0
votes
0answers
1 views

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. ...
-1
votes
0answers
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 ...
1
vote
0answers
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 ...
1
vote
1answer
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 ...
-2
votes
0answers
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
votes
2answers
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 ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
4
votes
1answer
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 ...
2
votes
1answer
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 $$ ...
4
votes
3answers
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 ...
1
vote
1answer
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 ...
0
votes
0answers
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 ...
0
votes
0answers
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 $x$, $y$ ...
-1
votes
0answers
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 ...
2
votes
0answers
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 ...
1
vote
0answers
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, ...
1
vote
1answer
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 ...
5
votes
0answers
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 ...
2
votes
1answer
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 ...
5
votes
0answers
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 ...
1
vote
0answers
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 ...
0
votes
0answers
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 ...
1
vote
0answers
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 ...
0
votes
0answers
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 $\phi$?
1
vote
0answers
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 ...
0
votes
0answers
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 ...
5
votes
0answers
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 ...
0
votes
0answers
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) ...
1
vote
0answers
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
votes
2answers
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 ...
2
votes
0answers
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 $E$. ...
2
votes
1answer
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 ...
1
vote
0answers
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 ...
3
votes
0answers
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 ...
1
vote
1answer
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 ...
2
votes
0answers
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 ...
0
votes
1answer
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 ...
0
votes
0answers
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 ...
4
votes
0answers
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 $P$ ...
1
vote
0answers
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: ...
3
votes
1answer
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 ...
1
vote
1answer
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 ...
1
vote
0answers
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 ...
-1
votes
0answers
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 ...
0
votes
0answers
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 ...
-4
votes
0answers
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..
5
votes
0answers
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 ...
2
votes
0answers
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
2answers
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? $\alpha(G\boxtimes G) \leq \alpha(H\boxtimes H)$ ...

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