# All Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### “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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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### 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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### 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 ...
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### “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 ...
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### 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 ...
### 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 ...