# All Questions

**0**

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3 views

### Is there any nonnegative bounded function satisfying the following property?

Is there a smooth funtion $f(r)$, $r\geq 0$, satisfying the following property: $0\leq f(r) \leq c$, $\int^{\infty}_{r_0}\frac{f(r)}{r}dr<\infty$ for some $r_0>0$, and there exists an sequence ...

**0**

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13 views

### Generality of topologies on groups with $(x,y)\mapsto xy^{-1}$ continuous

Let $(G,\mathcal T)$ be a completely regular topological space. Is there a group structure on $G$ such that the function
$$f:G\times G\to G$$
$$f(x,y)=xy^{-1}$$
is continuous at $(1,1)$?

**0**

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**0**answers

14 views

### Why does $\pi_t$ preserve pullbacks in this special case?

Let $X$ be a fibrant pointed cosimplicial space.
Following Bousfield-Kan, let $\text{lim}^{\partial \Delta_{n+1}} X = M^{n}X$ be the nth matching object of $X$. Onecan then show that there is a ...

**2**

votes

**1**answer

33 views

### A “good scale” that is not really a scale

I don't know much about singular cardinal combinatorics, so I apologize in advance if I write something that is wrong or looks funny. First let me recall some basic definitions.
Let $\lambda$ be a ...

**0**

votes

**1**answer

17 views

### Error on parity bits of Reed-Solomon error correction code

I'm trying to figure this out but it seems never to be covered in articles explaining Reed-Solomon codes. If I have a string with 64 characters (bytes) and 4 parity bytes for error checking and ...

**2**

votes

**2**answers

33 views

### Which criteria guarantee an orthogonal circuit in $\mathbb R^3$ to be rigid?

For $n\ge4$, define an orthogonal circuit or O-circuit as a closed circuit of $n$ unit segments in $\mathbb R^3$ such that any two neighboring segments form a right angle. (Physically this could be ...

**3**

votes

**1**answer

119 views

### Use a graphic tablet to write in Latex or MathML

I have a Graphic Tablet and I am looking for a software which have the following features:
Math equation recognition I want to write and solve math equations in Graphic Tablet and auto recognized to ...

**3**

votes

**1**answer

23 views

### Uniformly permutation and the length of a size biased cycle

The cycle containing $1$ of a uniform permutation has length which is uniformly distributed. I was wondering if the converse is true:
Suppose $\sigma$ is a permutation on $\{1,\dots,n\}$ and let ...

**0**

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**0**answers

72 views

### q-th powers and roots of polynomials

Let $p,q,r$ be integers with $r\ge2$; let $f$ be a polynomial of the form $f(X) = g((X+1)^r)$, which is not a $q$-th power. Let $\omega$ be a $p$-th root of unity.
Show that the polynomial ...

**0**

votes

**0**answers

23 views

### Largest eigenvalue of the sum of hermitian matricies

Is there an expression for the largest eigenvalue of the sum of two hermitian matricies in terms of the spectrum of the same matricies?

**7**

votes

**1**answer

111 views

### Vanishing eigenvalues of Jacobian

Let $f: \mathbb{R^2}\to \mathbb{R^2}$ be a Schwartz function. If the eigenvalues of $Df$ vanish everywhere, must $f$ be constant? Does an analogous result hold when we replace $2$ by $n$?
Any ...

**-2**

votes

**0**answers

74 views

### Mathematics of volleyball [on hold]

I'm working on a mathematical model that should calculate probabilities of various things in the game of volleyball and I thought it might not be a bad idea to see if there is already some research on ...

**3**

votes

**1**answer

25 views

### Are there superexponential Pfaffian functions?

This question is motivated by model theory, but it's really an analysis question (which means it may have an easy analysis answer that I just don't have the background for). Here's the main question, ...

**-2**

votes

**0**answers

39 views

### Example of a not tight family of delta measures with bounded support on $\mathbb R$

I am looking for an example of a not tight family of (Dirac) delta measures on $\mathbb R$ where their supports are bounded.

**1**

vote

**0**answers

82 views

### Rational map and diophantine sets

A subset $A$ of $\mathbb{Q}^m$ is a diophantine set over $\mathbb{Q}$ if there is $P(\vec{a},\vec{x}) \in \mathbb{Q}[a_1,...,a_m,x_1,...,x_n]$ such that $\forall \vec{a} \in \mathbb{Q}^{m}$,
...

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**0**answers

22 views

### Repeatedly changing queue behavior

I'm not sure if this question is suited to MO. I will happily delete if not.
Situation
Consider a general queueing system $\mathscr{S}$, whose customer arrival times are independent, and whose ...

**1**

vote

**0**answers

18 views

### Semi-simple controlling operator

I've just come across this paper by Coleman and Edixhoven called "On the semi-simplicity of the $U_p$ operator on modular forms", where (as the title says) they show that the $U_p$ operator is ...

**0**

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33 views

### breadth of a ﬁnite p-group

The breadth of an element $x$ in a ﬁnite $p$-group G is deﬁned to be that integer $b = br(x)$ such that $p ^b = |G : C_ G (x)|$, while the breadth $br(G)$ of $G$ is the
supremum of $\{br_ G (x) | x ...

