# All Questions

**7**

votes

**1**answer

270 views

### Prove that …, f(x-2), f(x-1), f(x), f(x+1), f(x+2),… is algebraically linearly independent without the Fourier transform

Suppose that $f$ is in $L^2(\mathbb{R})$ and consider the set of integer translates of this function, $V=\{f(x-k):k\in\mathbb{Z}\}$. This set is linearly independent: taking the Fourier transform of ...

**1**

vote

**0**answers

85 views

### Default Orientation of Vectors [on hold]

When I started studying math in 1982 in Germany, there seemed to have been a change in the choice of the default orientation of vectors; while it was row-vectors till then, it changed to ...

**2**

votes

**1**answer

144 views

### Reference request for instantons

I've been researching instantons lately and I'd like to learn more about them but would like some help finding what to read. I have read about the ADHM equations and their noncommutative analogues. ...

**4**

votes

**1**answer

311 views

### Connections between Standard, Hodge and Tate conjectures on algebraic cycles?

What implications would a solution of the Standard Conjectures have on the Hodge and Tate Conjectures and reverse?

**23**

votes

**3**answers

2k views

### Escape the zombie apocalypse

Consider zombies placed uniformly at random over $\mathbb{R}^2$ with asymptotic density $\mu$. You are placed at a random point and can move with speed $1$. Zombies move with speed $v\leq 1$ straight ...

**0**

votes

**0**answers

49 views

### Multiplicativity of the Ideal Norm

I asked this question on StackExchange twice, and was never able to get an answer. This is not quite a research-level question, but it is sufficiently difficult and interesting from a pedagogical ...

**1**

vote

**1**answer

105 views

### Why is the Tate local duality pairing compatible with the Cartier duality pairing?

This question is a follow up to Why is the norm map dual to restriction under Tate local duality?
Let $A$ and $B$ be dual abelian schemes over a base scheme $S$. For an integer $n \ge 1$, consider ...

**2**

votes

**1**answer

179 views

### Is the ordinary locus affine?

Let $p$ be a prime number and let $Y$ over $\mathbb F_p$ be a Siegel modular variety, with minimal compactification $X$. It is well known that $X^{\operatorname{ord}}$, the ordinary locus of $X$ is ...

**9**

votes

**1**answer

173 views

### Do direct limits (filtered colimits) commute with pullbacks, in C*-algebras?

I asked this question already on math.stackexchange, but maybe it is also useful to ask this here, since it was not answered there.
Suppose we have three directed sequences of $C^*$-algebras, say ...

**2**

votes

**0**answers

43 views

### optimization problem, any solution?

The objective is as follows:
$\min_{\mathbf{F}} a Tr(\mathbf{F} \mathbf{F}^H) - Re\{\mathbf{b}\mathbf{F}^H \mathbf{C} \mathbf{F} \mathbf{d}\}$
$s.t.\ \ \ Tr(\mathbf{F} \mathbf{F}^H)<p$
where $a$ ...

**0**

votes

**0**answers

33 views

### A solution of a q-difference equation

Is it possible to find a solution of the $q$-difference equation
$$f(q^{-1}x)-f(qx)=x(a-x)f(x),$$
with $f(0)=1$, (perhaps) in terms of basic hypergeometric series? Or in another rather explicit form? ...

**-1**

votes

**0**answers

64 views

### Can first and second fundamental form be considered as differential 1-forms? [on hold]

Let $(M,g)$ be an abstract surface embedded into $\mathbb{R}^3$ via $f:M \to \mathbb{R}^3$. Denote the first and second fundamental form by $I$ and $II$, respectively and the smooth vector fields on ...

**6**

votes

**1**answer

153 views

### Horn's inequalities for n matrices

Where I can find necessary and sufficient conditions on eigenvalues of Hermitian matrices with the relation $$A_1 + A_2 + ... + A_n = A_0 ,$$
i.e. Horn's inequalities for n matrices?
Can such ...

**1**

vote

**1**answer

113 views

### Conjugate surfaces: informations about the orbits

Consider a complex algebraic variety $X$ (namely a $\mathbb C$-scheme, of finite type, geometrically integral and separated); if $\sigma\in\textrm{aut}(\mathbb C)$, then is well defined the complex ...

**0**

votes

**0**answers

135 views

### Basketball shots and stopping rule

Moved over from StackExchange.
You are taken to play a basketball game where you can shoot basketballs at n slots using a machine that is equally likely to shoot the balls into those n slots. You can ...

**5**

votes

**0**answers

143 views

### Are inclusions from spaces of $C^\infty$ sections into spaces of $C^k$ sections homotopy equivalences?

[EDIT: The answer to my original question was obviously no, as user56365 pointed out. Here is what I should have asked.]
For finite-dimensional smooth manifolds $E,M$, let $E\to M$ be a smooth fibre ...

**0**

votes

**0**answers

31 views

### discrete dynamical system [on hold]

sir,
I am doing research work in dynamical systems in the area alpha limit sets.I came across a situation where i can find some properties of alpha limit sets analogous to omega limit sets.I am ...

