# All Questions

I am employing a large cardinal notion that has been used explicitly before, and I am wondering if someone has given it a good succinct name. A cardinal $\kappa$ is huge if there is an elementary $j ... 2answers 160 views ### p-adic analogue of the Strong Law of Large Numbers Is there a$p$-adic analogue of the Strong Law of Large Numbers? In particular, suppose that$f_i: \mathbb{Z}_p \longrightarrow \mathbb{Q}_p$for$i = 1,2,\ldots$is an sequence of random variables ... 0answers 114 views ### Can a numerical system be built following these ideas? (decomposition of infinity) [on hold] I have been some time thinking on how to reconcile non-Archimedean extentions of real line with results on summation of divergent series. Now suppose$\Omega$is an infinite quantity, the number of ... 0answers 16 views ### How do i find the maximum area for a crate, that has to fit inside a shape? [on hold] Here's the shape: http://i.stack.imgur.com/WrY7V.png h is equal to: 3.57meters and d is equal to 5.28 meters, I've tried to setup a formula for the area, but i cant seem to get a valid one. Any help ... 0answers 26 views ### Is the order convergence topology on a poset always Hausdorff? In this post two topologies on a poset$(P,\leq)$were defined: the interval topology$\tau_i(P)$and the order convergence topology$\tau_o(P)$. It turns out that$\tau_i(P)$is always$T_1$and ... 1answer 57 views ### Does every locally compact Hausdorff space admit a locally finite open covering by relatively compact sets? Let$X$be a locally compact Hausdorff space. Does there exist a locally finite open covering consisting of relatively compact sets? 1answer 335 views ### Class field towers It is known (Golod and Shafarevich) that the class field tower of a finite extension$K$of$\mathbb{Q}$may be infinite. But is it always finite for$K=\mathbb{Q}[\zeta]$where$\zeta$is a root of ... 3answers 91 views ### Extension of conformal map and annulus My question is the following : suppose you have a doubly-connected open set$\Omega \subset \mathbb{C}$, that is a domain bounded by 2 non-intersecting circles$C_1$(the interior) and$C_2$(the ... 1answer 43 views ### ideals of polynomial ring of two variables generated by two elements Let$f,g$be two polynomials in$\mathbb{Z}[x,y]$, given by $$f(x,y)=x^4-3xy+y^2,$$ $$g(x,y)=x^5-4xy+3xy^2.$$ Let$I=(f,g)$be the ideal in$\mathbb{Z}[x,y]$generated by$f$and$g$. Is ... 0answers 76 views ### X^2 + 4 = y^5 is there any solution to this [on hold] is there any integer solution to the given equation? i have tried to solve the problem considering modulo of different prime but it just aint working it'd be nice if i get a solution soon 0answers 65 views ### Does Kaplansky's Zero Divisor Conjecture hold valid for (torsion-free) residually finite groups? Kaplansky's Zero Divisor Conjecture states that the group algebra$KG$has no zero divisor for any field$K$and any torsion-free group$G$. Does Kaplansky's Zero Divisor Conjecture hold valid ... 1answer 70 views ### Stochastic differential equation associated with an optimal control problem We know how to find the stochastic differential equation (Hamilton-Jacobi-Bellman equation, HJB) of the control problem where a process$X_t$is controlled up until it is stopped at a stopping time ... 0answers 200 views ### Reference for “if the set$A$is Suslin, then every$\Sigma^1_1(A)$set is Suslin” Does anyone know of a reference for one or both of the following facts (in$\mathsf{ZF}$)? If the set of reals$A$is Suslin, then every$\Sigma^1_1(A)$set of reals is Suslin. If$T$is a tree on ... 0answers 35 views ### Generation of compact Lagrangians over fields with characteristic 2 Let$\pi:X\rightarrow\mathbb{C}$be a Lefschetz fibration, and assume that the fibers are exact or monotone. A classical result of Seidel says that all the closed weakly unobstructed Lagrangian ... 0answers 54 views ### induced map on tangent bundles from blow up morphism Suppose$X$is the plane nodal curve over$\mathbb{C}$. Then we can mimic what we do in differential geometry to define the "tangent bundle" over$X$as a subvariety of ... 0answers 125 views ### Limit Group decomposition [on hold] In the article Limit groups and groups acting freely on$\mathbb{R}^n$-trees by Vincent Guirardel, after the statement of Theorem 7.1 on page 1430, the author concludes: "Hence, a limit group can be ... 