**0**

votes

**0**answers

1 view

### Are there other nontrivial integer solutions to the equation $9x^3 -1 = y^3$ besides $(x,y) =(1,2)$?

Does the above Diophantine equation have other nontrivial integer solutions besides $(x,y)=(1,2)$ ?

**2**

votes

**0**answers

35 views

### Is it possible to make an algorithm that could predict the likelihood that a program will halt?

Today I began to read about computability theory. I do not even have an elementary understanding of the topic but it certainly got me thinking. I know there is there is no 'one-for-all' algorithm that ...

**5**

votes

**0**answers

25 views

### Fundamental units with norm $-1$ in real quadratic fields

If we have distinct primes $p \equiv q \equiv 1 \pmod 4,$ with Legendre $(p|q) = (q|p) = -1,$ there is a solution to $u^2 - pq v^2 = -1$ in integers and the fundamental unit of $O_{\mathbb ...

**0**

votes

**0**answers

11 views

### Examples of real orbits with irrational period

Im looking for examples of periodic orbits on the real line given by piecewise analytic functions $g$.
More specific at most 2 pieces.
Im talking about integer iterations starting at $f(0)=0$ and with ...

**8**

votes

**2**answers

157 views

### What are the implications of the simple loop conjecture?

Drew Zemke recently posted a preprint on arXiv proving the Simple Loop Conjecture for 3-manifolds modeled on Sol.
Simple Loop Conjecture: Consider a 2-sided immersion $F\colon\, \Sigma\rightarrow ...

**0**

votes

**0**answers

51 views

### Problem related to Frobenius coin problem

Call a pair of integers $a,b\in\Bbb N$ with $\mathsf{gcd}(a,b)=1$ a good coprime pair if
$$ax+by=rs\mbox{ and }ax'+by'=tu\mbox{ for some }r,s,t,u,x,y,x',y'>0$$
$$\implies \mbox{} av+bw=ru\mbox{ and ...

**-6**

votes

**1**answer

38 views

### Simple bimodule over matrix ring [on hold]

Let given not trivial simple $R$- $R$ bimodule $M$, where $R$ - $n\times n$ matrix algebra over field $\mathbf{F}$. Is it true that $M$ is uniquely defined?

**-1**

votes

**0**answers

41 views

### Does this product over primes converge for all non-principal Dirichlet Characters for $\Re(s) > \frac12$?

I like to expand on this this question:
Numerical evidence suggests that the following product over primes ($p$):
$$\displaystyle F_n(s):= \prod_{p}^\infty ...

**1**

vote

**0**answers

15 views

### Positivity of semiclassical pseudodifferential operators

Let me first give some background. (My reference is Martinez's book An introduction to semiclassical and microlocal analysis)
Let $m\in\mathbb{R}$, and ...

**6**

votes

**2**answers

142 views

### Spectrum of Ring of Smooth Functions on $\mathbb{R}^n$

When we define smooth manifold, we starting with topological space $M$ which localy homeomorphic to $\mathbb{R}^n$ and setting up sheaf $\mathscr{F}(M)$ of functions on it which localy isomorphic to ...

**0**

votes

**0**answers

232 views

### Has this paper on the Tate-Shafarevich conjecture been peer-reviewed? [on hold]

It seems to be an "attempt" at serious research, but it strikes me as odd is that nobody seems to be using the result:
http://arxiv.org/abs/1309.7675

**0**

votes

**0**answers

42 views

### Regarding a new divergence function of two probability distributions

Let $X$ and $Y$ be two continuous random variables with common support and with PDF $f(x)$ and $g(y)$. For any constant $b$ with the support of $X$ and $Y$, and any constant $0 \leq \alpha \leq 1$, ...

**3**

votes

**1**answer

102 views

### Is there a description of variation of (mixed) Hodge Structures in terms of a Deligne operator?

A complex Mixed Hodge Structure is given by a complex vector space $V$ together with a descending filtration $W$ and two ascending filtrations $F,\bar{F}$ that satisfy the condition
\begin{equation}
...

**0**

votes

**0**answers

30 views

### Random process & probability problem met in wireless communication

A random process r obeys the following distribution:
$p(r,ṙ)=rb_0\exp(−\frac{r^2}{2b_0})\sqrt{2πb_2}exp(−\frac{\dot{r}^2}{2b_2})$, where $\dot{r}$ is the derivative of r in the time domain.
You can ...

**2**

votes

**0**answers

34 views

### Geometric unfolding of a difference equation

Does anyone know a link to the (superb) slides of a talk given by Zeeman in 1996, I think (with same title as this question)? It used to be at www.math.utsa.edu/ecz/gu.html .

**-1**

votes

**0**answers

66 views

### On the Theory of Infinite Step Processes of Sequential Decision Making

On the border of Set Theory and Game Theory there is a broad class of Infinite Step Processes of Sequential Decision Making that can be characterized by the main following property: a Future ...

