**5**

votes

**3**answers

168 views

### Generating (or availability of) large strongly regular graphs

Are there collections of already generated large strongly regular graphs available to download? By large I mean $n >= 200$ where $n$ is the number of vertices. I found Ted Spence's page on srgs, ...

**7**

votes

**1**answer

70 views

### Arithmetic Points are Dense on a Hida Family

I am reading the paper "Constancy of the Adjoint L-invariant" by H. Hida (http://www.math.ucla.edu/~hida/ConstP.pdf).
Correct me if I'm wrong, but I've read/heard that the arithmetic points $p \in ...

**-3**

votes

**0**answers

36 views

### summation of non-linear function [on hold]

Can anyone have idea for dealing with the two following series summations
$$ \sum_{i=1}^n \dfrac{1}{a+b x_i}=c $$
$$ \sum_{i=1}^n \dfrac{x_i}{a+b x_i}=d $$
I need to find the values of 'a' and ...

**9**

votes

**0**answers

93 views

### The operator $\left(q\frac{d}{dq}\right)^s$ and fractional derivatives of modular forms

Recall the notion of a "nearly holomorphic modular form" introduced by Shimura:
A function $f : \mathfrak h \to \mathbb C$ is said to be nearly
holomorphic of level $\Gamma_1(N)$, weight $k$ and ...

**1**

vote

**0**answers

88 views

### Reference request: Ebin

I'm after the paper The manifold of Riemanian metrics by D. Ebin. A link to the reference is:
http://www.ams.org/mathscinet-getitem?mr=0267604
The paper seems to be very hard to track down. Can ...

**1**

vote

**0**answers

33 views

### General Markov Chains on same Probability Space?

A Markov chain $(X_i)_{i\in \mathbb{N}}$ on a measurable space $(E,\Sigma)$ is (see e.g. Revuz or Meyn/Tweedie) constructed on the following probabilty space.
$$ \Omega = \{ (x_l)_{l \in \mathbb{N}} ...

**3**

votes

**0**answers

26 views

### “Spherelike” embedding for smooth Fano polytope

Let $\mathbb{R}^n$ be a vector space with Euclidean inner product and $\mathbb{Z}^n \subset \mathbb{R}^n$ be a lattice. Let $P$ be a full dimension convex lattice polytope in $\mathbb{R}^n$ containing ...

**3**

votes

**0**answers

35 views

### A lower bound for orthogonal partial circulant matrices

Let us call an $m$ by $n$ matrix with $m<n$ a partial circulant matrix it is the first $m$ rows of some square circulant matrix.
Consider partial circulant matrices whose elements are either $-1$ ...

**4**

votes

**0**answers

63 views

### Undecidability of the existential theory

Do you know if I can find the proof that the existential theory of $\mathbb{Z}$ with the structure of addition , divisibility and the relation $(\exists s \in \mathbb{Z})m=np^s$ is undecidable, ...

**21**

votes

**0**answers

199 views

### Does $\Bbb{CP}^{2n} \# \Bbb{CP}^{2n}$ ever support an almost complex structure?

This question has been crossposted from Math.SE in the hopes that it reaches a larger audience here.
$\Bbb{CP}^{2n+1} \# \Bbb{CP}^{2n+1}$ supports a complex structure: $\Bbb{CP}^{2n+1}$ has an ...

**2**

votes

**0**answers

34 views

### Questions about holomorphy and zeros of the symmetric power $L$-function

Let $f$ be a primitive form of an even weight $k$ for the full modular group and let $L(Sym^rf,s)$ be the symmetric $r$th $(r\geq 2)$ power $L$-function associated to $f.$ I have three questions ...

**3**

votes

**3**answers

124 views

### Asymptotic expression for $j$ which satisfies $\binom{n}{j}/j! \sim k$ as $n\to\infty$

Suppose $k>0$ is some fixed constant, and $n$ is a positive integer tending to infinity. Find $j\equiv j(n,k)$ such that
$$ \frac{\binom{n}{j}}{j!} \sim k. $$
The asymptotic expression for ...

