# All Questions

**-1**

votes

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**3**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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 ...