# All Questions

**1**

vote

**1**answer

47 views

### A metric associated with a continuous surjective map $f:X\to Y$

Assume that $f:(X,d_{1})\to (Y,d_{2})$ is a continuous surjective map between compact metric spaces. We define another
metric $d_{f}$ on $Y$ With $$ d_{f}(a,b)=Hd(f^{-1}(x), f^{-1}(y))$$ ...

**1**

vote

**0**answers

19 views

### Characterizing the real analytic Eisenstein series

Consider the classical real analytic Eisenstein series
$$
E(z,s)=\sum_{(m,n)\neq(0,0)}\frac{y^s}{|mz+n|^{2s}},
$$
where $z=x+iy$. We think of $E(z,s)$ as a function on ...

**0**

votes

**0**answers

27 views

### Zero-mean assumptions concerning r.d.'s when reading graduate-level probability texts

I'm reading through T. Taos book on random matrices (to be found here), and it is frequent to make without-loss-of-generality certain reductions when proving theorems as for example Hoeffdings ...

**0**

votes

**1**answer

28 views

### Nagakami behavoir

Is the sum of square Nagakami random variables Erlang distributed?
What is the distribution of euclidean norm of complex Nagakami?
Cheers!

**0**

votes

**0**answers

14 views

### Help in finding distribution of the following function of random variable

Let $X_1$ and $X_2$ be independent complex Gaussian random variables, $$X_1 \sim \mathcal{CN}(0,\sigma)$$
$$X_2 \sim \mathcal{CN}(0,\sigma)$$
If $X= aX_1 + bX_2$ where $a,b$ are constants then the ...

**-3**

votes

**0**answers

32 views

### What is induction to n^(n-1) >= n! for n=9,10 [on hold]

Can somebody help me? How do I prove n^(n-1) >= n! for n=9,10..... by induction?

**2**

votes

**0**answers

51 views

### A homological criterion for collapsibility?

On page 256 of Kirby and Siebenmann one finds the following lemma (its proof an "elementary exercise", so they only give a hint):
Taking $A$ to be a point and iterating this collapsing lemma, this ...

**4**

votes

**1**answer

192 views

### Parity of primes [duplicate]

While working on a completely different (combinatorial) problem, I ran a simple program to calculate the parity of the first ~50000 primes (number of 1s in their binary representation modulo 2). The ...

**1**

vote

**1**answer

20 views

### Are sums of 0-1 Pareto efficient vectors Pareto efficient?

Suppose we have a (not necessarily square) matrix $A$ whose entries are $\in \{0, 1\}$, and for all pairs of columns $x, y$ the entries of $x - y$ are either all non-negative or all non-positive. Then ...

**5**

votes

**1**answer

157 views

### Dimension of Hilbert scheme?

I have a subvariety $V \subset X$, and I want to compute the dimension of the connected component of $\textrm{Hilb}(X)$ containing $[V]$.
I can give explicit deformations of $V$ showing that the ...

**0**

votes

**0**answers

34 views

### Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute?

Specifically, are there "nice" (ie, not too obscure or contrived) examples of families of objects, where say for each objects $A,B,C$ in the family, the canonical isomorphism from $A\rightarrow C$ is ...

**0**

votes

**0**answers

45 views

### Spectral sequence and HOM functor

I work with the category $A-{\rm Mod}$ of left modules over a unital ring $A$, but I could ask the same question for any abelian category with enough projectives. Let $M$ and $N$ be two $A$-modules ...

**0**

votes

**0**answers

23 views

### Number of graphs with n vertices and k edges up to isomorphy [duplicate]

Is there a way to figure out the number of individual graphs with n vertices and k edges up to isomorphy?
I'm particularly looking at graphs with:
n = 25, k = 50
n = 50, k = 170
n = 100, k = 700

**0**

votes

**0**answers

27 views

### Rate of convergence in narrow convergence

Does anyone help me in the following question?
I have a sequence of probability measures $\mu_n$ and know that $\mu_n$ converges narrowly to a probability measure $\mu$. Is there any way to estimate ...

**0**

votes

**0**answers

10 views

### Bounding a function pointwise from bound on the expectation [migrated]

Suppose we have a Lipschitz continuous positive function with bounded expectation Eg < a. What can be said about the point-wise bound ?

**2**

votes

**0**answers

95 views

### What are the minimal degrees of the real and imaginary part of an algebraic complex number?

Let $z=a+bi\in\mathbb C$ with $b\ne0$ be an algebraic complex number of minimal degree $n$. It is obvious that $a=\dfrac {z+\bar{z}}2$ and $b=\dfrac {z-\bar{z}}{2i}$ are also algebraic. For $n=3$, it ...

**-7**

votes

**0**answers

75 views

### An alternative Generalization of The Riemann Zeta Function [on hold]

If we consider the Riemann Zeta Function as follows
$$\zeta(s)=\underset{n=1}{\overset{\infty}{\sum}}\cfrac{1}{n^{s}}=\cfrac{1}{1^{s}}+\cfrac{1}{2^{s}}+\cfrac{1}{3^{s}}+\cdots.$$
could we generalize ...