**1**

vote

**0**answers

17 views

### Are the integer index finite depth irreducible subfactors Kac-coideal?

Is it known whether or not the integer index finite depth irreducible subfactors (planar algebra) are Kac-coideal subfactors: $(R^{\mathbb{A}} \subset R^{\mathbb{I}})$, with $\mathbb{A}$ a finite ...

**7**

votes

**0**answers

79 views

### What is the geometric fixed points of an (equivariant) Eilenberg Maclane Spectrum?

The following was posted to math.stackexchange to no avail: http://math.stackexchange.com/questions/908756/an-exercise-in-homology-computation-what-is-the-geometric-fixed-points-of-an-e
The question ...

**5**

votes

**3**answers

222 views

### Ore's Conjecture for perfect groups

We know that Ore's Conjecture is a theorem now. Does anyone know a counterexample to Ore's conjecture for perfect groups? I believe there should be one, but I dont have a counterexample. Thanks.

**1**

vote

**2**answers

142 views

### Taking matrix derivative with MATLAB or Wolfram Alpha [on hold]

I want to take the derivate of a rather complicated matrix expression. Is it possible to do this in MATLAB or Wolfram Alpha? Here is what I am trying to calculate:
\begin{equation}
\frac{\partial}{ ...

**0**

votes

**0**answers

51 views

### The trivility of Besov space for large parameter

For all $s>0$, $1\le p<+\infty$ and $u\in L^p(\mathrm{d}x)$, we define
$$D_{s,p}(u)=\sup_{r>0}\frac{1}{r^{sp+n}}\int_{\mathbb{R}^n}\int_{B(x,r)}|u(y)-u(x)|^p\mathrm{d}y\mathrm{d}x$$
and
...

**0**

votes

**0**answers

20 views

### Formula for Value of Games Without Saddle Points [on hold]

I've read that the value of a game with payoff matrix
[ a b ]
[ c d ]
that has no saddle points is
(ad − bc)/(a + d − b − c).
Does anyone know what the general ...

**0**

votes

**0**answers

60 views

### Bounds for Betti numbers

Why the graded Betti numbers of ideal $I \subset k[x_1 , \cdots , x_n]$, are bounded by the graded Betti numbers of $\mathrm{gin}(I)$?
(Where $\mathrm{gin}(I)$, is the generic initial ideal of $I$ ...

**5**

votes

**0**answers

140 views

### Geometric meaning of the black hole horizon

It is widely accepted that the singularity of the Schwarzschild metric at the event horizon is purely an artifact of the coordinates and no physical singularity exists at the horizon. However, as ...

**0**

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**0**answers

16 views

### Appropriately choosing the parameter so that one function maximizes while other minimizes

Suppose we have two functions $f$ and $g$ of some variables $x,y,z\in R$. Our goal is to appropriately choose the values of $x,y,z$ such that $f$ is maximized while $g$ is minimized.
Here, I am not ...

**4**

votes

**1**answer

92 views

### In a Simplicial group the Degenerate elements don't intersect the kernel of the face maps.

Let $G_{\bullet}$ be a simplical group. I denote by $D_n \subset G_n$ the subgroup generated by all the degeneracy maps $s_i:G_{n-1} \to G_n$.
I also denote $$M_n = \bigcap_{i>0} \mathrm{Ker} d_i ...

**0**

votes

**0**answers

30 views

### Sign of Laplacian in a N-Dimensional Space Under Other Specific Conditions

Consider that $f: \mathbb{R}^N \to \mathbb{R} $ is infinite times differentiable and is smooth over the entire domain. Take $N$ to be large. Also at point $\mathbf{x_0}$:
$$
...

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votes

**0**answers

44 views

### numerical and functional mixed optimization problem $\max f - \min f +\int_{-1}^1 (f'(x)-x)^2dx$

Given a function $g(x)$ and its domain, we want to get another function $f(x)$ whose derivative is approximately $g(x)$, but so that $f(x)$ itself has small variation. For example, for ...

**2**

votes

**0**answers

124 views

### The topology of the classifying space of U(n)

In $\textit{Atiyah and Bott: The Yang-Mills equations over riemann surfaces}$, there is a sentence about the topology of BU(n) (i.e. the classifying space of U(n)):
Here $K(\mathbb{Z},n)$ means the ...

**1**

vote

**0**answers

44 views

### Method used in fmincon() of Matlab? [on hold]

We are using the Matlab optimization toolbox function fmincon() to solve a constrained minimization with only equality constraints. We wish to find out which particular constrained optimization method ...

**-8**

votes

**0**answers

235 views

### Who know about Rumek proof [on hold]

Rumek has actually shown that the usual ZFC axioms
for mathematics are in fact
inconsistent. For example, Rumek has been able to prove from the ZFC
axioms that both 2+2 = 4 and 2+2 = 5.
...

**3**

votes

**2**answers

261 views

### Aspheric functors and Grothendieck fibrations

Following Grothendieck, let us say that a category is aspheric if its nerve is weakly contractible and a functor $u : \mathcal{A} \to \mathcal{B}$ is aspheric if for every object $b$ in $\mathcal{B}$, ...

