-2
votes
0answers
25 views

Length in time to find the longest range of primes between 2 and a 13 million character digit? [on hold]

I am trying to run a program that tells me how many prime numbers there are in a range of numbers. I run it in intervals of 10,000 to 100,000. How long would the program take to determine all the ...
0
votes
0answers
6 views

Distribution of Wishart Sample Eigenvalues for Multiple Roots

I am interested in finding an asymptotic approximation to the latent roots $l_1>\dots>l_p$ of a white noise Wishart matrix $nS\sim W_p(n,I)$ as $n\rightarrow\infty$ (where $p$ is fixed). In ...
1
vote
1answer
53 views

Examples of intuition from fields other than Physics to solve math problems

This is a chaser for the examples of using physical intuition to solve math problems question. Physical intuition seems to be used relatively frequently for solving math problems as well as stating ...
-4
votes
0answers
26 views

Limit question without L'hopital's rule? [on hold]

Stuck here with this one and I'm not allowed to use L'Hopital's rule. lim x->0 sin(3x^2)/(tan5x)^2 Please help?
4
votes
0answers
13 views

Does an equivalence of fusion categories depend on choice of simple objects within isomorphism classes?

Let $C$ be a fusion category with simple objects $X_1,...,X_n $, and let $Y_1,...,Y_n$ be objects with each $Y_i$ isomorphic to $X_i$. Is there a monoidal auto-equivalence $F:C \rightarrow C $ which ...
1
vote
1answer
10 views

What's the current state of one-rule semi-Thue system termination problem?

What's the current state of one-rule semi-Thue system termination problem? Search produces a lot of references, but it's hard to find out if decidability of this problem has been proven or not.
-2
votes
0answers
36 views

How to show a matrix can't be written as exponential? [migrated]

How can I show the matrix $$A = \left( \begin{array}{c c} -2 & 0 \\ 0 & -1 \\ \end{array} \right)$$ can't be written as $A = exp(a)$? I've tried to write A like $$A = \left( ...
2
votes
0answers
22 views

Nilradical of a Lie algebra associated to a associative algebra

Let $A$ be a finite dimensional (unital) $K$-Algebra. By $A^{\circ}$ we denote the associated $K$-Lie-algebra of $A$ with respect to the product $a\circ b:=ab-ba$. In addition, we denote by ...
0
votes
1answer
31 views

Ask for a good reference for the calculus involving singular continuous measure

I am not an expert on measure theory. I am sorry if this question is too simple for some experts here. Suppose the measure $\mu$ is singular continuous on $\mathbb{R}$, such as the cantor measure. ...
1
vote
0answers
29 views

Explicit equations for conormal bundle to an affine toric variety

Let $L \subset \mathbb{Z}^n$ be a lattice and let $X_L$ be the closed toric subvariety of $\mathbb{C}^n$ cut out by the lattice ideal $I_L = \{x^{l_+} - x^{l_-} \,| \, l_+, l_- \in \mathbb{N}^n \text{ ...
-2
votes
0answers
27 views

A Function $ g[0,\infty) \mapsto [0,1)$ Sharply Changing on Both Ends [on hold]

I need a function $ g[0,\infty) \mapsto [0,1)$ that sharply decreases near 0 and sharply increases near 1. Preferably, it wouldn't be defined in a piecewise manner. Can anyone provide an example, ...
3
votes
1answer
30 views

On the conformal removability of Jordan curves

We say that a compact subset $E$ of the Riemann sphere $\mathbb{C}_\infty$ is (conformally) removable if every homeomorphism of $\mathbb{C}_\infty$ conformal outside $E$ is actually conformal ...
-3
votes
1answer
22 views

convex upper bound of a non-convex function [on hold]

is there any formula for finding convex upper bound of a non-convex function? Like for finding convex lower bound of a non convex function, fenchel dual exists.
0
votes
0answers
22 views

preservation of localness among certain Krull domains

The following question essentially appeared (http://math.stackexchange.com/questions/931801/preservation-of-localness-among-certain-krull-domains) on math.SE a while ago, but nobody has done anything ...
0
votes
0answers
26 views

On the global and local hermitian space

Let $E/F$ be a quadratic extension of number fields and $v$ a finite place of $F$. Then I am wondering if there is a global hermition vector space over $E$ such that for all finite places $v$, local ...
6
votes
0answers
59 views

Periodic group with bound on order of finite subgroups

I have asked the same question previously on stackexchange without any answer (http://math.stackexchange.com/questions/923638/periodic-group-with-bounded-subgroups): I am looking for infinite ...
0
votes
1answer
122 views

Are there any references for the measures without any growing tails? [on hold]

I am trying to find whether there are any references to characterize measures without any growing tails. For example, the Lebesgue measure and the following measure \begin{equation} ...
1
vote
1answer
57 views

Strictly positive solutions of a random linear system

Suppose $B\in\mathbb{R}^{m\times n}$ is a random binary matrix with i.i.d entries and $c\in \mathbb{R}^m$ is a strictly positive vector, that is $c_i>0$ for $i=1,2,\cdots m$. Also assume $m<n$, ...
3
votes
1answer
78 views

