# All Questions

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### Explict form of $E_\infty$-morphisms between differential graded commutative algebras

This is a partial duplicate to this MO question, I apologize for that. I'm asking since the answers there still do not allow me to work out an answer to my question, which is a bit more specific.
...

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3 views

### regular locus of an affine domain

Let $A$ be an affine domain over a field $k$ (need not be algebraically closed). Let $\mathfrak{p}$ be a prime ideal of $A$, such that $A_{\mathfrak{p}}$ is a regular local ring. Does there always ...

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9 views

### Aperiodic graphs

The concepts of being non-periodic and aperiodic for tilings have obvious versions for connected graphs with a countable set of vertices and a finite number of edges meeting at each vertex. A graph ...

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**1**answer

12 views

### Linear intersection number and maximum degree

This question is inspired by a Andrew D. King's comment in Linear intersection number and coloring (not chromatic) number
A linear hypergraph is a pair $\pi=(X, L)$ where $X\neq \emptyset$ is a set ...

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17 views

### Inverse Trigonometric Functions [on hold]

I have the following question:
for which I need to prove the above to be x/2
I tried to first convert it to :
then multiply and divide by
to get this:
But have no idea what to do next , ...

**3**

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**2**answers

157 views

### Maryam Mirzakhani's works

Maryam Mirzakhani has made several contributions to the theory of moduli spaces of Riemann surfaces.
Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics ...

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21 views

### K-theory of coherent sheaves on complex manifolds: references and gamma-filtration?

For a complex manifold $X$ one has an exact category of locally free coherent sheaves; so it seems to be no problem to define certain $K$-theory (I do not know whether the $K$-groups given by the ...

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16 views

### Norm on C$^*$-algebra

Let $A$ be a C$^*$-algebra, $x$ a non-zero positive element of $A$ such that ||x|| = 1, $r(x)$ is the range projection of $x$ in $A^{**}$, $e = 1 - r(x)$, $I := A \cap e A^{**} e$, $(x_n)$ and $(\rho ...

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**1**answer

44 views

### Abstract connectedness

Is there an abstract structure that characterizes connectedness, analogously to how topological spaces characterize continuity?
Here's one way to make this question more precise: if $(X,T_X)$ is a ...

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**1**answer

35 views

### Exact reference for Liouville theorem

It seems hard for me to find that the solution of the following equation
$$
\Delta u+e^u=0
$$
defined on a simply-connected domain $D\subset R^2$ must be of form
$$
...

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**3**answers

66 views

### Application of Fraïssé construction in set theory

As you know Fraïssé limit construction and its generalization, Hrushovski's construction, have many applications in model theory to build models with interesting property.
Now I would like to know ...

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**1**answer

44 views

### Matrices over a finite field with given Jordan normal form over the algebraic closure

Can one describe the (conjugacy classes of) square matrices over a finite field such that over the algebraic closure of this finite field their Jordan normal form consists of one Jordan block? (Such ...

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15 views

### Alternative form for weighted least squares

Coefficients $\beta$ can be estimated from $y$ by weighted least squares with:
$ \beta = (X^T\Sigma^{-1}X)^{-1} X^T \Sigma^{-1} y $
where $\Sigma$ is the covariance matrix of the noise.
Let $N$ be ...

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56 views

### Averages over integer points of the sphere

A paper of William Duke sketches a proof that integer points on the sphere are equidistributed.
$$ V_N = \{ (x,y,z) \in \mathbb{Z}^2 : x^2 + y^2 + z^2 = N \} $$
Up to reflections across the $x$, $y$ ...

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13 views

### Hypergraphs that can be represented by simply closed curves respecting edge intersection

Good evening. Hypergraphs can be drawn by representing each vertex as a point in the plane and each hyperedge as a closed curve that contains the points corresponding to the vertices that belong to ...

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17 views

### Reference that contains examples of absolutely indecomposable representations of quivers over a finite field

Is there a reference that lists/discusses examples of absolutely indecomposable representations of quivers over a finite field (absolutely indecomposable = does not decompose into a direct sum over ...

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25 views

### $\lim_{t\rightarrow 0}P\left(X_t >0\right)=\frac 1 2$ for continuous semimartingales?

I am trying to prove the following Lemma, which seems intuitive, but I still have doubts:
Lemma
Given a Brownian motion $\{W_t,\mathcal F_t:0\le t \le1\}$, two progressivley measurable processes, ...

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**1**answer

41 views

### Dihedral extension of 2-adic number field

Sorry if the question is too long and maybe elementary.
I am reading a paper by Hirotada Naito on "Dihedral extensions of degree 8 over the rational p-adic fields". To generate dihedral extension ...