**9**

votes

**2**answers

334 views

### Multiplicative Identity for all elements in SU(n)

Let $\{P_i\}$ be a subset of $SU(n)$ such that for any $U$ in another subset (or perhaps subgroup) $H$ of $SU(n)$: $$P_1UP_2U\cdots P_mU=I$$ where $I$ is the identity element. Is there a sequence ...

**4**

votes

**1**answer

62 views

### Reference request: Continuity of unique maximizer of linear functional on convex set

Does anyone know reference for a theorem of the following sort:
Proposition: Let $K \subset\mathbb {R}^n$ be a compact convex set, and assume that
$$f(w):=\operatorname{argmax}_{x\in K}w(x) $$ is ...

**0**

votes

**0**answers

43 views

### Involution on $\chi^{\infty}(\mathbb{R}^{n})$

Is there a Lie algebraic involution $\theta$ on $\chi^{\infty}(\mathbb{R}^{n})$ which restriction to linear vector fields is the involution
$\theta(A)=-A^{tr}$ for $A\in M_{n}(\mathbb{R})$?
...

**6**

votes

**0**answers

79 views

### Can $Ded(\kappa)$ be a supremum?

Definition If there is a dense linear order w/o endpoints of size $\lambda$ with a dense subset of size $\kappa$ then write $D(\kappa,\lambda)$. $Ded(\kappa)=\sup_\lambda \{D(\kappa,\lambda)\}$.
It ...

**5**

votes

**2**answers

110 views

### Poisson ideals vs. ideals generated by Poisson central elements

Let $R$ be a Poisson algebra (over $\mathbb C$, say) with Poisson center $Z = \{c \in R : \{c,R\} = 0\}$ and consider two types of ideals $I \leq R$:
$I = \langle (c_i) \rangle$ is generated by ...

**10**

votes

**2**answers

424 views

### Cut and Fold Polyhedron!

I have two convex polyhedra such that their sums of side areas are equal. It is true that I can cut one of them and flatten it on the plane, then fold the flattened polygon to reach the other ...

**4**

votes

**2**answers

102 views

### Heat kernel asymptotics for the sublaplacian on a contact Riemannian manifold

Let $\Delta$ denote a Laplace-type differential operator on a compact Riemannian manifold $(M,g)$. The asymptotics of the heat kernel and the heat operator trace of $\Delta$ are well-known (cf. ...

**0**

votes

**1**answer

96 views

### Double Markovity

Suppose we have a double Markov relation for three random variables $X$, $Y$ and $W$ as follows
$$X\to W\to Y,$$ and $$X\to Y\to W.$$
How to prove that there exist functions $f$ and $g$ such that
...

**3**

votes

**0**answers

65 views

### Connection between framed cobordisms and zero sets

Let $W\subseteq M\times[0,1]$ be a framed submanifold (a framed cobordism in $M$) and $2w<m-1$ where $w,m=\dim W,M$. Assume that $M$ is compact and that $W\cap M\times \{0\}$ is the zero set of a ...

**-1**

votes

**0**answers

18 views

### Problem with equation structure and re-arrangement [on hold]

I am creating a program which used an equation for photo-efficiency in certain types of plants. Because of the limits of the programming (or maybe my abilities with said language). I need to break ...

**1**

vote

**1**answer

157 views

### Problem of book Kunen [on hold]

Suppose $P$ is a notion of forcing in $M$ such that $\left | P \right | \leq \omega_{1}$ and $P$ is ccc. Suppose further $\Diamond$ holds in $M$. How does one show that $\Diamond$ also holds $M[G]$?

**0**

votes

**0**answers

174 views

### Questions about the Collatz conjecture-also known as the “3x+1 problem” [on hold]

Let "F(k,m)" denote the following recursive function of two positive integer variables. For all k, F(k,1)=k. For all k and all m, if F(k,m) is even, then F(k,m+1)=F(k,m)/2. For all k and all m, if ...

**1**

vote

**1**answer

67 views

### Contour integral around semi-circle

Can one use contour integration to evaluate $\int^{\pi}_{0} \frac{1}{1-\rho*sin(\theta)}d\theta$ for $0<\rho<1$? This would be trivial if the upper limit were $2\pi$ as we could let ...

**0**

votes

**0**answers

45 views

### If the $L$-series does not vanish

I refer to this paper http://wstein.org/papers/shark/shark.pdf
At the top of page 24, we are dealing with the issue where the $L$-series does not vanish for the case where $p$ is good and ordinary. ...

**4**

votes

**1**answer

147 views

### Hypercovers of sheaves in classical and quasi-categories

I am interested in relating the definition of hypercovers in the $\infty$-topos of sheaves on an $\infty$-Grothendieck site to the classical definition of hypercovers of presheaves on a Grothendieck ...

**3**

votes

**1**answer

137 views

### Positive definite quadratic forms on Banach spaces

This is a question about characterizing Hilbert spaces in terms of quadratic forms. Let $X$ be a real Banach space and $E$ a bounded quadratic form on it, it is called positive definite if ...