**0**

votes

**0**answers

14 views

### A weak topology generated by weakly $p$-summable sequences

Let $1\leq p<\infty$ and $X$ be a Banach space. $N_{p}(X)$ is to denote the subspace $\{x^{**}\in X^{**}:$ there exists a weakly $p$-summable sequence $(x_{n})_{n}$ in $X$ such that the sequence ...

**3**

votes

**0**answers

112 views

### Hochschild cohomology of SU(2)

I have a question about the computation of an Hochschild Cohomology. Or at least about a space which really looks like a cohomology space. All the functions i consider are assumed to be smooth.
Let's ...

**1**

vote

**3**answers

298 views

### Exact formula for $\sum_{n=0}^{+\infty}\frac1{n^2+1}$

Actually, as the corresponding integral $\frac{\ln(\cos x)}{1-x}$ or something like that) cannot be expressed in closed form by Liouville theorem, this shouldn't exist, but I believe I have seen it ...

**1**

vote

**0**answers

13 views

### Efficient packing in Gaussian measures on Hilbert spaces

Let $B(0,1)$ be the unit ball in a separable Hilbert space $H$ with a Gaussian measure $\mu$ on it. For a small $r > 0$, can we have $x_i \in B(0,1)$, $0 < r_i \leq r$ and a constant $K > 0$ ...

**0**

votes

**0**answers

14 views

### Math Education Paper Request [migrated]

If this is the wrong forum for this post I apologize but I'm not sure of another well-suited medium for this question (and any reference to one is appreciated).
I am wondering if any research in ...

**0**

votes

**0**answers

18 views

### Uniqueness of the reduced rank QR decomposition

Let $A$ be a $n\times n$ matrix that is a real, symmetric, positive semidefinite and has rank $r$.
I read about the rank reduced $QR$ decomposition (here for example) as the QR variant where $A=QR$ ...

**3**

votes

**1**answer

458 views

### A generalized theorem of Hall's marriage theorem

We all know Hall's marriage theorem as following:
A bipartite graph $G$ with bipartition $\{ A,B \}$ contains a matching of $A$ if and only if $|N(S)|\geq |S|$ for all $S\subseteq A$.
And I am ...

**8**

votes

**1**answer

127 views

### “Fractally self-similar” numbers

This is another question about visualization of Ford circles, the previous one being Confusion with practically implementing rational approximations. Here is an output of zooming into Ford circles at ...

**-2**

votes

**0**answers

39 views

### Why standard deviation is preferred over mean deviation? [on hold]

I was doing my homework when I come across both these quantities which tells us dispersion in data. But, I am able to understand mean deviation as it tells on an average how much a value deviates from ...

**4**

votes

**1**answer

91 views

### geometric interpretation of derivation between two algebras

Given a smooth manifold $M,$ it is well known that any derivation of the algebra of smooth functions $C^{\infty}(M)$ can be seen (or it is associated to) a smooth vector field on $M.$ I am looking for ...

**3**

votes

**0**answers

34 views

### orthogonal projector onto the set of convex functions

Let $\Omega\subset \mathbb R^d$ be an open, convex domain, and consider the Hilbert space $L^2(\Omega)$. Each sum of convex functions is convex, hence the subset $Conv(\Omega)$ of all convex functions ...

**-1**

votes

**0**answers

61 views

### On simple complex loops [on hold]

To apply Jordan theorem, a curve $\Gamma$ must be a simple closed continuous curve. (Its parametrization is injective)
Now consider an element $[\gamma] \in H_1(\mathbb{\Omega})$ (singular homology, ...

**2**

votes

**2**answers

33 views

### Affine hull of a set of non-negative matrices with fixed row-sums

Fix any non-negative matrix $M \in \mathbb{R}_{\geq 0}^{m \times n}$ that contains no zero-row and no zero-column.
Further, fix any positive vector $r \in \mathbb{R}_{> 0}^m$.
With $nz(M) := ...

**-9**

votes

**0**answers

36 views

### Interesting Pemutation 65+ [on hold]

Ques no. 6& 7 on
http://s30.postimg.org/l6o96cfdt/Screenshot_2015_11_30_15_26_44.jpg
It is very interesting question please answer it

**-7**

votes

**0**answers

35 views

### Permutation 235 [on hold]

Ques no. 3&4 on
http://s21.postimg.org/li25onft3/Screenshot_2015_11_29_23_08_54.jpg
It is very interesting
Please answer it

**0**

votes

**0**answers

18 views

### Sum of N Gamma distributed random variables being N a Gamma distribution random variable [migrated]

Thanks in advance.
Let X a gamma-distributed random variable having scale θ and shape k:
$$
X \sim \Gamma(k, \theta) \equiv \textrm{Gamma}(k, \theta)
$$
with its probability density function is:
$$
...

**-1**

votes

**1**answer

44 views

### Maximal induced cycles on $n$-clique graphs

For any set $X$ we set $[X]^2 = \big\{\{a,b\}: a, b\in X\text{ and } a\neq b\big\}$.
We say a simple undirected graph $G=(V,E)$ is an $n$-clique graph if there are $S_1,\ldots,S_n\subseteq V$ such ...

