# All Questions

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### Infinite sequence avoiding a countable set of words

As an application in group theory, I would need an infinite sequence over a finite alphabet, that avoids countably many words, each of length at least 10^8. I have found several results about avoiding ...
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### Periodic points in C^2

I came up with a problem which is similar to the following quesitons: Consider a map: $f(x,y)=(y^2-2,xy-2)$. It is seems that the number of periodic points of given period is bounded. I want to ...
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### $IM=mM$. can we say that $I$ is a reduction ideal of $m$?

Definition. Let $R$ be a Noetherian ring􀀀, $I$ a proper ideal,􀀀 and $M$ a finite $R$-module. An ideal $J\subset I$ is called a reduction ideal of $I$ with respect to $M$ if $JI^nM = I^{n+1}􀀀M$ for ...
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In chapter 6, specifically in the section about suspensions a proof is given that ∑2 = S^1. The book says that $\mathrm{transport}^{x \mapsto g(f(x)) = x}(\mathrm{refl}_N, \mathrm{merid}(y)) = ... 1answer 96 views ### Topological Grothendieck Construction Let$C$be a small category and$F\colon C^{op}\rightarrow Set$a functor. The Grothendieck construction is the category$F\wr C$with objects being pairs$(c,x)$where$c$is a object of$C$and ... 0answers 62 views ### Computing coefficients to power sums Is it possible to find the (distinct) coefficients of monomials such as $$(x_{1}^{3}+x_{2}^{3}+x_{3}^{3}+x_{4}^{3})^4\cdot(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2})\cdot(x_{1}+x_{2}+x_{3}+x_{4})^{2}$$ ... 0answers 53 views ### Why does the critical line for Riemann's zeta function lie at real part 1/2 rather than real part 0? [on hold] Sorry for the un-mathematical way of formulating this question in the title, feel free to edit the title if that seems more appropriate. What I actually like to know is: Is this yet another instance ... 1answer 40 views ### Homotopy bounds in simply connected complete Riemannian manifolds Let$M$be a simply connected complete Riemannian manifold, and let$x\in M$. Does there exist a nondecreasing function$R:\mathbb R_+\to\mathbb R_+$such that, for every$r>0$and all paths ... 2answers 52 views ### Matrices congruent to each other via a permutation Consider the collection of all integer matrices and partition them via an equivalence relation$A\sim B\Leftrightarrow \exists$a permutation matrix$P$such that$B=PAP^T$. Is some canonical form ... 0answers 40 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. ... 0answers 27 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 ... 0answers 35 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 ... 1answer 19 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 ... 0answers 23 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 , ... 3answers 529 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 ... 0answers 35 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 ... 0answers 33 views ### Norm on C$^*$-algebra [on hold] Given two orthogonal elements$a,b$in a C$^*$-algebra$A$(i.e.$a b^* = b^* a=0$) we have$\| a + b\| = \max\{ \|a\|, \|b\|\}$. How do I show? 1answer 135 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 ... 1answer 62 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 $$... 4answers 153 views ### Application of Fraïssé construction in set theory As you know Fraïssé limit construction and its generalization, Hrushovski's construction, have many applications in model theory to build models with interesting property. Now I would like to know ... 0answers 53 views ### Matrices over a finite field with given Jordan normal form over the algebraic closure [migrated] Can one describe the (conjugacy classes of) square matrices over a finite field such that over the algebraic closure of this finite field their Jordan normal form consists of one Jordan block? (Such ... 0answers 16 views ### Alternative form for weighted least squares Coefficients \beta can be estimated from y by weighted least squares with: \beta = (X^T\Sigma^{-1}X)^{-1} X^T \Sigma^{-1} y where \Sigma is the covariance matrix of the noise. Let N be ... 0answers 76 views ### Averages over integer points of the sphere A paper of William Duke sketches a proof that integer points on the sphere are equidistributed.$$ V_N = \{ (x,y,z) \in \mathbb{Z}^2 : x^2 + y^2 + z^2 = N \} $$Up to reflections across the x, y ... 0answers 23 views ### Reference that contains examples of absolutely indecomposable representations of quivers over a finite field Is there a reference that lists/discusses examples of absolutely indecomposable representations of quivers over a finite field (absolutely indecomposable = does not decompose into a direct sum over ... 0answers 34 views ### \lim_{t\rightarrow 0}P\left(X_t >0\right)=\frac 1 2 for continuous semimartingales? I am trying to prove the following Lemma, which seems intuitive, but I still have doubts: Lemma Given a Brownian motion \{W_t,\mathcal F_t:0\le t \le1\}, two progressivley measurable processes, ... 1answer 92 views ### Dihedral extension of 2-adic number field Sorry if the question is too long and maybe elementary. I am reading a paper by Hirotada Naito on "Dihedral extensions of degree 8 over the rational p-adic fields". To generate dihedral extension ... 0answers 82 views ### Variety acquiring rational point over any quadratic extension Does there exist a variety X over \mathbb{Q} (or a number field) such that it has no rational points over \mathbb{Q} but acquires points over any quadratic extension \mathbb{Q}(\sqrt{d})? If ... 1answer 104 views ### Converse to Weil Restriction of Scalars Let k be a field of characteristic zero (I'm only interested in number fields), and let \mathbb{G}_{/k} be a linear algebraic group defined over k which is almost k-simple (all normal ... 0answers 68 views ### Degenerate linear recurrence sequences Let (u_n)_{n \geq 0} be a linear recurrence given by$$u_n = a_1 u_{n-1} + \cdots + a_k u_{n-k} \quad \forall n \geq k ,$$where u_0, \ldots, u_{k-1}, a_1, \ldots, a_k \in \mathbb{Z}. We recall ... 0answers 36 views ### Diffusion in a bounded domain Let us consider an \mathbb{R}^d diffusion$$dX_t = dW_t +\mu(X_t)dt.$$Let further D\subset \mathbb{R}^d be a bounded connected open domain. By Y^D we denote the diffusion X restricted to ... 0answers 22 views ### Integral Domains [migrated] I have to proof that (\ N_A,1_A,T) are a Peano system where \ T:N_A\rightarrow N_a \ x \mapsto x+1_A , x \in N_A and \ N_A= \{n 1_A|n\epsilon N \} where N are the natural numbers and A is an ... 0answers 33 views ### H^1 convergence of eigenfunctions of Schrödinger operators [migrated] Consider the Schrödinger-Operator with Potential V\in L^\infty(\Omega) with Dirichlet boundary conditions$$ H^D=-\Delta + V $$and let u_{i,n}\in H_0^1(\Omega) be the first, nonnegative ... 0answers 51 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? 0answers 81 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 ... 0answers 45 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 ... 0answers 61 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 ... 0answers 34 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) ... 0answers 132 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 ... 2answers 346 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 ... 0answers 33 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. ... 1answer 51 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 ... 0answers 63 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 ... 0answers 77 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 ... 1answer 51 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 ... 0answers 59 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 ... 2answers 82 views ### Inverse of a matrix expression Let$$X_i = \left(I - P\left(I - t_it_i^T\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 ... 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 ... 0answers 90 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$P$... 0answers 48 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: ... 1answer 160 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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