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65 views

### Variety acquiring rational point over any quadratic extension

Does there exist a variety $X$ over $\mathbb{Q}$ (or a number field) such that it has no rational points over $\mathbb{Q}$ but acquires points over any quadratic extension $\mathbb{Q}(\sqrt{d})$?
If ...

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**1**answer

92 views

### Converse to Weil Restriction of Scalars

Let $k$ be a field of characteristic zero (I'm only interested in number fields), and let $\mathbb{G}_{/k}$ be a linear algebraic group defined over $k$ which is almost $k$-simple (all normal ...

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54 views

### Degenerate linear recurrence sequences

Let $(u_n)_{n \geq 0}$ be a linear recurrence given by
$$u_n = a_1 u_{n-1} + \cdots + a_k u_{n-k} \quad \forall n \geq k ,$$
where $u_0, \ldots, u_{k-1}, a_1, \ldots, a_k \in \mathbb{Z}$. We recall ...

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29 views

### Diffusion in a bounded domain

Let us consider an $\mathbb{R}^d$ diffusion
$$dX_t = dW_t +\mu(X_t)dt.$$
Let further $D\subset \mathbb{R}^d$ be a bounded connected open domain. By $Y^D$ we denote the diffusion $X$ restricted to ...

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22 views

### Integral Domains [migrated]

I have to proof that ($\ N_A,1_A,T)$ are a Peano system where $\ T:N_A\rightarrow N_a$ $\ x \mapsto x+1_A , x \in N_A$ and $\ N_A= \{n 1_A|n\epsilon N \} $ where N are the natural numbers and A is an ...

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33 views

### $H^1$ convergence of eigenfunctions of Schrödinger operators [migrated]

Consider the Schrödinger-Operator with Potential $V\in L^\infty(\Omega)$ with Dirichlet boundary conditions
$$ H^D=-\Delta + V $$
and let $u_{i,n}\in H_0^1(\Omega)$ be the first, nonnegative ...

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50 views

### Asymptotic sequence and asymptotic expansion [on hold]

If $(f_k(x))$ is an asymptotic sequence as x to infinity and $\phi=a_0f_0+a_1f_1+a_2f_2+...$ (equality) where $a_i$ are constant.
Is $a_0f_0+a_1f_1+a_2f_2+...$ an asymptotic expansion of $\phi$?

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76 views

### Good covering of a sphere

Consider a sphere $S_r(0)$ with center at zero and radius $r$ in the Hamming space $\{0,1\}^n$.
We will be interested in covering this sphere with balls of radius $\rho < r$.
We know that there ...

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42 views

### The right expansion of a square root matrix

I have some issues in finding an asymptotic expansion for a square root matrix and I have already posted a question (Asymptotic expansion square root matrix). Somebody redirected me to a post where ...

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59 views

### Spectral Sequences of Parametrized Spectra

I apologize if this question is of the form "what are some interesting problems in bla" but I was wondering if anybody have studied the following set-up:
Suppose that I have a parametrized spectra ...

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31 views

### Intersection and union of torsion classes

One of the main result in
Cassidy, C., M. Hébert, and G. M. Kelly. "Reflective subcategories, localizations and factorization systems." Journal of the Australian Mathematical Society (Series A) ...

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130 views

### “For sufficiently large” vs. “For all sufficiently large” [on hold]

A purely grammatical question: Do people generally prefer:
"For sufficiently large x,..." or
"For all sufficiently large x,..."
or not care? Or might you use either according to context? The meaning ...

**3**

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**2**answers

240 views

### Category of Gödel Codings? [Reference Request]

Consider computation with the integers $\mathbb{Q}$. The traditional theory of recursive functions on $\mathbb{N}$ applies to $\mathbb{Q}$ by the identification of $\frac{a}{b} \in \mathbb{Q}$ with ...

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28 views

### Global existence for infinite dimensional ODE

Let us consider the ODE $\hskip3pt \dot x=F(t,x)\hskip3pt $ in an infinite-dimensional Banach space $E$, where the flux $F$ is defined and continous from the whole $\mathbb R\times E$ into $E$.
...

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**1**answer

49 views

### Bounds on Hilbert-Schmidt norm of difference of products of matrices

I suspect the following is well-known, but don't know of a reference (and it is not close to the area I normally work in).
I have two sequences of matrices $Q_{1},\ldots,Q_{k}$ and ...

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62 views

### dimension of a scheme and degree of an L-function [on hold]

I try to understand correctly the notion of scheme, as Serre in the third volume of his Oeuvres defines zeta and L-functions in this context. What seems interesting to me is that he states a theorem ...