0answers 52 views ### Gaussian Measure for Random Matrix [on hold] I am doing physics and do not have enough mathematical background. so the question may be trivial, I apologize for that. any help and suggestion for readable papers/books would be highly appreciated. ... 1answer 66 views ### Balls from bin with replacement, distinct elements, concentration inequality Draw$n$numbers, denoted by$a_1, a_2, \ldots, a_n$, from set$[n]$, that is, for each$i$,$a_i$is a uniformly random number from$[n]$. Let$A = \{a_1, a_2, \ldots, a_n\}$. Then $$... 0answers 71 views ### Unbounded polynomials [migrated] Let p(x) be a polynomial of degree d on R^n, and let \tilde{p}(x) be the homogeneous components with degree d, then how do we prove that: if \tilde{p}(x) is unbounded below, then p(x) ... 2answers 134 views ### On Bohr-MollerupTheorem [on hold] In http://mathworld.wolfram.com/Bohr-MollerupTheorem.html, Bohr-Mollerup Theorem is given where it is stated that \Gamma function is the unique log convex function that satisfies ... 0answers 133 views ### Monoidal Forgetful/Free Adjunction for E_2-algebras Suppose I am given two E_2-ring spectra A and B and a morphism of E_2-rings \phi:A\to B. Then I have E_1-monoidal categories of modules LMod_A and LMod_B. Moreover I have morphisms ... 2answers 186 views ### A question involving Mazur's Lemma Consider the Mazur's Lemma (H. Brezis - "Functional analysis, ..."): "Assume (x_n) converges weakly to x. Then there exists a sequence (y_n) made up of convex combinations of the x_n's that ... 1answer 121 views ### Reflexive sheaves on stable curves Let C be a stable curve over an algebraically closed field of positive characteristic and \mathcal{F} be a reflexive sheaf on C. Is \mathcal{F} locally free? EDIT Is the projective dimension ... 1answer 174 views ### Asymptotic limit of truncated Legendre sieve Consider the truncated sum$$ S(x):=\sum_{\substack{{d\mid P(\sqrt{x})}\\{d\leq x}}}\mu(d)/d, $$where P(z) is the product of all primes less than or equal to z, and \mu(d) is the Möbius ... 1answer 203 views ### Can states on commutative Banach algebras be understood as probability measures? Suppose \mathcal{A} is a commutative Banach algebra. Is there always a measurable space (\Omega,\mathcal{F}) such that there is a bijective correspondence between states on \mathcal{A} and ... 1answer 96 views ### Base change of regular schemes [on hold] Let R be a complete DVR with fraction field K, X be a regular scheme flat over R. Let L be a finite field extension of K and Q be the integral closure of R in L. Denote by Y:=X ... 1answer 103 views ### compact inclusion of domains of unbounded operators Let L be a positive self-adjoint operator defined densely on L^2(M) where M is a compact manifold. Also, let \mathcal{D}(L) \subset H^1(M). It is known that \mathcal{D}(L) \subset ... 0answers 53 views ### Pointwise (a.e) evaluation of \sum_{n \geq 0}(u,w_n)_{L^2}w_n and equalities in L^2 Let w_n be a orthonormal basis of L^2(\Omega). Given u \in L^2 we can write$$u=\sum_{n \geq 0}(u,w_n)_{L^2}w_n.$$Suppose w_n are the eigenfunctions of the Neumann Laplacian. We can write ... 1answer 125 views ### How to show that there's a continuous function separating convex sets of Radon measures? First, the setup: X is a compact set. By Riesz's representation theorem C(X)^*={all Radon measures on X}. K is a convex, closed set of probability measures. m is a probability measure out of ... 1answer 165 views ### Is the analytic version of the Whitney Approximation Theorem true? I initially asked this question on MSE but I haven't had any luck. The Whitney Approximation Theorem states that any continuous map between smooth manifolds is homotopic to a smooth map. If the ... 0answers 29 views ### Conditional probabilities [on hold] Does it make sense to say :$$\mathbb{P}\left(A|C\cap B|C\right)=\mathbb{P}\left(\left(A\cap B\right)|C\right)$$And have we an associativity : ... 3answers 187 views ### A question on flasque sheaf Let 0\to \mathscr{F}'\to\mathscr{F}\to\mathscr{F}''\to 0 be an exact sequene of sheaves. It is well known that \mathscr{F} flasque iff \mathscr{F}'' flasque provided \mathscr{F}' is flasque. ... 0answers 80 views ### Is there a version of decomposition theorem for smooth open manifolds in dimensions grater than 3? [on hold] Is there a version of decomposition theorem http://www.jstor.org/stable/2034963 for smooth open manifolds in dimensions grater than 3? There is two things about the cited theorem: it is for ... 