# All Questions

**0**

votes

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3 views

### Dessin d'enfant and moduli space of bordered/punctured hyperbolic Rieman surfaces

Belyi's theorem states that if a Riemann surface could be defined as an algebraic curve over an algebraic number field, then this Riemann surface could be described by a Dessin d'enfant. I have two ...

**0**

votes

**0**answers

4 views

### Convergence of unitary products on a Hilbert space

First: I'm sorry for the basic question--I can move it to Math SE if necessary...
Let $X$ be a Hilbert space and suppose $\{U_k\}_k$ is a sequence of unitary operators on $X$. Let $||\cdot||$ be the ...

**0**

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**0**answers

4 views

### Arnold chord conjecture

Recently I've started learning about the Arnold conjecture for the number of Reeb chords on a Legendrian submanifold of a contact manifold. It says that under some conditions, the number of Reeb ...

**0**

votes

**0**answers

10 views

### “Sheaf” on the nerve of a category

So I have the nerve of a category and want to communicate information about the sets at each level in the simplicial set (nerve). Is there a way to regard the nerve as a category itself? Then one ...

**2**

votes

**1**answer

87 views

### Supercommutator of exterior multiplication operators and their adjoints

Let $\mathfrak{h}$ be a complex Hilbert space and consider Grassmann algebra $\mathcal{F}=\bigwedge\mathfrak{h}$ with its induced inner product. For $\omega\in\mathcal{F}$ we also consider the ...

**0**

votes

**1**answer

34 views

### Normalization of complete intersection

Let A be an integral complete local ring over a field which is complete intersection.
Let B be a normalization of A.
Q. Is B gorenstein?
I guess that even the normalization of gorenstein local ...

**5**

votes

**1**answer

184 views

+50

### Any similar Lagrange's identity inequality

we know Lagrange's identity
$$(a^2_{1}+a^2_{2}+a^2_{3})(b^2_{1}+b^2_{2}+b^2_{3})=(a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3})^2+\sum_{i=1}^{2}\sum_{j=i+1}^{3}(a_{i}b_{j}-a_{j}b_{i})^2$$
then we have ...

**2**

votes

**1**answer

454 views

### optimization of inverse matrix with constraint on matrix elements

everyone! I have this optimization problem with constraint.
$D$ and $T$ are symmetric matrices, where T is known and D is the unknown parameter.
$x$ and $v$ are two known p-dimensional vectors.
The ...

**-1**

votes

**0**answers

12 views

### Condition to be Fourier coefficients for an periodic function

It is well known that a periodic function $f(t)$ satisfying Dirichlet conditions has its unique Fourier series representation.
Inversely, I wonder what conditions is needed for sequence $\{c_n\}_{n ...

**5**

votes

**2**answers

122 views

### Homotopy groups of Moore spaces

Is there anything known about the homotopy groups of the Moore spaces $M(\mathbb Z_m,n)$ if $m\neq 2$ and $n \geq 2$?

**5**

votes

**1**answer

88 views

### Interior periodic points of area preserving homeomorphisms of a pair of pants

A celebrated result of Franks shows that any area preserving homeomorphism of the closed annulus $A$ with at least one periodic point (possibly along the boundary) has infinitely many interior ...

**1**

vote

**0**answers

56 views

### Finding the infimum using a piecewise isometry

Given a finite set of unit circles in the plane such that the area of their union $U$ is $S$, what is the largest possible bound $kS$ for some constant $k$ such that there exists a subset of ...

**9**

votes

**2**answers

598 views

### Undecidable puzzles

There are plenty of popular NP-hard puzzles,
for example, generalized Sudoku ($n^2 \times n^2$-board), Flow (I cannot give a source for this), Minesweeper, etc.
Recently, I read a bit about aperiodic ...

**0**

votes

**0**answers

29 views

### Number of solutions to a modular congruence

What methods are there for determining the number of solutions to modular congruences of the form $a^m \equiv b^n k \pmod{p}$ with $1 \leq a,b \leq p-1$ where $p$ is a prime?
In the case $m,n$ ...

**3**

votes

**1**answer

684 views

### sum of the series $\sum_{n=1}^\infty \frac{(-1)^{(n-1)}}{\sqrt{n}}$?

Hi,
We know that the series $\sum_{n=1}^\infty \frac{(-1)^{(n-1)}}{\sqrt{n}}$ is convergent and it is oscillating. and numerically it is almost 0.6048986434.
I want to know what is the exact limit ...

**-2**

votes

**0**answers

35 views

### Probability problem - no idea where to start

I have been working on this question for a few days and I am completely lost on how to solve it. Any suggestions, comments, hints are greatly appreciated.
Participants are competing in a ...