**3**

votes

**3**answers

92 views

### Simplifying a Taylor polynomial that involves Stirling numbers of the second kind

I am currently trying to evaluate a complicated function $f$ at a point $x+a$ using a high order Taylor polynomial about the point $a$. The polynomial has the standard form:
$$\sum_{n=1}^k ...

**2**

votes

**0**answers

41 views

### Polynomials with positive coefficients passing through fixed points/range of Vandermonde matrices

I'll give two equivalent statements of the setup, then give my questions.
Fix integers $M \leq N$ and define the Vandermonde-like matrix $V_{M,N}[i,j] = (1 - \frac{i}{M})^{j-1}$ for $i \in ...

**2**

votes

**1**answer

31 views

### Bounding the difference in the value of a strongly convex function at its integer minimum and other integer points

I am currently working on a problem where I have to minimize a $m$-strongly convex function
$$f ~: ~\mathbb{R}^n \rightarrow \mathbb{R}^+$$
over a bounded integer lattice,
$$L = \mathbb{Z}^n \cap ...

**5**

votes

**0**answers

53 views

### What's the relation between half-twists and star structures on Hopf algebras?

A star structure on a Hopf algebra is an antilinear antiautomorphism squaring to 1 and satisfying some further axioms. A Hopf algebra with a star structure is then a star algebra and a Hopf algebra in ...

**-4**

votes

**0**answers

32 views

### Multivariate Calculus: Switching the Order of Integration [on hold]

This is confusing the heck out of me... I am asked to switch the order of integration of the following function:
$$
\int_{0}^{1} \int_{0}^{1-x} \int_{0}^{x+y} f[x,y,z] dz dy dx
$$
The order of ...

**1**

vote

**0**answers

43 views

### What is the Segre class of a generating line of a cone

Suppose $U=\textrm{Proj}\ k[X,Y,Z,W]/(XY-Z^2)$ is the projective closure of an affine cone, let $V$ be a generating line of the cone $V=V(Y,Z)$, how do we calculate the Segre class $s(V,U)$?
(We can ...

**1**

vote

**0**answers

55 views

### Representing trigonometric functions in a form of rational functions

Here I introduced a non-Archimedean numerical system in which the real numbers are extended by elements $\omega_-$, $\tau=\omega_-+1/2$, $\omega_+=\omega_-+1$ in such a way that standard parts of ...

**2**

votes

**0**answers

52 views

### Positive existential theory of $(\mathbb{Z}; +, |_n)$

I am reading a paper and there is the following theorem:
Let $n$ be a fixed integer, and $n >1$.
Denote divisibility in $\mathbb{Z}[\frac{1}{n}]$ by $|_n$, thus for
all $x, y \in ...

**3**

votes

**0**answers

126 views

### Deformation of finite coverings between smooth projective varieties

Assume that we have a finite covering $$f \colon X \longrightarrow Y,$$
where $X$ and $Y$ are smooth, complex projective varieties of dimension $n$. Therefore we obtain a splitting $$f_* \mathscr{O}_X ...

**3**

votes

**0**answers

126 views

### vector spaces with uncountable dimension and a nice basis

Unlike the reals considered as a vector space over the rationals, I know of a number of nice examples of vector spaces with uncountable dimension that have a nice basis.
For example, the space of ...

**0**

votes

**0**answers

52 views

### Properties of a specific antichain of a lattice formed by the cartesian product of finite ordered sets

Introduction
Let $X$ be a poset of all $n$-tuples, $x = (x_1, x_2, ..., x_n)$, where $0 \leq x_i \leq m_i - 1$ for $i = 1, ..., n$ together with the relation $x \prec y$ defined so that for ...

