-1
votes
0answers
7 views

whatever happened to the conference International Symposium on Voronoi Diagrams in Science and Engineering (ISVD)?

I am not sure of a better place to ask this, hopefully someone here knows something... I've been "away" from computational geometry topics for a bit and thought I'd catch up in some way by checking ...
0
votes
0answers
15 views

On the derivative of a distance function

I have a question about the derivative of a distance function. Let $D \subset \mathbb{R}^{d}$ be a connected and unbounded open subset with smooth boundary. $B(z,r)$ denotes the open ball of radius $...
0
votes
0answers
17 views

is shuffle a Monad?

In the list monad, your map $TT \rightarrow T$ takes a list of lists and concatenates them to form a list. There is another way to take a list of lists and create a list, which is to shuffle randomly ...
0
votes
0answers
9 views

Contractions in convex metric spaces

Let $M \subset \mathbb{R}^n$ be open, bounded and convex and equip $M$ with an unbounded metric $d$ that induces the Euclidean topology. Is there always a map $f : M \to M$ and two constants $C_1 > ...
1
vote
0answers
24 views

Compute the kernel of multiplication of algebraic numbers

Let $\lambda_1, \cdots, \lambda_n$ be the roots of a polynomial $g(x)$ of $n$-degree with rational coefficients. (Hence obviously they are algebraic numbers.) Consider a function $f: \mathbb{Z}^n\...
0
votes
0answers
15 views

Kazarnovskii pseudovolume

Let $\Gamma\subset\mathbb C^n$ be a convex polytope and let $h_\Gamma(z)=\max_{v\in\Gamma}{\rm Re}\langle z,v\rangle$ be its support function with respect to the standard scalar product on $\mathbb C^...
2
votes
0answers
28 views

Must this extension of a DVR be unramified?

Let $A$ be a normal domain, and $P$ a height 1 prime, then $A_P$ is a DVR. Let $K$ be the fraction field of $A_P$, and let $L$ be a finite Galois extension of $K$ of degree $e$, let $B$ be the ...
0
votes
1answer
13 views

Limit of iterative addition of a mean-preserving spread

Suppose I iteratively add a given mean-preserving spread to a random variable. In the limit, will exactly half the mass be above $0$? Formally: Let $X$ be a random variable, and let $\varepsilon_1,\...
1
vote
0answers
8 views

Day convolution on the category of copresheaves on the opposite of a monoidal closed category

I asked this question on math.stackexchange (http://math.stackexchange.com/questions/1871328) but didn't get an answer so I decided to ask it here too. If $\mathcal{C}$ is symmetric monoidal closed, ...
0
votes
0answers
23 views

How about cutting a Mobius strip along a non-self-intersect curve between two boundary points

Take any two boundary points of a Mobius strip, and connect them by a non-self-intersect curve C. Cut the Mobius strip along C, then we will get a belt homeomorphic to a disc, or a union of a ...
2
votes
1answer
39 views

Generation in finite simple groups of Lie type

Let $S$ be a finite simple group of Lie type and $p$ be a prime such that $|S|_p=p$. I want to get some restrictions on $S$ with the conditions that $S$ is generated by elements of order $p$ and the ...
0
votes
0answers
36 views

Systole of a flat surface

Is the systole (length of the shortest saddle connection) of a flat surface $(X,\omega)$ ($X$ is a Riemann surface and $\omega$ an abelian differential on it with zeros in the points $\Sigma=\{p_1,\...
4
votes
3answers
57 views

Expected distance between points drawn from different distributions

Let $X$ and $Y$ be independent random variables, with $X_1,X_2$ being independent copies of $X$ and $Y_1,Y_2$ being independent copies of $Y$. Then (is it true that) $2\mathbb{E}|X-Y|\geq\mathbb{E}|...
0
votes
0answers
45 views