**1**

vote

**0**answers

51 views

### Finitely co/continuous monad induced by an operad

It is well known that any operad on a nice monoidal category induces a monad.
I was wondering which conditions can be imposed on the operad $T$ (say, in a monoidal closed $\cal V$) so that the ...

**1**

vote

**0**answers

97 views

### What is God's number for the WrapSlide puzzle?

WrapSlide is a slide-puzzle (reminding of Rubik's Cube) consisting of a 6x6 grid of coloured tiles which are separated into four quadrants of 3x3 tiles. When it is unmixed all the tiles in a quadrant ...

**-4**

votes

**0**answers

23 views

### First-order nonlinear ordinary differential eqauation [on hold]

can someone help me to solve this equation? I have been trying a few methods. Thanks.
y'=(y/x)*((xy + 1)/(xy - 1))

**1**

vote

**1**answer

40 views

### Wave equation with linear coefficients

The following pde came up in a physics problem:
$$
(Cy+D)\frac{\partial^2 u}{\partial x^2}-(Ay+B)\frac{\partial u^2}{\partial y^2}-A\frac{\partial u}{\partial y} =f(x,y),
$$
A,B,C,D are fixed ...

**-2**

votes

**0**answers

33 views

### T is not compact operator [migrated]

I want to show that if $T$ is a bounded operator between two Hilbert spaces and $T$ is not compact then there exists an orthonormal sequence $y_{n}$ and an $R>0$ such that $\forall n\in ...

**-3**

votes

**0**answers

32 views

### Find the integral [on hold]

How can we find the integral of the 1/(1+x^4) in the interval -infinity to +infinity.I tried to find and got it to be pi/sqrt(2). Am I correct? Please help me with an appropriate method. I tried to ...

**3**

votes

**1**answer

96 views

### When are all sums of the elements of a set different?

Consider a set $S = \{x_1, \dots, x_n\} \subset \mathbb{Q}\setminus\{0\}$ and assume that for any $I, J \subset [n]$ with $I \neq J$ we have that
\begin{equation}
\sum_{i \in I} x_i \neq \sum_{j \in ...

**1**

vote

**0**answers

19 views

### Recognizing bridgeless cubic graph with special 2-factor

A 2-factor of graph $G(V, E)$ is a set of vertex-disjoint cycles that cover $V$. It is known that every connected bridgeless cubic graph contains a 2-factor (and a perfect matching).
I conjecture ...

**6**

votes

**2**answers

108 views

### Painting $n$ balls from $2n$ balls red, and guessing which ball is red, game

The game
Lucy has $2n$ distinct white colored balls numbered $1$ through $2n$. She picks $n$ different balls in any way she likes, and paint them red. She then giftwrap all the balls so that it is ...

**0**

votes

**0**answers

52 views

### What is the difference between the moduli space of curves and the moduli space of orbi-curves?

I feel that I should already know the answer to this, but it never sits quite right in my head. Let's look at something relatively concrete.
One way you can look at the moduli of hyperelliptic curves ...

**1**

vote

**1**answer

105 views

### Does Schur's Lemma hold in this case? Regular representations of $S_n$ over $\mathbb R$

Warning I am a physicist and I am not familiar with a lot of the machinary of representation theory.
I consider the regular representation of $\mathbb S_n$ over reals $\mathbb R$ ($\mathbb R \mathbb ...

**1**

vote

**0**answers

40 views

### Looking for the manuscript “Uniform polytopes” by N. Johnson

The manuscript Uniform Polytopes (1991) by Norman Johnson is cited in the wikipedia page on uniform polytopes (http://en.wikipedia.org/wiki/Uniform_polytope).
Is there an electronic copy of this ...

**0**

votes

**0**answers

14 views

### Intuitive explanation of multi-objective optimization of $z = (1-x) \times (1-y)$

I have managed to reduce an optimization problem in the domain of distributed systems into the following formula:
$$
\Gamma = (1-\varepsilon_\alpha) \times (1-\varepsilon_\beta)
$$
in which both ...

**0**

votes

**0**answers

10 views

### Functional representation of adapted jointly measurable stochastic processes

It seems like the question stated here in MSE has no answer yet and seems therefore for me to be not of a basic question type. For this reason I move it to MO.
Let $X_t : \Omega \to E, \ t \geq 0$ be ...

**5**

votes

**1**answer

156 views

### Meaning of $g_d^r$ in algebraic geometry

As an editor I often encounter the symbol $g_d^r$ as a noun. I tried googling but I only get papers where the symbol is used without a definition. Can someone supply a reference to a definition? ...

**0**

votes

**0**answers

18 views

### Projective dimension of a sub-ideal

Let $\mathbf{k}$ be a field, and let $S=\mathbf{k}[x_1,x_2,\ldots,x_n]$. Let $I\subset J$ be finitely generated monomial ideals in $S$. Is it true that the projective dimension of $I$ is either ...