**7**

votes

**0**answers

85 views

### Convergence rate of Fagin's 0-1 law for first-order properties of random graphs

Fagin's 0-1 law for first-order properties of random graphs states that, for every first-order sentence in the logic of graphs, the probability that a uniformly random $n$-vertex graph models the ...

**0**

votes

**0**answers

53 views

### Hodge metric on pair

I am looking for the definition of Hodge metric, like definition 2.2 here
https://hal.archives-ouvertes.fr/hal-00322845/document
But instead of Vector bundle if we have divisor $D$ with conic ...

**1**

vote

**0**answers

46 views

### Consecutive integers divisible by consecutive small numbers

Given $n$, what is the largest set of consecutive integers in $[n,2n]$ can we have so that each integer is divisible by a distinct element from $[\log n,2\log n]$ (no partiular order)? So apriori I am ...

**-1**

votes

**0**answers

39 views

### Recognition of a transversal in finite group [on hold]

Given a subset $T$ of a finite abelian group $G$ with $|T|/ |G|$, how can we determine if $T$ is a transversal of some subgroup of $G$?

**2**

votes

**0**answers

91 views

### mod 2 Bockstein and the Steenrod square

Let $M$ be a manifold, $n$ be a positive integer and $x\in H^1(M;\mathbb{Z}_2)$. I want to find some checkable sufficient conditions imposed on $M$ such that $x^n\neq 0$ can imply $x^{2n}=Sq^n ...

**2**

votes

**0**answers

61 views

### Generalizing von Staudt's synthetic construction of the complex numbers

Starting from the real projective plane described synthetically/axiomatically, it is possible to construct the complex projective plane directly without passing through coordinates: one adjoins two ...

**6**

votes

**0**answers

85 views

### Adding minimal subsets to $\aleph_\omega$

Given a cardinal $\kappa,$ recall that $X \subset \kappa$ is called fresh (over $V$), if $X \notin V,$ but $X \cap \alpha \in V$ for all
$\alpha < \kappa.$
Question. Is it consistent that there ...

**0**

votes

**0**answers

88 views

### On the Frobenius coin problem [on hold]

Is there an $n_0\in\Bbb N$ such that for every $n\in\Bbb N_{>n_0}$ there are $a,b\in\Bbb N$ with $n<a,b<2n$ with $\mathsf{gcd}(a,b)=1$ such that
1. if $ax+by=rt$ for some $x,y>0$ with ...

**0**

votes

**0**answers

27 views

### On a conjecture about Riemannian metric with positive sectional curvature [duplicate]

What is the last status of the following conjecture? Is it still open? What partial or similar results are known up to now?
Conjecture: $S^2\times S^2$ admits a Riemannian metric with positive ...

**1**

vote

**0**answers

111 views

### Many-sorted nominal sets as sheaves

The category of nominal sets can also be presented as the Schanuel topos, the category of sheaves on $\mathbb{I}^\mathsf{op}$ under the atomic topology, where $\mathbb{I}$ is the category of finite ...

**1**

vote

**2**answers

271 views

### Polynomials which always assume perfect power values

Let $f(x)$ be a non-constant polynomial with integer coefficients. It is a well-known result that if $f(n)$ is a square for all integers $n$, then $f$ must in fact be the square of a polynomial (see, ...

**2**

votes

**0**answers

16 views

### Fractional parts of two multiples [duplicate]

There is a theorem (I can't remember its name) saying that for any irrational number $x$ and any $0<a<b<1$, there exists a positive integer $n$ such that $\{nx\}\in (a,b)$, where $\{\cdot\}$ ...

**-2**

votes

**1**answer

27 views

### Systems with zero output for periodic inputs [on hold]

I need help with the following question:
Suppose you have an LTI system which produces the 0 output in response to any periodic input with period T. Show that the impulse response h(t) of the system ...

**2**

votes

**0**answers

61 views

### Integral representation of the complex homogeneous polynomial $z_1\cdots z_n$

Consider the transform (see e.g., (5.1) in this paper):
\begin{equation*}
\Lambda_\mu(q)(z) := \int_{\Delta_n} ...

**1**

vote

**1**answer

137 views

### Least simultaneous quadratic non-residue

Suppose $p,q$ are distinct primes with least quadratic non-residues $n_p$ and $n_q$ respectively. Can one bound the least $n$ for which $\left(\frac{n}{p}\right)=\left(\frac{n}{q}\right)=-1$ in terms ...

**0**

votes

**0**answers

30 views

### Complexity of $\mathsf{gcd}(a,b)\bmod N$

Given $a,b\in\Bbb N$ where each $a,b$ is $n$-bits, we can compute $\mathsf{gcd}(a,b)$ in $cn^{1+\epsilon}$ bit operations for some fixed $c\geq1$.
My query is given $N,a,b$ where $a,b$ is $n$-bits ...

**4**

votes

**0**answers

152 views

### Reference request: category of sheaves of O-modules with coherent cohomology

Suppose $X$ is a smooth algebraic variety (say, in characteristic $0$). It's a folklore result that $D^b\text{Coh}(X)$ is equivalent to the derived category of complexes of sheaves of ...