Strong convergence on Dual of Reflexive Banach Space

Let $\mathcal{H}$ be a separable Hilbert space and let $\mathfrak{S}_{p}(\mathcal{H})$, $1<p<\infty$, denote the $p$-th Schatten class of compact operators acting on it. Suppose we have a net ...
0
votes
0answers
74 views

congruences: number theory [on hold]

We have the following Diophantine equation on $l, m, n$ (all belong to natural number) $(4a^2 - y^2)^l + (4ay)^m = (4a^2 + y^2)^n$, where $a$ and $y$ both belong to natural number with $(a, y) = 1$, $...
0
votes
0answers
30 views

Mappings of random processes $\varphi(X(t))$

I am interested in problems of the following type. Let $X(t)$ be a planar random process and $\varphi:\mathbb R^2\to\mathbb R^2$ be a mapping. Then what can we say about the image $Y(t) = \...
-2
votes
0answers
41 views

proof Hadamard's Inequality [on hold]

Theorem 4.2. Hadamard’s Inequality. Suppose A is positive semidefinite of size n. Then |A|≤ [A]11···[A]nn. Proof. Let A be any positive semidefinite matrix of size n. Note that In is a postive ...
1
vote
1answer
59 views

The midpoint geodesic

Let $(M,g)$ be a complete simply connected Riemannian manifold with non-positive curvature. Because of the Hopf-Rinow theorem, any two points are connected by a geodesic segment. Pick three distinct ...
1
vote
1answer
131 views

Does composite number of the form $6k + 1$ has at least three non-totient divisors?

If $n$ is composite then $\phi(n) < n-1$ (Euler's totient function) hence there must be one or more divisors of $n-1$ which do not divide $\phi(n)$. For lack of a better terminology, let us call ...
-2
votes
0answers
23 views

How to compare to geometric curve [on hold]

noisy image original image In original image i have a curve representing human contour, and in noisy image with human contour curve some additional noisy curves are there. I want to remove the noisy ...
1
vote
0answers
31 views

Lattices without nontrivial dense elements

This question arose from another one of mine, Homotopy type of some lattices with top and bottom removed. An element $d$ of a bounded lattice $L$ is called $\mathit{dense}$ if $$ \forall x\in L\ (d\...
1
vote
0answers
28 views

Unique Fixed Point in a Simplex

I have a vector $(X_1,X_2,...,X_n)$ and satisfy the constrain $\sum_iX_i=1$. Then an operator is defined as $X_i=F_i(\textbf{X})\textbf{X}$, so in fact the operator is $T:\Delta^n\rightarrow\Delta^n$. ...
9
votes
0answers
177 views

Has the following problem posed by Deligne in the official description of the Hodge conjecture been solved?

Towards the end of his official description of the Hodge conjecture, Deligne asked the following question: Let $A$ be an abelian variety over the algebraic closure $\mathbb{F}$ of a finite field ...
-1
votes
0answers
27 views

Determinants of block matrices with non-square diagonal and square anti diagonal elements [on hold]

Is there a way to find the determinant of $X$ in terms of its sub-matrices $A,B,C_0$ and $R_0$? $$X = \begin{bmatrix} AC_0 & -I_n\\ 0_{(n-1)} & R_0B \end{bmatrix} \in \mathbb{R}^{(2n-1) \...
2
votes
0answers
46 views

Proof that the length function $\ell: \operatorname{Teich}(S) \to \mathbb{R}^\mathcal{S}$ is injective without the $9g-9$ theorem

In Chapter 10 about Teichmüller spaces of Farb and Margalit's "A Primer to Mapping Class Groups", the length function $$\ell: \operatorname{Teich}(S) \to \mathbb{R}^\mathcal{S}$$ is described, where $...
1
vote
1answer
80 views

Mapping Class Group (MCG) of connected sum of 3-torus and $S^2\times S^1$

I know that the MCG (isotopy-classes of orientation preserving homeomorphisms) of 3-torus $(S^1\times S^1 \times S^1)$ is $SL(3,Z)$, since it is an Eilenberg–MacLane space, giving $ MCG(T^3)=Out(\pi_1(...
-4
votes
0answers
24 views

which universties in USA and europe have intersted in delay differentail equations or functional differential equations? [on hold]

I am in master degree now about delay differential equations and I need after master degree get scholarship for Phd so which university is intersest on delay differential equation or functional ...
20
votes
0answers
626 views

What was achieved on IUT summit, RIMS workshop?