**0**

votes

**0**answers

62 views

### Probability that d-Brownian Motion ,d>3, avoids a set A

In other words, the probability that Brownian motion stays within $A^{c}$. So far I found that it is 1, for random cylinders and thorns (http://www.math.upenn.edu/~pemantle/papers/burdzy.pdf).
What ...

**0**

votes

**0**answers

83 views

### Could anyone help me with a problem regarding fundamental groups? [on hold]

Let G be a group and x be an element of G. N is the least normal subgroup of G containing x. If there is a normal, path-connected space whose fundamental group is isomorphic to G, then I have to show ...

**-3**

votes

**0**answers

51 views

### Counting sets of tuples [on hold]

I am looking to count the size of certain sets created by taking the product of multivariate functions $F,Q,\ldots$, where the input arguments come from finite sets $D_1, D_2$.
For example,
...

**2**

votes

**0**answers

40 views

### Reducing $\ell_1$ norm of non-full-rank matrices

I have two matrices ${\bf{X}}_{p\times r}$ and ${\bf{Y}}_{r\times q}$ with $r<\min(p,q)$. Matrix ${\bf Y}$ does not have full row rank (i.e., rank$({\bf Y})<r$). Can I build two new matrices ...

**4**

votes

**0**answers

157 views

### Quotienting disk inside sphere result in sphere

Let $S^k$ be a topological $k$-dimensional sphere. Let $D^k$ be a $k$ dimensional disk that includes in $S^k$. Let
$q: D^k \to D^r$ be a map and $r \leq k$. Let
$$W = S^k \sqcup D^r/\sim$$
where ...

**6**

votes

**0**answers

131 views

### Mukai flops and derived categories

As proved by Kawamata and by Namikawa, if $M$ and $M'$ are complex projective varieties which are related by a Mukai flop (elementary transformation) along projective spaces $W\subset M$ and ...

**8**

votes

**2**answers

469 views

### Maximal ideals are prime (history thereof)

Please can someone tell me the history of the simple argument that any maximal ideal of a commutative ring or distributive lattice is prime? (It is understood that we have found the maximal one using ...

**3**

votes

**1**answer

129 views

### Vector Laplace Beltrami operator of the Gauss map

Consider an abstract surface $(M,g)$ embedded into $\mathbb{R}^3$ via $f:M \to \mathbb{R}^3$. Denote by $N:M \to \mathbb{R}^3$ the Gauss map (normal field) of the surface. Write the Laplace Beltrami ...

**3**

votes

**2**answers

129 views

### Bochner's theorem for measures of positive type

Is there a version of Bochner's theorem characterizing measures of positive type on a locally compact group? By a measure of positive type on the group $\Gamma$, I mean a measure $\mu$ satisfying ...

**0**

votes

**0**answers

49 views

### Rank 2^n quadratic form with non trivial invariant e_n

I advise you to have a look this question of mine first
Rank four quadratic Form with non trivial discriminant in I(k)
From quadratic form theory its well known that for a field $k$ and the ...

**2**

votes

**2**answers

150 views

### Examples of cubic Julia sets

I'm looking for information on explicit cubic filled Julia sets with interesting properties such as:
Having two different finite attractors (such as $f(z)=z^3-1.5z$)
Being disconnected with ...

**3**

votes

**3**answers

84 views

### graded generalization of the Moyal–Weyl product

Has anyone written about the graded generalization of the Moyal–Weyl product/star product, that is, where the original algebra is already graded? Is it just a matter of signs?

**4**

votes

**1**answer

93 views

### Clifford algebras for quadratic modules over ringed spaces

What is the earliest possible reference for definition and basic properties of Clifford algebras associated to quadratic modules over a ringed space? The ringed space does not need to be locally ...

**0**

votes

**1**answer

24 views

### Bivariate skew-normal distribution [on hold]

I'm using the Gaussian distribution as a weight function for solving pde's.
I'm interested in skewing the function. For one-dimensional problems, it was easy to
derive the resulting skewed Gaussian ...

**4**

votes

**0**answers

60 views

### First return time in an interval for N particles rotating on the circle at constant random speeds

Here is my problem: draw N velocities $v_1,v_2,\dots,v_n$ in $[-\pi,\pi]^N$ from some measure (Haar measure of uniform independent for simplicity) and make $N$ particles rotate around the circle with ...

**-2**

votes

**0**answers

64 views

### Calculating of the sum $\sum_{i=1}^{n} \large{\frac{i}{i+1}}$? [on hold]

How can i calculate the sum $\sum_{i=1}^{n} \large{\frac{i}{i+1}}$?

**-1**

votes

**0**answers

68 views

### Can a linear map on a finite-dimensional subspace be extended to the whole space “trivially”? [on hold]

I have a question concerning the extension of continuous linear maps.
Let $X$ be a normed vector space and let $U$ be a finite-dimensional subspace of $X$. Furthermore, let $\varphi:U\rightarrow Y$ ...