**8**

votes

**2**answers

210 views

### Free $k[x_1, \dots, x_n]^{S_n}$-module?

Let $\text{char}\,k = 0$ and $n \ge 2$. What is the easiest way to see that $k[x_1, \dots, x_n]$ is a free $k[x_1, \dots, x_n]^{S_n}$-module with basis$$x_2^{m_2}x_3^{m_3} \dots x_{n-1}^{m_{n-1}} ...

**11**

votes

**3**answers

174 views

### Curvature of a finite metric space

I am sorry to ask a very vague question, but:
What are good ways to define the curvature of a finite metric space?
The best way I can think of is: the curvature of a finite metric space $M$
is ...

**10**

votes

**2**answers

684 views

### Can I find Fermat's complete works anywhere?

I admire the mathematician very much and want to look at his writings. Is there anywhere in book or web form that has a collection of his writings?

**0**

votes

**0**answers

73 views

### Chern classes of ideal sheaf of locally complete intersection

Let $C\varsubsetneq X$ be a reducible locally complete intersection closed pure $1$-dimensional subscheme in a smooth projective variety of dimension $3$ over a algebraically closed field $k$ of ...

**0**

votes

**0**answers

21 views

### Quantification of the extent of periodicity in a time series using fractal analyses

I need metrics to quantify and compare the extent of periodicity between any two given time series, considering the time series were "almost periodic". By "almost periodic" I mean: if I were to take ...

**-3**

votes

**0**answers

60 views

### Eigenvalues of a random matrix [on hold]

For test cases i generated a random real uniform distributed matrix with
entries from the intervall $[0,1]$.
Here is the MATLAB Code i used
...

**2**

votes

**0**answers

65 views

### cohomology ring of base-point-preserving maps on the 3-sphere

I find that $\text{Map}_*(S^3;S^3)=\Omega^3S^3$. I want to find the cohomology ring of $H^*(\Omega^3S^3;\mathbb{Z}_2)$.
In the paper On configuration spaces, their homology, and Lie groups, I find ...

**5**

votes

**0**answers

92 views

### How “small” can an ordinal be made by forcing?

I know that forcing essentially does not change the ordinals, but by small I mean in comparison with other ordinals whose definition might not be stable under forcing, like the smallest uncountable ...

**-3**

votes

**0**answers

37 views

### eigenvalues of cycle and its complement [on hold]

I am trying to find the eigenvalue of cycle graph and its complement. How to simplify.Suppose $\omega^{1}+\omega^{n-1}=2cos (2\pi/n) $, then, $\omega^{\frac{n-1}{2}}+\omega^{\frac{n+1}{2}}=?$ Is it ...

**2**

votes

**1**answer

187 views

### Indecomposable decomposition for a commutative ring

Let $R$ be a commutative ring with identity. We say that $R$ has an indecomposible decomposition if it can be wrighten as a finite direct sum of indecomposiable rings.
Is there any characterization ...

**2**

votes

**0**answers

92 views

### Can such categorical notion of action be formalized?

I'm wondering if it's possible to find an universal construction for a general concept of action for (single-sorted?) finite product sketches, such that one of those is "acting" on the second in the ...

**3**

votes

**2**answers

179 views

### Example of measure of non-compactness

I can't understand the following example of measure of non-compactness, which was given in this article.
Definition: A non-negative function $\phi$ defined on the bounded subsets of $X$ will be ...

**6**

votes

**3**answers

526 views

### Category theory for Algebraic Geometry

How much of category theory should I know to view schemes, sheaves and cohomology concepts as concrete cases of abstract categorical concepts? Is there a textbook of category theory for AG people?

**3**

votes

**2**answers

154 views

### bar construction and loop space cohomology

Let $X$ be a topological space. Then its chain complex $C_{*}(X)$ is naturally a coalgebra (as explained here Does homology have a coproduct?). In particular if $X$ is simply connected we have that ...