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73 views

### Deligne-Lusztig and Character sheaves

Consider: $G$ - a nice group ($GL_n$) over a finite field $F$. $X$ - the flag variety. Consider a nice $G$-equivariant $l$-adic sheaf $\mathcal{M}$ on $X \times X$, equipped with Weil structure.
Fix ...

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**1**answer

48 views

### Stalks of higher direct image under open embedding

Let $U$ be an open subset of $\mathbb P^1$ without two points (say $t=0$ and $t=\infty$) and $j: U\to \mathbb P^1$ be an open immersion. Ground field $k$ is algeraically closed. Let $G$ be the group ...

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57 views

### Errata for Getzler-Kapranov “Cyclic operads and Cyclic homology”

Do you know if anyone made an errata for the Getzler-Kapranov paper "Cyclic operads and Cyclic homology"? I was trying to read it, and I have found (at least I think I did) quite a few typos not all ...

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votes

**1**answer

41 views

### Inverse of a matrix expression

Let
$$X_i = \left(I - P\left(I - t_i^Tt_i\right)\right)^{-1}$$
where $P$ is an $N\times N$ matrix and $t_i$ is a vector of $N$ elements.
Is there a way to simplify this expression in order to ...

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7 views

### Encoding and Transforming Data for a Logistic Regression

When running a logistic regression, the result of the regression is a value that could fall in $(-\infty, \infty)$. You run it through the logistic function and get a value in $(0, 1)$. So far, so ...

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83 views

### Is the moduli space of curves arising from wild ramification smooth?

Fix a natural number $g$, a prime $p$, and a $p$-group $P$.
Let $C$ be a smooth projective curve of genus $g$ with a faithful action of $P$ and an isomorphism $C / P \cong \mathbb P^1$ such that $P$ ...

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42 views

### Yang-Mills Functional and Energy

I have a question about the meaning of Yang-Mills Functional.
It is stated everywhere that the Yang-Mills Functional is a measure of energy. But the formal definition of the Yang-Mills Functional is:
...

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**1**answer

148 views

### Motivic integration in positive characteristic: how much is known?

It seems that in papers on motivic integration people usually assume the base field to have characteristic $0$ (and algebraically closed?). My question is: how much can one prove over a positive ...

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**1**answer

92 views

### Upper bound of derivative of exponential map

We know that for any simply connected surface $M$,whose Gaussian curvature $K\leq 0$, for any $p\in M$, $exp_p: T_pM\to M$ is diffeomorphism.
We know that for any $v\in T_pM$ and $w\in ...

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65 views

### Integral Cohomology of Symmetric Groups

Does anybody know a reference for the explicit description of the integral cohomology ring of $S_5$ and $S_6$. I can not find them anywhere in the internet. For $S_4$, I found C. B. Thomas's nice ...

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31 views

### A smooth family of symplectic forms [migrated]

Let $A(t)\in\mathbb R^{2n\times 2n}$ be a smooth family of nondegenerate skew-symmetric matrices, $t\in\mathbb R$. Then $A(t)$ represents the family of symplectic forms $\omega_t(u,v)=\langle ...

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51 views

### On quasi-equivalence of norms [on hold]

Two norms $p(v),q(v)$ are equivalent if there exist two real constants $c,C$, with $c > 0$ such that for every vector $v$ in $V$, one has that: $c q(v) ≤ p(v) ≤ C q(v)$.
If $V$ is discrete module ...

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21 views

### does log liklihood can take a value greater than 1??or its between 0 and 1? [migrated]

please anybody who know the answer reply to my question..i got the log likelihood probability value as -34.82 so I am not getting whether the answer which i have got is right or not..

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87 views

### vanishing of Lie algebra cohomology with coefficients in an infinite-dimensional module

Let $G$ be a real semisimple Lie group, $K$ its maximal compact subgroup, $\mathfrak g, \mathfrak k$ the corresponding Lie algebras. Let $V$ be a locally convex, Hausdorff vector space, which is a ...

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36 views

### Linear intersection number and coloring (not chromatic) number

A linear hypergraph is a pair $\pi=(X, L)$ where $X\neq \emptyset$ is a set and $L\subseteq {\cal P}(X)$ has the following properties:
for $e\in L$ we have $|e|\geq 2$;
if $e_1\neq e_2 \in L$ then ...

**1**

vote

**2**answers

227 views

### Independence Number of Graphs

Suppose $\alpha(G)\leq\alpha(H)$ where $G$ and $H$ are graphs, and $\alpha(.)$ is the independence number of graph. Is the following statement true?
$\alpha(G\boxtimes G) \leq \alpha(H\boxtimes H)$ ...