined on $(\Omega, ...

**0**

votes

**1**answer

93 views

### Open subset of the moduli space of stable sheaves on a noetherian scheme

This is my question:
Given a projective noetherian scheme $X$, the structural sheaf $\mathcal{O}_X$ is a coherent sheaf, so every locally free sheaf is coherent. This means that the family of stable ...

**3**

votes

**1**answer

310 views

### How to prove a Proposition of Rouquier?

Proposition 7.15 in Rouquier's paper (see Publication paper) "Dimension of triangulated categories J. K-theory, 1 (2008) 193-256" as follows, for details please see Rouquier's paper (or arXiv):
``Let ...

**3**

votes

**0**answers

207 views

### Is it possible to find explicit formula for the product $\prod_{d|n,\ d>1} (1-\mu(d)/\varphi(d))^{\varphi(d)}$?

I am trying to calculate the following product
$$
\prod_{d|n}_{d>1} \left( 1-\frac{\mu(d)}{\varphi(d)} \right)^{\varphi(d)}
$$
where the functions $\varphi$ and $\mu$ are Euler's totient and ...

**3**

votes

**2**answers

216 views

### Cohomology of the toric variety $X_\Sigma=\mathbb C^2\sqcup \mathbb C^2\big/\left((x,y)_1\sim(x^{-1},y^{-1})_2\right)_{x,y\neq 0}$

I'm writing a thesis on Chow rings of toric varieties and am looking for a reference on the singular cohomology ring of the blowup of $\mathbb C^2$ at xy=0, i.e. at the coordinate axes. The ...

**0**

votes

**0**answers

19 views

### Apply 'splitting' in regenerating codes in locally repairable codes

In network coding for distributed storage system, regenerating codes are known to exist only in theory due to its complex implementation in storage system. In the codes, 'splitting' is applied in the ...

**18**

votes

**1**answer

705 views

### A conjectured formula for Apéry numbers

A conjecture by the late Romanian mathematician Alexandru Lupas.
Posted in sci.math in 2005, but no proof was found.
Physicist Alan Sokal just reminded me of it, saying it was related to something he ...

**0**

votes

**0**answers

70 views

### Action of the (special) orthogonal group on differential forms

I was told that the following facts are true. I am looking for a reference to them.
1) The action of $O(n,\mathbb{C})$ on $\wedge^l\mathbb{C}^n$ is irreducible for any $l$.
2) The action of ...

**1**

vote

**1**answer

44 views

### invertible unbounded linear maps defined on a Hilbert space

It is well-known that, assuming the axxiom of choice, there are unbounded linear maps defined not only on a dense subset but on all of Hilbert space. Is it possible that such a map is invertible?

**2**

votes

**0**answers

138 views

### Bott's Formula for Grassmannians

Bott's Formula gives the dimension of the cohomology $H^{q}(\mathbb{P}^{n}, \Omega_{\mathbb{P}^{n}}^{p}(k))$ of the $k$-twisted sheaf of $p$-differential forms on the projective space ...

**0**

votes

**2**answers

106 views

### Terminology for beads/necklace/bracelet problem [on hold]

I'm new to mathoverflow but hopefully anyone here can point me in the right direction.
The problem is as follows, imagine you have 4 beads, lets give them numbers 1,2,3,4. Now I want the unique ...

**0**

votes

**0**answers

79 views

### How many possibilities would you have in an android lock pattern, always using all 9 moves? [migrated]

We are doing some research and wanted to know how many possibilities you would have if you would use all 9 dots/options in an (android) swipe lock pattern.
What would the formula be to get to this ...

**4**

votes

**3**answers

316 views

### In the category of sets epimorphisms are surjective - Constructive Proof?

The statement that surjective maps are epimorphisms in the category of sets can be shown in a constructive way.
What about the inverse?
Is it possible to show that every epimorphism in the category ...

**-6**

votes

**0**answers

54 views

### Let (A,≼A) and (B,≼B) be partially ordered sets. Define C = A×B and define the relation ≼ on C by (a,b)≼(a′,b′) ⇐⇒ (a≼A a′)∧(b≼B b′) [on hold]

Let (A,≼A) and (B,≼B) be partially ordered sets.
Define C = A×B and define the relation ≼' on C by (a,b)≼'(a′,b′) ⇐⇒ (a≼A a′)∧(b≼B b′).
(a) Prove that ≼' is a partial order on C.
(b) Prove that if ...

**4**

votes

**1**answer

142 views

### Endomorphisms of a maximal ideal of a local ring

Let $R$ be a commutative local ring with maximal ideal $\mathfrak{m}$. Is it true in general that $\text{Hom}_R(\mathfrak{m},\mathfrak{m})\cong \text{Hom}_R(\mathfrak{m}, R)$? What if the Krull ...

**-2**

votes

**0**answers

49 views

### Convergence of empirical random variable

Let $X$ be a RV on the real line, of probability measure $P_X$, and let $X_n$ for $n=1,...,N$ be an iid sample from $P_X$.
The Glivenko-Cantelli theorem says that the empirical measure, $P_N$, ...