Containment of two varieties with a lot of intersection

Given a projective variety $X\subset \mathbb P^n$ and a curve $C\subset \mathbb P^n$, when can I conclude that $C\subset X$, from the fact that $C$ and $X$ have 'many' points in common. I.e., is there ...
-2
votes
0answers
23 views

What does it mean for a stochastic sequence to be “stochastically smaller” than some other stochastic sequence? [on hold]

A relatively simple type of random graph is the Erdős-Rényi random graph. The graph created by means of the following process: Let $V$ consists of $n \in \mathbb{N}$ vertices, and let each edge of the ...
26
votes
2answers
383 views

Does iterating a certain function related to the sums of divisors eventually always result in a prime value?

Let define the following function for integers (from 2): $f(x)=\sigma(x)-1$, where $\sigma$ is the sum of the divisors of $x$. For example $f(6)=6+3+2=11$, $f(5)=5$. Note that $x$ is a fixed point for ...
-4
votes
0answers
32 views

Help? Algebra question about ratios and proportions [on hold]

A community center is going on a trip to Philadelphia via several buses. The ratio of men to women to children is 1:2:3. If there are 150 people going on the trip, how many men are going? How many ...
2
votes
1answer
38 views

Unbiased sample from a product

Let $X = (x_1,\ldots,x_n)$ be an i.i.d sample from distribution $F%$ and let $y = \prod_{i=1}^n x_i$ Can we derive a randomized, unbiased. estimator $\hat{y}$ of $y$ that on average considers only a ...
0
votes
0answers
68 views

Squarefree Parts of Mersenne Numbers with prime exponent [on hold]

The $n$-th Mersenne number is $M_n=2^n−1$. Write $M_n=a_n b^2_n$ where $a_n$ is positive and squarefree. In the discussion Squarefree Parts of Mersenne Numbers , the lower bound of $a_n$ has been ...
-7
votes
0answers
115 views

Does $\pi$ encode the prime numbers? [on hold]

I have a question regarding whether or not $\pi$ encodes the sequence of primer numbers. It is common knowledge that $$ \zeta (2) = \sum_{i = 1}^{\infty} \frac{1}{n^2} = \prod_{p \in \mathbb{P}} ...
0
votes
1answer
17 views

Zeroes of Sturm-Liouville solutions as a function of the (complex) eigenvalue

Given the Sturm-Liouville type (time independent Schroedinger) equation \begin{equation} \frac{d^2 y}{d x^2} - \left(\mu + V(x)\right) y = \lambda \, y,\quad x \in \mathbb{R} \end{equation} where ...
4
votes
1answer
64 views

Geodesic flow on infinite surfaces

The geodesic flow on a compact hyperbolic surface (i.e. a surface with a riemannian metric of constant curvature $-1$) has been well-studied, in particular it has been known for a long time that it is ...
0
votes
1answer
32 views

Monotonicity of the gap of permutated sequence

Let $a$ be an arbitrary sequence and denote by $\mbox{gap}_k(a) = a_{(k)} - a_{(k+1)}$, where $a_{(k)}$ is the $k$th largest component of $a$. Of course, $k+1$ should be no larger than the length of ...
1
vote
2answers
73 views

Non-DS circulant graphs

Let $p$ be a prime number greater than or equal to 11. Are there any cospectral non-isomorphic circulant graphs on $p$ vertices.
2
votes
1answer
182 views

Can the Grothendieck ring of varities over a field $k$ be defined for non separated schemes?

The Grothendieck ring of varieties over a field $k$ is the abelian group generated by isomorphim classes $[X]$ of separated, reduced $k$-schemes $X$ of finite type with the relation $[X]=[Y] + ...
0
votes
0answers
44 views

numerical method (implicit) for nonlinear pde

If $\newcommand{\lbar}{\underline{\lambda}}$ $$ \lambda(t)= \lbar+(\lambda_0-\lbar)\exp \left( (\mu-\frac{1}{2}\sigma^2)t+\sigma W^\lambda_t\right) $$ and $\mu$ , $\sigma$ , $\lbar$ , $\lambda_0$ , ...
9
votes
1answer
1k views

Go I Know Not Whither and Fetch I Know Not What

Next day: apparently my original question is harder, by far, than the other bits. So: it is a finite check, I was able to confirm by computer that, if the polynomial below satisfies $$ f(a,b,c,d) ...
3
votes
1answer
118 views

Unusual augmentation of a filtration

consider a probablity space $(\Omega,\mathcal{F}, \mathcal{P})$ and a filtration $(\mathcal{F}^0_t)$. In general $(\mathcal{F}^0_t)$ doesn't satisfy the usual conditions (it is not both complete at ...
0
votes
0answers
114 views

Decomposition of symmetric homogeneous polynomials

Can every symmetric polynomial of degree $r$ in $d$ variables that has no constant term be written as a sum of the $r$th powers of linear polynomials in $d$ variables and a homogeneous polynomial of ...
5
votes
2answers
174 views