I would like to know what was achieved in the workshop towards the verification of abc conjecture's proof and the advance of understanding of IUT in general. A comment from a participant: C ...
-4
votes
0answers
29 views

Differentiation with composite, product and quotient rule [on hold]

This is a simple question but I hope someone can give a detailed explanation of how to solve the question. Differentiate y=xtan√x.
1
vote
0answers
74 views

How did the $\operatorname{div}_x$ “disappear”?

Given $E(x,t) := \nabla_x (\frac 1{|x|} * \rho)$ where $\rho : \mathbb R^3 \times [0,\infty) \to \mathbb R$ is defined by $\rho(x,t):=\int_{\mathbb R^3} f(x,v,t) dv$, I have understood that $$\rho(x,t)...
1
vote
0answers
24 views

Quantifying how much a vector gets turned toward the expanding direction of an $\mathrm{SL}(2,\mathbb R)$ matrix

Consider a matrix $B\in \mathrm{SL}(2,\mathbb R)$. Let $s$ be a vector that is pointing in the most contracted direction of $B$, and let $u$ be the image under $B$ of a unit vector pointing in the ...
8
votes
1answer
135 views

How to compute modular forms of weight one on Shimura curves?

Classical modular forms of weight $k\geq 1$ can be computed explicitly by exhibiting their $q$-expansion. When the weight is at least two, the most standard method uses modular symbols. When the ...
3
votes
0answers
85 views

How do sutured TQFT fit into the larger TQFT picture?

In https://arxiv.org/abs/0807.2431, Honda--Kazez--Matic introduce a definition of (1+1 dimensional) sutured TQFT; see also e.g. Mathews http://arxiv.org/abs/1006.5433 and Fink https://arxiv.org/abs/...
2
votes
0answers
43 views

Special values of real analytic Eisenstein series

Given $\tau$ in the upper half plane, define the normalized real-analytic Eisenstein series by $$ E(\tau, s) = \frac{1}{2} \sum_{(m,n)}' \frac{y^s}{|m\tau + n|^{2s}} $$ It is initially defined for $\...
1
vote
0answers
44 views

Reference for $q^{\eta\sum_{i}t_{\lambda_{i}}\otimes t_{\mu_{i}}}$ part of an expression for universal $R$-matrix of a quantum group algebra

The Wikipedia entry for quantum groups states that a quantum group $U_{q}\left(\mathfrak{g}\right)$ has an infinite formal sum that plays the role of an $R$ matrix, which is the product of two factors,...
0
votes
0answers
43 views

Homomorphism from integral module generated by roots of unity to cyclic group?

Let $S$ be the set of all roots of unity. Consider the $\mathbb{Z}$-module, $\mathbb{Z} S$, as an additive abelian group (that is, $\mathbb{Z} S$ is the subset of complex numbers that can be ...
4
votes
0answers
58 views

Traces in finite extensions of integrally closed domains

$\def\fp{\mathfrak{p}}\def\fq{\mathfrak{q}}$I'm looking for a reference for the following commutative algebra fact. Let $A$ be an integrally closed integral domain, with field of fractions $K$. ...
2
votes
0answers
30 views

Torsionless not separable abelian groups

A torsionless abelian group $A$ is one for which any element $a\neq 0$ can be sent to a nonzero element of $Z$ by some homomorphism $A\rightarrow Z$ (integers). Equivalently, $A$ can be embedded as a ...
-1
votes
0answers
35 views

