# All Questions

**0**

votes

**0**answers

15 views

### Commutation of limits and pullbacks

i know that i asked this question already on stackexchange, but maybe it is also useful to aks this here:
Suppose we have three directed sequences of $C^*$-algebras, say ...

**0**

votes

**0**answers

11 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

22 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

36 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 ...

**3**

votes

**0**answers

34 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 ...

**0**

votes

**0**answers

23 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

68 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 ...

**2**

votes

**0**answers

39 views

### Is the set of $C^\infty$ sections a strong deformation retract of the space of $C^k$ sections?

For finite-dimensional smooth manifolds $E,M$, let $E\to M$ be a smooth fibre bundle. Let $k\in\mathbb{N}=\{0,1,\dots\}$, and let $U$ be an open subset of the total space $J^kE$ of the $k$-jet bundle. ...

**0**

votes

**0**answers

18 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 ...

**0**

votes

**0**answers

71 views

### Multiplicative Identity in a (SU(n)) Group

Let ${P_i}$ be members of $SU(n)$ such that for all $U$ in a subgroup [or subset] $H$: $$P_1UP_2U\cdots P_nU=I$$ where $I$ is the identity element. Are there ${P_i}$ can $H$ be enlarged to the whole ...

**1**

vote

**0**answers

21 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

35 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

41 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

76 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 ...

**8**

votes

**2**answers

289 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 ...

**2**

votes

**0**answers

40 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

**0**answers

49 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

50 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

14 views

### Problem with equation structure and re-arrangement [migrated]

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 ...

**0**

votes

**1**answer

122 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

157 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

56 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

40 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. ...

**3**

votes

**1**answer

61 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

100 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

35 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.
What about for connected and compact sets (traps)? Any other ...

**0**

votes

**0**answers

77 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

47 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

33 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 ...

**3**

votes

**0**answers

112 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 ...

**4**

votes

**0**answers

98 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

436 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

119 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

104 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

48 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

**1**answer

83 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

71 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?

**3**

votes

**1**answer

82 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

21 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

47 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

60 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

64 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 $\varphi:U\rightarrow Y$ ...

**7**

votes

**1**answer

195 views

### Why does this antisymmetric product factor out a determinant?

Consider a generic $n \times n$ matrix $M$.
Define the $(n-1) \times n$ matrix $M_q$ to be $M$ with the $q$th row omitted, and assume that $M_q$ possesses a right inverse, $R_q$:
$$R_q = M_q^T (M_q ...

**0**

votes

**0**answers

34 views

### asymptotic notation with graph colouring

This is my first ever post so I hope this is an appropriate question.
Basically I am looking at the paper here: http://homepages.math.uic.edu/~mubayi/papers/biclique.pdf
Namely theorem 5.
Now, feel ...

**1**

vote

**2**answers

154 views

### Extending vector bundles from subvarieties

Let $X$ be a smooth projective variety and let $Y\subset X$ be a smooth subvariety. Given a vector bundle $E$ on $Y$, when can $E$ be extended to a vector bundle $\tilde E$ on $X$? I.e., are there ...

**1**

vote

**0**answers

117 views

### On functoriality of the Leray spectral sequence

The Leray spectral sequence is functorial in the following sense: given a commutative square of spaces,
$$\begin{matrix} A & \to & B \\ \downarrow & & \downarrow \\ C & \to & D ...

**-2**

votes

**0**answers

48 views

### An integral identity [on hold]

For all $n>1$ and $0<i<n$ we have the following identity?
$$\int\limits_0^{\pi} \frac{\cos(nx)-\cos(i\pi)}{\cos x-\cos(i\pi/n)}dx=0.$$

**5**

votes

**2**answers

171 views

### String diagrams for bimodules over noncommutative algebras?

I'm trying to do some calculations with bimodules (over Azumaya algebras, as it happens), and I need a string diagram notation that mixes the tensor product over the base ring (a symmetric monoidal ...

**1**

vote

**0**answers

16 views

### Gelfand Kirillov dimension of induced modules

How does the Gelfand-Kirillov dimension of induced modules behave?
In patricular, if $S$ is an Ore extension of $R$, how is the GK-dimension of an $R$-module say $N$ related to the GK dimension of $N ...

**3**

votes

**0**answers

97 views

### Small remarkable matroids

Working on phased matroids (a generalization of oriented matroid to the complex case) I've found an interesting formula for computing the inner Tutte group (and, hence, all the Tutte groups) ...