0answers 52 views ### Trapped Billiard trajectories on non-convex billiard tables Let \Omega be a domain in \mathbb{R}^2 with smooth boundary. A billiard trajectory is a continuous curve c: \mathbb{R}\supseteq I \longrightarrow \overline{\Omega} such that c(t) \in ... 0answers 43 views ### What is a constant-rank matrix definition? [on hold] I have had no luck finding a definition of constant-rank matrix. Even less luck with an intuitive example. My interest is to understand when can I apply a formula for the derivative of the ... 0answers 33 views ### If Linear equations solution is inconsistent? [on hold] Hello, If my Linear equation system's martix is inconsistent. There is no point to check homogenus system's solution, and I can safely say that the asked system has no solutions. Or am I wrong? 0answers 77 views ### When can the rank of a submodule be bigger than the rank of the module itself? [migrated] It is well known that the dimension of a subspace is less than or equal to the dimension of the vector space it is contained in. The same is true e.g. for modules over a principal ring. I am looking ... 0answers 30 views ### References to study Weak and Strong Topologies and aproximations on function spaces of manifolds I´m studing weak and strong topologies and aproximations on the function space C^{\infty}(M,N) of two manifolds M and N. I´m using the book Differential Topology of Morris Hirsch but it is a ... 0answers 61 views ### Graph theory and topology [on hold] I have related topological ideals with vertex magic totallabeling in graph theory. Is there any possibility to relate vertex magic totallabeling with generalized topology in a very interesting way? ... 2answers 791 views ### When does Vopěnka's principle hold? Vopěnka's principle (VP) is the statement that, given any proper class \{\mathcal{A}_\eta: \eta\in ON\} of first-order structures in the same language, there are some \alpha\not=\beta with ... 1answer 401 views ### learning Deligne-Lusztig theory Can someone give me a roadmap for learning Deligne-Lusztig theory? (Except for the original article by Deligne and Lusztig) Edit: You may assume knowledge of representation theory of finite groups ... 2answers 144 views ### Common roots of polynomial and its derivative Suppose f is a uni-variate polynomial of degree at most 2k-1 for some integer k\geq1. Let f^{(m)} denote the m-th derivative of f. If f and f^{(m)} have k distinct common roots ... 0answers 206 views ### A question about Weil restriction Let \pi:\tilde{C}\rightarrow C be a ramified cover between two smooth curves. And consider a group scheme \mathcal G over \tilde{C}, I have found two definitions for Weil restriction: ... 0answers 167 views ### Is dimension invariant under blow-ups? Let X'\rightarrow X be a blow-up of a finitely dimensional scheme X in a center D. Under which assumptions one has \dim X'=\dim X? Do you know a proof or a reference for a proof? Do you know ... 0answers 43 views ### Is any model category simplicially enriched? Let \mathcal{M} be a model category. Let F\: : \: \mathcal{M}\to\mathcal{M}^{\boldsymbol{\Delta}} be a functorial cosimplicial frame. Then the function complex between two objects ... 1answer 77 views ### “Diagonalizing” an associative algebra Consider the associative algebra A with generators T_i and rule T_i*T_j=\Sigma_kC^{ij}_k*T_k. Even if it makes no sense for a fusion ring (my momentary pet :-) to change basis it is still possible ... 1answer 51 views ### Interval topology and order convergence topology Throughout this post, let (P,\leq) be a poset. The interval topology \tau_i(P) on P is generated by$$\{P\setminus\downarrow x : x\in P\} \cup \{P\setminus\uparrow x : x\in P\},$$where ... 0answers 25 views ### Definition of equi-absolute continuity [on hold] Could someone provide (or point me to) a definition of equi-absolute continuity for functions defined on an open bounded subset$\Omega \subseteq\mathbb{R}^n$? I only managed to find a definition for ... 1answer 79 views ### Create matrix containing values in [0,1] where sum of all diagonals and anti-diagonals is fixed The problem I am facing sounds at first glance pretty simple. However, as very often, it seems more complicated than I first assumed: I want to calculate a matrix$P = (p_{j,k}) \in \mathbb{R}^{n ...
Is there anything known about group actions of $C_{p}\rtimes C_{p}^{*}$ on the ring of real polynomials $\mathbb{R}[X_{1},\ldots,X_{n}]$, where $C_{p}$ denotes the cyclic group of order $p$ and $p$ is ...