**5**

votes

**1**answer

101 views

### Are Anderson $T$-motives motives for the function field analogy?

this question is related to this one Geometry for Anderson's motives?, though the previous one doesn't answer exactly my question.
Let $\mathbb{C}_{\infty}$ be the function field analog of ...

**-5**

votes

**0**answers

36 views

### Calculus question on limts [on hold]

Can't solve this algebraically. Answer would be greatly appreciated. Thanks.
lim x->0 ( ( (sin^2 x)(1-cos x) ) / 2x^4 )

**3**

votes

**0**answers

30 views

### Ferenczi: minimal, uniquely ergodic, sublinear complexity systems are not strongly mixing

The following result is on page 26 of this paper by Ferenczi [PDF].
Corollary 3. A minimal and uniquely ergodic system of sub-affine complexity cannot be strongly mixing (i.e., $\mu(T^nA \cap B) ...

**-4**

votes

**0**answers

70 views

### Free groups and varietal product [on hold]

I will be so thankful if some one help me.
My knowledge in free group is not deep.
Suppose $S$ is the variety of p-groups of class at most 2 and exponent p.
Question one) For any $n$, is there a ...

**2**

votes

**0**answers

49 views

### Internal categories in an endofunctor category

Here we see the definition of an internal category in a monoidal category. We also know that endofunctor categories support a monoidal product which is actually functor composition. It is the case ...

**-1**

votes

**0**answers

12 views

### 3D Vector projection on a Plane [migrated]

I want to Project a Vector on to a Plane. Assume, you have a Central Point (1,1,1) and you want to move (0,0,3) in z-direction. How can I project the end of this movement (point) on a plane with ...

**-5**

votes

**0**answers

118 views

### What books I have to study to get into Riemann hypothesis (from almost zero) [on hold]

Could anyone help me with my own self-learning process to get in Riemann hypothesis from the level of 1st year of technical Bsc college? What minimal number of books (and which one) I have to study to ...

**1**

vote

**0**answers

53 views

### Are all complex zeros of $Li_s(i)\, + \, Li_{1-\overline{s}}\,(-i)$ equal to the $\rho$'s?

Take the well known square relationship for polylogarithms:
$$Li_s(z)\, + \, Li_{s}(-z)=2^{1-s}Li_s(z^2)$$
Assume $z=i$:
$$Li_s(i)\, + \, Li_{s}(-i)=2^{1-s}Li_s(-1)=-2^{1-s}\,\eta(s)$$
with ...

**0**

votes

**0**answers

107 views

### excess intersection theory

Can the excess intersection theory be applied to the following problem:
I have a non-singular irreducible variety $X$ of dimension $k$ and degree $d$ and $k+1$ hyperplane sections of $X$, ...

**18**

votes

**1**answer

268 views

### Is fixed point property for posets preserved by products?

Recall that a Partially Ordered Set (poset) $P$ has the fixed point property (FPP) if any order preserving function $f:P\longrightarrow P$ has a fixed point.
Theorm : Suppose $P$ and $Q$ are posets ...

**1**

vote

**0**answers

42 views

### What are the first non-maximal non-group-subgroup simple subfactors?

Definition: For an irreducible (finite index) subfactor $(\mathcal{N} \subset \mathcal{M})$, an intermediate $(\mathcal{N} \subset \mathcal{P} \subset \mathcal{M})$
is normal if the biprojections ...

**0**

votes

**1**answer

48 views

### Schur norm for self-adjoint operators

If $A$ is a $n \times n$ complex matrix then the Schur norm of $A$ is given by $$ || A||_S := \max_{||B||=1} ||A*B||,$$ where $||. ||$ is the operator norm and $*$ is the Hadamard (entry-wise) ...

**1**

vote

**0**answers

41 views

### The relation on the set of functions

Let $\varphi: \mathbb{R}^{2} \to \mathbb{R}$ be a symmetric (not necessarily continuous) function (so, $\varphi(x,y)=\varphi(y,x)$ $\forall (x,y)\in \mathbb{R}^{2}$),
let $\mathcal{F}$ be the set of ...

**9**

votes

**1**answer

153 views

### Finite subgroups of mapping class groups

Given a closed, oriented surface $\Sigma$ of genus greater than 1, let $Mod(\Sigma)$ denote the mapping class group of orientation preserving diffeomorphisms of $\Sigma$ up to isotopy. Given any ...

**6**

votes

**1**answer

67 views

### $RUCar^{V}$-semiproperness implies properness

This is a claim in Shelah's Proper and Improper Forcing, more specifically Claim 2.3(1) of Chapter X (p. 484). The proof of the claim is "Easy" but I cannot quite figure it out. There must be some ...

**3**

votes

**1**answer

110 views

### Optimal lower bounds for the sum of digits in base $b$

Let $b \geq 2$ be an integer and let $s_b(n)$ be the sum of the digits of the base-$b$ representation of the nonnegative integer $n$
(e.g., $s_{10}(726)=7+2+6$). From the weak law of large numbers, it ...