**0**

votes

**0**answers

43 views

### K-Permutations with forbidden numbers [on hold]

This question has some references to programming and not as many mathematical terms as you might like, but I think it's more appropriate in a mathematics forum.
Introduction (Skip if you are ...

**6**

votes

**1**answer

100 views

### Which finite p-groups occur as commutators of finite p-groups?

Let $p$ be a prime number. For which finite $p$-groups $H$ there is a finite $p$-group $G$ such that $[G,G] \cong H$?

**-1**

votes

**0**answers

35 views

### maximal abelian subgroup [on hold]

let M(G) denote the set of orders of maximal abelian subgroups of G. If M(G) = M(H), for some group H then what can we say about the prime numbers that divide the order of each group G and H?

**4**

votes

**1**answer

103 views

### “Inverse problem” for the zeta function [duplicate]

Let $C$ be a smooth, projective, geometrically irreducible curve, of genus $g$, over a finite field $\mathbb{F}_q$. By the Weil conjectures, the zeta function has the shape
$$
...

**8**

votes

**1**answer

926 views

### How can I have a copy of this old paper by Frobenius?

How can I have a copy of this old paper and a translation of it?
Frobenius, G. (1902). Uber primitive Gruppen des Grades n und der Klasse n - 1. S. B. Akad. Berlin 1902, 455-459.

**5**

votes

**1**answer

163 views

### What does the sum of the reciprocals of all the highly composite numbers converge to?

I've calculated the sum of the reciprocals of all the $156$ first highly composite numbers up to $10^{18}$:
$\sum \dfrac{1}{HCC(n)} = \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{6} + \dfrac{1}{12} + ...

**10**

votes

**13**answers

1k views

### Obscure Names in Mathematics [on hold]

I recently stumbled over the "Happy Ending Problem" (cf e.g. http://en.wikipedia.org/wiki/Happy_Ending_problem), which made we wonder, if there are other conjectures, theorems or problems, whose names ...

**1**

vote

**0**answers

48 views

### Uniqueness of the maximum derivative of a rational function

This may seem like an elementary question, but bear with me; you'll find that it is actually quite hard. Consider the function
$$f(x)=\frac{a_nx^n}{\sum_{i=0}^n a_ix^i}$$
with all $a_i\geq 0$ and ...

**1**

vote

**2**answers

75 views

### Deformation quantization of a closed Riemann surface with genus >1

Quantization of of an elliptic curve can be done in different ways.
In C^*-algebraic version,
one can start with the C^*-algebra ...

**-2**

votes

**0**answers

43 views

### Proving how many divisors of a prime factorization (including 1 and n) there are [on hold]

I'm trying to figure out this problem but I'm not sure where to start. Could anyone explain to me the question a bit more in depth or give a few hints?
The problem is,
Let n in Z+ with prime ...

**0**

votes

**0**answers

18 views

### Comparing the inverse of a diagonally dominant matrix [migrated]

I have a $d \times d$ matrix $A$ whose entries are bounded (C1): $I - \epsilon X \preceq A \preceq I + \epsilon X$, where $I$ is the identity matrix and $X = 11^\top - I$ is the matrix with ones ...

**-4**

votes

**0**answers

25 views

### How to know which make which surjective and which Tor is correct to represent them surjective for codordism [on hold]

when A connect B through cobordism
A --- cobordism ----B
from view of function, when define surjective
there exist a function g to make f surjective such that g ...

**-2**

votes

**0**answers

87 views

### Is the configuration space of infinite sphere contractible?

Let $\Sigma$ be suspension.
Let $S^0$ be $0$-sphere.
Let $\Sigma^\infty S^0$ be the union $\cup_n \Sigma^n S^0$ with respect to the inclusion $\Sigma^kS^0\subset \Sigma^{k+1}S^0$.
Let ...

**18**

votes

**1**answer

320 views

### Making $\mathbb{Q}$-cohomology integral

Let $X$ be an algebraic variety (say, smooth and projective) over $\mathbb{C}$, and fix $$\alpha\in H^i(X^{\text{an}}, \mathbb{Q})$$
with $i>0$.
Does there always exist a variety $Y$ and a ...

**-1**

votes

**0**answers

16 views

### state of art pseudo-boolean optimization solver [on hold]

I am actually constructing engineer application based on pseudo-boolean optimization. I want to ask what is the current status (how many variables, interaction parameters) the solver could generally ...

**0**

votes

**0**answers

161 views

### A problem of a hacked article [on hold]

I am surprised by the fact that a journal published an article that I have in arxiv for a few months. The date of publication is after the date that I have in arxiv. The submission date in the ...

**3**

votes

**2**answers

272 views

### Intuition behind $\zeta(2) = \frac{\pi^2}{6}$ [on hold]

In literature, there are many proofs of the well-known result $$\zeta(2) = \frac{\pi^2}{6}.$$
However, as far as I know, they do not offer an intuitive explanation of why this result should be true. ...