# All Questions

1answer
39 views

### Lightning strike fractal formula

I need to generate random gold ore channels for a game, I was thinking they would look kinda like lightning strikes. Anyone know any good fractals (recursive functions) that looks like it? Or ...
0answers
38 views

### How can I (iteratively) solve these equations? [on hold]

I am by no means a mathematician at all (programmer) so I need some pointers on how to solve the following equations - if someone could point me to a method that would work, that would be very ...
1answer
11 views

### generate analytically bivariate correlated data

How does one generate correlated binomial data when one is given marginal probabilities of each and also the correlation coefficient. The following code in SAS for example works best when we want ...
0answers
15 views

### Does it require Reedy fibrancy when we want the totalization to be weakly equivalent to the homotopy limit?

This question arises when I am reading the last two Chapter of Hirschhorn's "Model categories and their localizations" In Part (2) of Theorem 19.8.4 of that book it says If ...
0answers
23 views

### How can we find the presentation of a group? [on hold]

Is it possible that to find the presentation of a group $G$ such that it is extension of $\mathbb{Z}_2\times \mathbb{Z}_2$ by $\mathbb{Z}_2$?
0answers
17 views

### Isotropic subspaces in a symplectic vectorspace over $GF(q)$

Let $V$ be a symplectic vectorspace of dimension $2n$, and $r\mid n$. Is this statement true?"There is an isotropic spread of $r$ dimensional subspaces in $V$". By an isotropis subspace I mean a ...
0answers
56 views

### Prove that the Log-Euclidean distance is negative-definite

Let $\Bbb{S}_{++}^n$ be the $\frac{n(n+1)}{2}$-dimensional Riemannian manifold of the symmetric positive definite (SPD) $n\times n$ real matrices. The Log-Euclidean distance between two points of ...
0answers
28 views

### Does null geodesic flow live on a natural compact bundle?

Let $(M,g)$ be a compact pseudo-Riemannian manifold (closed or with boundary). A geodesic $\gamma:(a,b)\to M$ is called null if $g_{ij}\dot\gamma^i\dot\gamma^j=0$. The geodesic flow can be seen as a ...
0answers
59 views

### What is the symmetry of SU(3) - when seen as a manifold? [on hold]

Simply asked: is it more correct to state that the symmetry of the SU(3) manifold is $Z_3$ or $S_3$? Or neither of the two? SU(3) has a kind of threefold symmetry; but which one exactly? When ...
1answer
73 views

### Jacobson-Morozov theorem

Jacobson-Morozov theorem for a semisimple algebraic group $G$ (presumably I am working over algebraically closed field) states that: given a unipotent u, there exists a homomorphism $\phi$ from $SL_2$ ...
5answers
583 views

### Algorithms for calculating R(5,5) and R(6,6)

Calculating the Ramsey numbers R(5,5) and R(6,6) is a notoriously difficult problem. Indeed Erdős once said: Suppose aliens invade the earth and threaten to obliterate it in a year's time unless ...
1answer
44 views

### Comparison of Lp norm of matrix and its entry wise norm. [on hold]

I need to know the relation between operator norm of a matrix i.e. $\Vert A\Vert_p$ for case of p=1 and 2 and its entry wise Frobenius norm $\Vert A\Vert_F$.
2answers
258 views

### Idea of using etale site

I have just read an article which mentions that, when Grothendieck considered using etale morphism, he did borrow the idea from Riemann that multivalued function on an open subset of complex plane ...
3answers
519 views

### Determining if a matrix is orthogonal

Let g be an element of $GL_n(\mathbb C)$. We know that there are orthogonal groups $O(\beta)=\{X\in GL_n(\mathbb C) \mid X^t\beta X=\beta\}$ for any $\beta$, invertible symmetric matrix. Though these ...
0answers
44 views

### Prove or disprove a claim about covering a polytope by convex polytopes in a certain way

Here is the claim: Given a polytope $K$ in a unit ball in $\mathbb{R}^d$, there exists a universal constant $C(d)>0$ depending only on $d$ and a countable collection of convex polytopes ...
0answers
43 views

### Relation between linear independence of lattice vectors and the toric variety defined by that lattice

I have been reading some basic and elementary work on toric varieties, but even though people assured me that toric varieties are very well understood, several questions remained. Setup. Let ...
0answers
85 views

### What is Jantzen's formula for the determinant of the Shapovalov form in the case of generalized Verma modules?

The best reference I found is [Kac, Kazhdan '79] which extends the results of Shapovalov and Jantzen to the case of infinite dimensional Lie algebras. Theorem 1 of this paper gives the Shapovalov ...
1answer
114 views

### Subgroup of Projective general linear group on complete discrete valuation ring

Let $R$ be a complete dvr and $k$ its residue field of positive characteristic. Let $H$ be a finite subgroup of $PGL_2(k)$ such that the order of $H$ is prime with $char(k)$. Is there some ...
1answer
168 views

### Time averages and differentiability

Let $\varphi_t : M \rightarrow M$ be a smooth flow on a smooth manifold $M$. We may assume (although I'm not sure if this is important) that the flow preserves a smooth volume form on $M$. Given a ...
1answer
472 views
+50

0answers
47 views

### Twisting by a multiplicative Character in Katz, Perversity and Exponential sums

Let $C(x_1,\ldots,x_n)$ be a nonsigular cubic form with integral coefficients. In his Proof that $C$ fulfills the Hasse-Principle, if $n\geq 9$, Hooley used the following estimate that was provided ...
0answers
28 views

### Euler equation formula [on hold]

when I am using Euler equation for Fourier transform integrals of type $\int_{-\infty}^{\infty} dx f(x) exp[ikx]$ I am getting following integrals: $\int_{-\infty}^{\infty} dx f(x) cos(kx)$ (for ...
0answers
56 views

### $F[[T]] \times F[[1/T]]$ fundamental domain, show compactness

Let $p$ be a prime number. What is the easiest way to see that $(\mathbb{F}_p((T)) \times \mathbb{F}_p((1/T)))/\mathbb{F}_p[T, 1/T]$ is compact? Here $\mathbb{F}_p[T, 1/T]$ is embedded in ...
2answers
720 views

### History of Geometric Analogies in Number Theory

My question, put simply, is: When did mathematicians/number theorists begin viewing questions in number theory through a geometric lens? For example, was it before Grothendieck introduced schemes to ...
2answers
93 views

### Is the boundary of an open, regular, bounded, path-connected, and simply connected set a Jordan curve

Trying to find weakest condition on an open bounded set to apply Carathéodory's theorem. My bounded open sets can be assumed to be pretty well-behaved, but I wonder if the above conditions are ...

15 30 50 per page