Deriving global probabilities from local dynamics

I am interested in growth dynamics and, in particular, how to derive difference/differential/stochastic equations from local behavior of a system. I tried posting first on math.stackexchange (https://...
0
votes
0answers
49 views

conjugacy classes of cyclic subgroups of order $k$ in $ {\rm GL}_n(\mathbb{Z}/p^m\mathbb{Z}) $

Let $p$ a prime numbers and $k$ be positive integer such that $(k, p) = 1$. And $m$ be the order of $p$ in $\mathbb{Z}/k\mathbb{Z}^×$. How many conjugacy classes of cyclic subgroups of order $k$ does ...
2
votes
1answer
66 views

Coefficients for Powers of the Mittag-Leffler Function

Considering the one parameter Mittag-Leffler function, $$E_{\alpha}(z)=\sum_{k=0}^\infty\frac{z^{k}}{\Gamma(\alpha k+1)}, \Re(\alpha)>0$$ Considering then the generating function for $E_\alpha(z^...
0
votes
0answers
36 views

Why is $R_{\Omega}R_{\Omega}^{*}=R_{\Omega}$ in matrix completion?

In the matrix completion literature, a restriction or sampling operator is defined as follows. Let $X$ be the unknown matrix to be recovered and $\{w_{\alpha}\}_{\alpha=1}^{n^2}$ be some orthonormal ...
1
vote
1answer
151 views

Identity from Lectures on the Theory of Elliptic Functions by Harris Hancock

I'm working on Example $4$, page $262$, of Harris Hancock's book Lectures on the Theory of Elliptic Functions which reads: Prove that $\dfrac{1}{\operatorname{sn}(iu,k)^2} + \dfrac{1}{\...
-1
votes
0answers
33 views

Trigonometry from two graphs [on hold]

My problem is that i have an image or rectangle which has line inside it which is rigid it will not move. I also have a graph with the same line but may be slightly bigger and may have a slightly ...
1
vote
0answers
116 views

Fibration when central fibre is a Calabi-Yau variety

Let $f\colon X\to Y$ be a surjective proper holomorphic fibre space such that X and Y are projective varieties and central fibre $X_0$ is Calabi-Yau variety and Y is also Calabi-Yau variety, then can ...
3
votes
0answers
84 views

Twisted derived Morita theory of schemes

It has been proved by Toën and Lunts-Schnürer that the dg category $\mathrm{L}_{qcoh}(X\times Y)$ of quasi-coherent sheaves over the product of two quasi-compact, quasi separated (and flat over a ...
0
votes
0answers
19 views

Rank of the Matrix under the following Constraints? [on hold]

Case 1: An nXm Matrix of Non-Negative Integers, and the scalars are allowed to have only binary values (i.e. 0 or 1)? Case 2: The calculation of the Binary Matrix in Gf(2) is a standard algorithm....
3
votes
0answers
56 views

Bott-type projections in $C^*$-algebras

Let $A$ be a unital $C^*$-algebra and $a\in A$. If $aa^*+1$ is invertible in $A$ then the element $$\beta(a)=(aa^*+I)^{-1}\left(\begin{array}{cc}aa^* & a \\a^* & I\end{array}\right)$$ is an ...
5
votes
1answer
109 views

Can a projective solvable group be transitive?

Let $p > 3$ be a prime number, and let $G \leq \mathrm{PGL}_2(\mathbb{F}_p)$ be a solvable subgroup. Is it possible that the action of $G$ on $\mathbb{P}^1(\mathbb{F}_p)$ is transitive?
-3
votes
0answers
38 views

Estimation of Uncertainty of parameters defined from Lognormal Particle Distribution [on hold]

I think I previously posted too simplified math question (OTL), so I would like to ask again with more specific examples and problems that I currently have for my cloud radar research. Let us assume ...

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