**5**

votes

**1**answer

43 views

### Volume satisfying inequality constraints (simplex subset)

Is there a way to find the volume of the "feasible region" of a standard simplex satisfying simple range constraints?
$x_1+x_2+...+x_n = 1$
$a_1 \le x_1 \le b_1$
$a_2 \le x_2 \le b_2$
$...$
$a_n \le ...

**6**

votes

**1**answer

419 views

### Segal's 1999 Stanford lecture notes on TQFT, where to find them?

I am trying to track down a copy of Graeme Segal's 1999 lecture notes on topological field theory. These are sometimes referred to as the "Stanford lectures" or something similar.
For many years ...

**-4**

votes

**0**answers

26 views

### What is the upper bound for training Linear separable set with Perceptron, Rosenblatt rule? [on hold]

I have the following neural networks problem and couldnt find any answer on the web. Any hints would help. I am not looking for a complete solution, just some pointing in the right direction.
...

**4**

votes

**1**answer

125 views

### Current status of the linearity of mapping class group

In the paper A faithful linear-categorical action of the mapping class group of a surface with boundary it is claimed that it was (as of 2014) still unknown that mapping class group is linear, but the ...

**4**

votes

**1**answer

83 views

### unordered configuration space over spheres and Euclidean spaces

For a topological space $X$, let $B(X,k)$ be the $k$-th unordered configuration space. Then
$$
B(\mathbb{R}^n,2)\simeq \mathbb{R}P^{n-1},
$$
$$
B(S^n,2)\simeq \mathbb{R}P^n.
$$
Hence
$
(*)
$
$$
...

**3**

votes

**0**answers

65 views

### Are all transversely oriented foliations given by closed forms?

This paper, "AF-algebras and topology of 3-manifolds" seems to claim on page 5 that a [transversely] oriented measured foliation on a compact surface is given by a closed form. On the other hand, the ...

**-2**

votes

**0**answers

84 views

### Fundamental Group of SL_2 [on hold]

I am thinking whether there is a simple criterion or visible method to know the fundamental group of SL_2(R), or SL_2(F) with an arbitrary field F.
Because SL_2(R) is already a 3-dimensional ...

**3**

votes

**2**answers

181 views

### Connectedness of moduli of vector bundles

Let $X$ be a smooth projective variety. Given two vector bundles $V_1$ and $V_2$ such that $[V_1]=[V_2]\in K^0(X)$, can one expect that $V_1$ and $V_2$ can be connected by a family of vector bundles? ...

**3**

votes

**0**answers

149 views

### Probability that an integer contains no $1\bmod 4$ prime factor

$n$ represents integer variable.
What is the probability that and integer contains at most $r(n)$ prime factors of form $1\bmod 4$ where $r(n)$ is a function of $\omega(n)$ (number of distinct prime ...

**0**

votes

**1**answer

33 views

### floating point representation via the perspective of TTE/computable analysis

Floating point numbers are not compatible with the usual theory of type 2 theory of effectivity (TTE), and not even the real-RAM model; there are functions that are computable in one model but not ...

**-4**

votes

**0**answers

104 views

### Are polls good approximations [on hold]

Let $X$ be a finite set and $A\subseteq X$ and $m$ be a natural number satisfying $m\le |X|$ and $\epsilon$ be a small positive number.
I'm interested to know if one selects a random $Y\subseteq X$ ...

**-1**

votes

**0**answers

33 views

### Obtaining z-transform of a multivariate nonlinear difference equation [on hold]

I need to obtain the z-transform of difference equations that are as follows:
My problem however is multivariate and looks like this:
x[k+1]=ay[k]+ ((x[k])^2)(y[k]) ...

**0**

votes

**1**answer

70 views

### Counting number of primorial factors

Denote $$P(n)=\prod_{p\in\mathsf{Primes}\leq n}p$$ signifying $n^{\mbox{th}}$ primorial.
We know that $P(n)$ has approximately $n/\log2$ bits ...