# All Questions

**2**

votes

**0**answers

24 views

### Silver's unpublished work on reverse Easton iteration

Silver was the first person who used the method of reverse Easton iterations in connection with large cardinals, and used it to force the failure of $GCH$ at some measurable cardinal.
At most papers ...

**0**

votes

**0**answers

11 views

### Proof for a Rank-One Decrease procedure

I came across this result in a paper in my area concerning rank-one decompositions. However, I am unable to understand one of the steps. I am reproducing the result here.
Let $X$ be a $N\times N$ ...

**2**

votes

**0**answers

22 views

### $L^2$ discrepancy bound for sequences in $[0,1)$

Given a sequence $x_1,x_2,\dots$, let $D_n$ be the $L^2$-norm of the function $f_n$ whose value at $t \in [0,1)$ is $nt$ minus the number of $1 \leq i \leq n$ with $x_i \leq t$. What can be said ...

**0**

votes

**0**answers

26 views

### How to find the triple recursion formula for Laguerre polynomial [on hold]

How to find the triple recursion formula for Laguerre polynomial $L_n(x)$ of degree $n$
$$L_n(x)=\frac{1}{e^{-x} n!}\frac{d^n}{dx^n}\left[e^{-x} x^n\right] $$
$n\geq 0 \text{ with } ...

**0**

votes

**1**answer

55 views

### Dimension of Inverse image

Suppose we have a smooth map between two smooth manifolds $f:M→N$ such that $\dim M>\dim N$, and let $p∈N$ be a critical value. Suppose we know that $X:=f^{-1}(p)$ is a differentiable manifold (or ...

**3**

votes

**0**answers

41 views

### Measure estimates of a trigonometric polynomial

Let $\Omega =(0,\pi)\times (0,2\pi)$ and let $\psi:\Omega\to \mathbb{R}$ defined by $$\psi(x,t)=\sum_{k,j=1}^d a_{kj}\sin(kx)\sin(jt)+b_{kj}\sin(kx)\cos(jt),$$ where $\int_\Omega \psi^2 = 1$. Let ...

**0**

votes

**1**answer

97 views

### A question on degree 4 binary forms

Suppose that we have a binary form $f(x,y) \in \mathbb{Z}[x,y]$ of degree 4, and that we explicitly have
$$\displaystyle f(x,y) = a_0 x^4 + a_1 x^3 y + a_2 x^2 y^2 + a_3 xy^3 + y^4,$$
so that $(0,1)$ ...

**6**

votes

**0**answers

79 views

### Does $S^4$ have a “symplecto-homeomorphic” structure?

The 4-sphere $S^4$ cannot be a symplectic manifold. In particular, it does not admit an atlas whose transition maps are symplectomorphisms $(\mathbb{R}^4,\omega_0)\to(\mathbb{R}^4,\omega_0)$. A ...

**-1**

votes

**0**answers

82 views

### Learning math from the very beginning with no previous knowledge [on hold]

I didn't do any math like calculus, functions, vectors, etc, not even in high school. I want to build my math knowledge up from the ground up. A friend recommended that I start with Principia ...

**0**

votes

**0**answers

22 views

### L2 norm of a M-Whittaker function

Let $M_{\kappa,\mu}(z)$ be the Whittaker function, as defined here http://en.wikipedia.org/wiki/Whittaker_function.
Does any one know the evaluation of the following integral?
...

**1**

vote

**0**answers

25 views

### on reductive monoids which are gorenstein

Let $M$ a reductive monoid, i.e. a integral normal affine scheme, which is a monoid whose group of units is a connected reductive group.
By Rittatore ...

**0**

votes

**0**answers

43 views

### Sum or difference of modulus of holomorphic functions [on hold]

Assume that $f$ and $g$ are two holomorphic functions defined in the unit disk. If $$|f|^2-|g|^2\equiv 1$$ or $$|f|^2+|g|^2\equiv 1,$$ then it seems that $f$ and $g$ are constants. How to prove this.

**5**

votes

**3**answers

123 views

### Does this property of a first-order structure imply categoricity?

Let $\mathfrak{A}$ be a first-order structure over a relational language and let $\kappa$ be an infinite cardinal. Lets say that $\mathfrak{A}$ has the $\kappa$-property if for every structure ...

**1**

vote

**0**answers

19 views

### Possible ways to create a graph representation from a distance matrix (through approximation)

Forgive me, Im not math professional, but a computer scientist at the beginning of my base research from my thesis, so bare with me if I miss something blatantly obvious.
I have a Euclidean distance ...

**-5**

votes

**0**answers

95 views

### Theory of mnemonics [on hold]

Even for the typical most skilled (human) number theorist it is hard to reproduce only the first 10 digits of $\pi$ in moderate speed (without physically reading them off).
On the other hand there ...

**0**

votes

**0**answers

42 views

### Is there any nonnegative bounded function satisfying the following property? [on hold]

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 ...

**5**

votes

**0**answers

184 views

### Group structure on an arbitrary completely regular topological space that makes $(x,y)\mapsto xy^{-1}$ continuous at $(1,1)$

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 $(1,1)$?

**1**

vote

**0**answers

35 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 ...

**5**

votes

**1**answer

232 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

27 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

72 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

168 views

### Use a graphic tablet to write in Latex or MathML [on hold]

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

45 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**

votes

**0**answers

90 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 ...

**1**

vote

**1**answer

84 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?

**12**

votes

**1**answer

296 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

88 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

80 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

97 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 $\forall \vec{a} \in \mathbb{Q}^{m}$,
...

**0**

votes

**0**answers

36 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

22 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**

votes

**0**answers

41 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

26 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 ...

**9**

votes

**0**answers

101 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 ...

**6**

votes

**3**answers

312 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

147 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

53 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

66 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 $I$ ...

**6**

votes

**0**answers

163 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**

votes

**0**answers

18 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

103 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 $\mathbf{x_0}$:
$$
...

**0**

votes

**0**answers

49 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

138 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

47 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 ...

**-9**

votes

**0**answers

264 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

272 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

**2**answers

128 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

41 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 )