Using Discrete Morse Theory to represent hom classes

In "vanilla" Morse theory, you can construct cycles representing integral homology classes of a smooth manifold from a Morse function on the manifold (by looking at the flow into/out of the critical ...
2
votes
0answers
33 views

Weighted graph similarity

I have the following problem. Consider an undirected biconnected graph with $n$ vertices and $m$ edges ($n \leq m \leq n(n-1)/2$). The $m$ edges of the graph are then "populated" by integer weights ...
1
vote
0answers
37 views

square tiled surfaces: Counting Saddle Connections vs Counting Square-Tiled Surfaces

I am reading Prime arithmetic Teichmuller discs in H(2) where they discuss the Siegel-Veech constant in a stratum $\mathcal{H}(2)$ of surfaces. However I see two definitions of Siegel-Veech constant: ...
1
vote
1answer
139 views

Name for class of matrix determinants

Let $M$ be an $n\times n$ matrix that's constructed as follows. Construct the right-most column of $M$ as $[\alpha_1(x_1),\cdots,\alpha_n(x_n)]^T$ for some class of fixed functions $\alpha_i(x)$. Now, ...
-8
votes
0answers
49 views

New formulas for Generating sin(nx) & cos(nx) [on hold]

I have proved formulas for generating $\sin (nx)$ and $\cos(nx)$ in term of only $\sin x$ and integer $n$, or $\cos x$ and integer $n$, such as: $$\sin(9x) = 9\sin x -120\sin^3 x + 432\sin^5 x – ...
-5
votes
0answers
69 views

Rookie looking for help with basic mathematical problem [on hold]

This should probably be very simple, but I'm just not very skilled in math :S. I want a function that takes one variable, x, ranging from 0-1. As the input approaches 0 so should the output. As the ...
1
vote
0answers
43 views

Decomposition of Lefschetz fibrations into surface bundles and Lefschetz fibrations over spheres

Assume that $M$ is a Lefschetz fibration with fiber genus $g$ over a base of genus $h>0$ (with at least one singular fiber). What obstructions exist to decomposing $M$ into a surface bundle $S$ of ...
-1
votes
0answers
59 views

Isogeny of abelian varieties over general fields [on hold]

We know that given an abelian variety $X$ over an algebraically closed field $K$ of characteristic $0$ and any integer $n$ the induced map $[n]:X \to X$ is an isogeny. As far as I understand this ...
4
votes
0answers
176 views

$x^2+1$ attaining almost prime values

Iwaniec, using the linear sieve, proved that $n^2+1$ can be a product of at most two primes infinitely often and furthermore a lower bound of the correct order of magnitude for the number of such ...
1
vote
0answers
25 views

Jacobi Polynomial asymptotics via saddle-point methods

I'm looking at asymptotics of a Jacobi polynomial: $P_{n-2}^{\alpha_n,\beta_n}(0)$, with $\alpha_n=(n-2)-N, \ \beta_n=[cn^{3/2}]-(n-2)$, where $c>0$ is a constant, $N=\binom{n}{2}$ and $[\cdot]$ is ...
1
vote
0answers
81 views

Level quantization of 7d $SO(N)$ Chern-Simons action

In 3d, one can write down the $SO(N)$ Chern-Simons action to be $$S(A)=\frac{k}{192\pi}\int_{M}\text{Tr}(A d A +\frac{2}{3}A^3),$$ where $A$ is an $SO(N)$ connection. The level quantization can be ...
1
vote
2answers
103 views

The zeros of alternating sign, binomial coefficient polynomials

I have a question regarding the zeros of the following polynomial, based on partial rows of pascal's triangle, $$f(x)=\sum_{k=a}^n\binom{n}{k}(-1)^{k}x^k,$$ where $a,n\in \mathbb{Z}^+,n>a.$ ...
-2
votes
0answers
51 views

Expected probability [on hold]

Suppose, given an integer N, N divides by its divisors(1, to N) and gain new number, repeats the procedure until it becomes 1. what is the expected number of divisions need number N become 1? Can ...
5
votes
2answers
154 views

Eigenstates of Fourier transformation

Let $\gamma$ be defined on $\mathbb R^n$ by $\gamma (x)=e^{-π x^2}$. With $\mathcal F$ standing for the Fourier transformation defined on the Schwartz space by $$ (\mathcal F u)(\xi)=\int e^{-2iπ ...
1
vote
2answers
94 views

When is the induced representation factored through the initial one?

Let $H$ be an open subgroup in a locally compact group $G$, $\iota:H\to G$ the embedding of $H$ into $G$, $\pi:H\to B(X)$ a unitary representation of $H$ in a Hilbert space $X$, and $\rho:G\to B(Y)$ ...
6
votes
1answer
140 views

Generalizing “variation of parameters”

I'm stuck on generalizing an ODE formula and could use your help! One way to think about "variation of parameters" is that it bakes the solution $z(t)=e^{At}z_0$ of $z'=Az$ (here ...

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