**6**

votes

**1**answer

252 views

### Integer valued polynomial through some points with rational coordinates

I asked this question on MSE about 5 months ago, but, even after offering a bounty, I didn't receive any answer, I hope this question isn't too easy for MO.
If we have a set of points $(x_i,y_i)$ ...

**3**

votes

**1**answer

102 views

### A query about Hatcher flow on arc complex

In the paper "Triangulations of Surfaces" Hatcher proved that the arc complex associated to a punctured surface is contractible. The main proof is divided into two parts. In the first part he assumes ...

**5**

votes

**0**answers

108 views

### Applications of anabelian geometry to Galois representations?

One aspect of anabelian geometry is the study of the action of the absolute Galois group of a field $K$ on the etale fundamental group $\pi_1(X_\overline K)$, where $X$ is a (anabelian) variety and ...

**2**

votes

**1**answer

71 views

### What is the minimal girth of a cayley graph for Alt(n) in which the girth relator is not a proper power?

First, a definition: a girth relator for a Cayley graph is a word that you get by reading the edge labels along a shortest loop. The girth relator is not usually unique, though it is often unique up ...

**0**

votes

**1**answer

87 views

### Dimension of binary motives of a quadric

Let $Q$ be a anisotropic quadric of dimension $d$ over $k$.
We work in the category of effective Chow-Motives over $k$.
Let $T$ be the Tate-Motive.
For a motive $M$ we write $M(l)$ for its $l$-th ...

**2**

votes

**3**answers

197 views

### Generic absence of non-trivial first integrals of geodesic flows

Is it true that given a smooth manifold M (with or without boundary), a "generic" metric g on M does not possess any non-trivial (non-constant) first integral for the geodesic flow induced by g on the ...

**8**

votes

**1**answer

313 views

### Notion of infinity in categories

Please excuse me if the question is too vague or uninteresting.
Let $\mathcal{C}$ be a category and $A$ an object in $\mathcal{C}$. Motivated by the equivalence of Dedekind-finiteness and finiteness ...

**1**

vote

**1**answer

200 views

### pontryagin dual and maps between spectra

Given two spectra $A$ and $B$, the set $[A,B]$ of homotopy classes of maps from $A$ to $B$ forms an abelian group. Can the dual abelian group $\text{Hom}([A,B],\mathbb{Q}/\mathbb{Z})$ be expressed as ...

**3**

votes

**0**answers

51 views

### Prove that the maximizing point configuration on the unit circle for a Vandermonde like functional is a picket fence

This is probably too hard for math.stackexchange, so I migrated it here.
For $\lambda_i \in S^1 \subset \mathbb{C}$, consider the functional $H(\{\lambda_1, \ldots, \lambda_n\}):= \sum_{j < k} | ...

**3**

votes

**2**answers

111 views

### Build a topological polytope with a specified CW-structure

I am a topologist and not quite familiar with the tools for building a polytope. I would like to build some topological polytope which is an somewhere in between permutohedron and associahedron which ...

**-3**

votes

**0**answers

39 views

### Recurrence relation of degree 4 [on hold]

how to get the general solution of a recurrence relation degree 4 having repeated root r=2; for a characteristic equation of r^4-8r^3+24r^2-32r+16=0 where a(0)=1, q(1)=4, a(2)=44, a(3)=272.2?

**2**

votes

**0**answers

87 views

### Can the commuting condition in Jordan-Chevalley decomposition be replaced with this global criterion?

Let $G$ be a reductive linear algebraic group defined over an algebraically closed field $k$ of arbitrary characteristic, and write $\mathfrak{g}$ for its Lie algebra.
The Jordan-Chevalley ...

**5**

votes

**0**answers

314 views

### A group allowing exactly 7 group topologies

Is there a group $G$ allowing exactly 7 group topologies on $G$: $\mathcal T_{trivial}, \mathcal T_{discrete}, \mathcal T_1, \mathcal T_2,\mathcal T_3,\mathcal T_4, \mathcal T_5$ with
$$\mathcal ...

**4**

votes

**4**answers

819 views

### How short can we state the Axiom of Choice?

How short can we state a principle which is equivalent with the Axiom of Choice under $ZF$? The principle should be a sentence in the language of set theory with only $\in$ and$=$ as extralogical ...

**-5**

votes

**0**answers

61 views

### Squares in a square grid [on hold]

How many $n$ square $a \times a$ permutation are in a grid $b \times b$? (They must never overap themselves)
The question seems simple, but it isn't at all.

**1**

vote

**0**answers

51 views

### Pseudomodules, “general coherence theorem”

A pseudomonoid is defined within a monoidal bicategory. It is like a monoid in a monoidal category except that the usual axioms hold up to coherent invertible 2-cells. Pseudomonoid is like a monoidal ...

**-3**

votes

**1**answer

64 views

### How to find a modular multiplicative inverse when GCD is not 1 [on hold]

I am working on a problem that requires finding a multiplicative inverse of two numbers, but my algorithm is failing for a very simple reason: the GCD of the two numbers isn't 1. I figured I must've ...