**1**

vote

**2**answers

54 views

### Convexity of truncated expectation

Let $k, n$ be two positive integers with $k \leq n$, and let $P = \{ (x_1, \dots, x_n) \in [0, 1]^n : \sum_i x_i = k \}$.
Given $x = (x_1, x_2, \dots, x_n) \in P$, let $X_i$ be the random variable ...

**0**

votes

**0**answers

24 views

### Mean curvature and submanifold

Consider $S^{N-1}$ the unit sphere and let us focus our attention on the cap
$$
G=S^{N-1}\cap\{x_N>0\}
$$
with boundary $\partial G= S^{N-2}\times\{0\}$: it is quite obvious to see that $G$ is a ...

**1**

vote

**2**answers

39 views

### What does the existence of self complemented elements tell us about a complete lattice?

Let $L$ be a complete lattice with an involution operation $*$ (a unary operation such that for any $x, y \in L$, $x \leq y$ implies $x^{*} \geq y^{*}$). Now, suppose that there is an element of $L$ ...

**0**

votes

**0**answers

27 views

### Groebner basis of algebraic system of polynomials

I have 8 polynomials with 8 unknowns as {p,L,x1,x2,y1,y2,z1,z2}, and the remaining are all known coefficients. The polynomials are as follows:
f1=h1*p - L*(h1*xb*y2 - h2*x1*y1 - h3*x2*y1) + h4;
...

**9**

votes

**1**answer

139 views

### Digital physics and “Gandy-like” machines

Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ...

**3**

votes

**0**answers

68 views

### Deformation quantization of Poisson bracket without star-product

Kontsevich's formality theorem implies in particular that star-products on a $C^\infty$-manifold $M$,
$$f\star g = fg + \sum_{k\geq1} \hbar^k B_k(f,g),\qquad f,g\in C^\infty(M),$$ where $B_k$ are ...

**0**

votes

**0**answers

52 views

### Taylor-Series e^e^x [on hold]

I'm new to the whole topic of Taylor-Series and I am trying to figure out the Taylor-Series of $e^{e^x}$. I got the derivatives but that doesn't help right now. I think I need the n-th derivative, ...

**-2**

votes

**0**answers

44 views

### Could it be possible to check if Pi is a normal number? [on hold]

So currently we don't know if Pi is a normal number and if it really contains all finite number sequences. Is it possible that we will know this in the future? Can we be sure one day?

**0**

votes

**0**answers

12 views

### Is the Lopatinski-Shapiro condition invariant under diffeomorphism?

If a PDE (eg. the heat equation with Robin BCs, or the elliptic version) on a bounded smooth domain $U$ satisfies the Lopatinski-Shapiro condition (for a definition see eg. Wloka), and if $T:U \to W$ ...

**5**

votes

**2**answers

224 views

### Kazhdan's property (T) vs. residual finiteness

I have asked this question already on mathstackexchange but got no answer (see http://math.stackexchange.com/questions/1795795/kazhdans-property-t-vs-residual-finiteness) and it was suggested that I ...

**1**

vote

**0**answers

25 views

### Reflexive subspaces of dual spaces

If $X$ is a Banach space, is it true that $X^{*}$ must contain an infinite dimensional reflexive subspace? I know of Gowers' example of a Banach space not containing $c_0$, $l_1$, or reflexive, but I ...

**16**

votes

**2**answers

491 views

### Nice sign-expansions of special surreal numbers

What is the "right" surreal generalization of the fact that a real number $r$ is rational if and only if its sign-expansion is eventually periodic?
I can think of more than one natural way to ...

**0**

votes

**0**answers

54 views

### Is the category Cat complete?

Let $Cat$ denote the 2-category of small categories. Is $Cat$ complete?
That is, given a diagram $\phi:J\rightarrow Cat$, does the limit over the diagram exist in $Cat$?

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136 views

### Warren's Theorem

At the end of page 12 in this document Noga Alon mentions Warren's Theorem on sign patterns: tau.ac.il/~nogaa/PDFS/tools1.pdf
Does anyone know of an intuitive explanation of the proof of it ? Also, ...

**3**

votes

**2**answers

80 views

### Cube Lemma on a cofibrantly generated (almost) model category

Suppose I have a complete and cocomplete category $\mathscr{C}$ with two sets of maps $I,J$ that are the candidates for generating (trivial) cofibrations on a model structure on $\mathscr{C}$.
The ...

**4**

votes

**3**answers

85 views

### Birationally transforming a quartic elliptic curve

Consider the elliptic curve
$$y^2=ax^4+cx^2+dx+f$$
I am aware that there are algorithmic methods for birationally transforming a nondegenerate cubic curve into the Weierstrass canonical form ...

**1**

vote

**1**answer

106 views

### Interpreting peano arithmetic without parameters

I will accept an answer in the form of references to the literature about my question as well as any other information. I am quite ignorant of the area and that will be clear from my question.
I ...

**0**

votes

**0**answers

33 views

### Finding the right σ-algebra. Question on uncertainty related to the secretary problem

Assume a number of iid. items is presented and the task was to stop under the objective of picking the best item.
In this setting it is relevant what is the distribution of the values of the ...

**2**

votes

**0**answers

88 views

### Show that $SL_2(\mathbb{F}_p)$ is quasi-random

Terry Tao gives this oblique definition of quasirandom group in his notes 3
$G$ is quasi-random (of order $D$) if all non-trivial unitary representations $\rho: G \to U(H)$ have dimension at ...

**47**

votes

**16**answers

7k views

### Collection of equivalent forms of Riemann Hypothesis

This forum brings together a broad enough base of mathematicians to collect a "big list" of equivalent forms of the Riemann Hypothesis...just for fun. Also, perhaps, this collection could include ...

**14**

votes

**4**answers

422 views

### Spectral theory of graph Laplacian besides $\lambda_2$

Most of what I've seen about the spectral theory of the graph Laplacian concentrates on $\lambda_2$, the second-smallest eigenvalue. This eigenvalue contains information regarding the connectivity of ...

**11**

votes

**1**answer

154 views

### Does a Kähler manifold always admit a complete Kähler metric?

Every smooth manifold admits a complete Riemannian metric. In fact, every Riemannian metric is conformal to a complete Riemannian metric, see this note. What about in the Kähler case?
Does a ...

**3**

votes

**1**answer

71 views

### The average number of a class of reduced, primitive, positive definite binary quadratic forms

Let $f(x,y) = ax^2 + 2bxy + cy^2 \in \mathbb{Z}[x,y]$ be a positive definite binary quadratic form with even discriminant. We say that $f$ is primitive if $\gcd(a,2b,c) = 1$ and it is reduced if $0 ...

**-2**

votes

**0**answers

80 views

### Math notation with no possible syntax errors [on hold]

It surely is possible for e.g. simple integer arithmetic
to invent a notation where every statement is syntactical
correct, just enumerate them - "#" means "0=0", "##" "0=1",
maybe "#...#" (239 of ...

**1**

vote

**0**answers

20 views

### What is the relation between roots of classical and Atkin modular polynomial?

Modular polynomials are a good tools in elliptic curves. I need to find the roots of $l$-th classical modular polynomial $\Phi_l(X,Y)$ over the prime field. Unfortunately the coefficients of these ...

**7**

votes

**4**answers

4k views

### Visualizing Orthogonal Polynomials

Recently I was introduced to the concept of Orthogonal Polynomials through the poly() function in the R programming language. These were introduced to me in the concept of polynomial transformations ...

**0**

votes

**0**answers

52 views

### Free Symmetric Operads

In the definition of operads, if we restrict our attention to S-modules where the action by the symmetric groups is free, then the free operads
have still an underling "free S-module"? Even the ...

**1**

vote

**0**answers

10 views

### Differential inequalities for a strictly diagonal dominant system of linear ODEs

Let $A$ be a real $d\times d$ matrix. The diagonal elements are strictly negative ($a_{ii}<0$) and the off-diagonal elements are non-negative ($a_{ij}\geq 0$ for $i\neq j$). $A$ is strictly column ...

**5**

votes

**1**answer

368 views

### What is the state in the WRT TQFT associated to a handlebody?

Let $Y^3$ be a handlebody with boundary $\Sigma$. By definition, there is some associated vector $v_{WRT}(Y^3)\in Z(\Sigma)$, the (finite dimensional) Hilbert space associated to $\Sigma$ by the ...

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votes

**0**answers

109 views

### Detecting Bijection between two Permutation Set [on hold]

Let, $L$ is a set of $n$ labels / colors (repetition of label/color is possible). Assume, there is a function $f$, that maps labels of $L$ to itself. this mapping is bijective.
Let, $\beta$ is a set ...

**-1**

votes

**0**answers

40 views

### “D” notation of a number [on hold]

I'm looking to understand what the meaning of the following notation is:
8.211D - 10
It's specifically from a program called Scilab but I've been unable to find what it represents in any of the ...

**1**

vote

**0**answers

31 views

### Continuously variable *space*

I'm trying to understand formally how and why a fiber bundle with fiber $F$ should be thought of as a gluing of homeomorphic copies of $F$ which varies continuously. I do not understand how this is ...

**2**

votes

**2**answers

157 views

### Relation of these two Dirichlet $L$-functions

Let $\chi$ and $\psi$ be two quadratic Dirichlet characters and let $L(s,\chi)$ and $L(s,\psi)$ their associated Dirichlet $L$-functions.
Is there a realtion between these two Dirichlet ...

**2**

votes

**1**answer

78 views

### Catalogs/numbers/constructions of non-isomorphic conference matrices

I am interested in complete catalogs of non-isomorphic conference matrices, similar to those of Hadamard matrices. Do such catalogs exist? If yes, then where could they be found, and what is an ...