# All Questions

0answers
4 views

What is the birational classification of (smooth projective) rationally connected 3-folds (over algebraically closed fields of characteristic $0$ or even $\mathbf{C}$, if $\mathrm{char}(k) = p > ... 0answers 4 views ### Formula to graph reverse s-curve that hits several known points I've been hitting my head against a wall with various formulas for a couple of days, and cannot seem to get one that works for the following points: ... 0answers 23 views ### Hilbert-Poincaré series of a polynomial ring with non standard grading Let us suppose we have as graded algebra$V=\mathbb{C}[z_0, ..., z_n]$with$\deg z_0=a_0, \ldots, \deg z_n=a_n$, where we can suppose that not all the$a_i’$s are equal to 1. We know that we can ... 0answers 12 views ### Question on the partial differential equations in complex space As is known most of the theory now developed for partial differential equations is in the real space, especially function space like Sobolev space, BMO space,$L^p$space, etc. However is there some ... 0answers 33 views ### A particular specialization of symmetric polynomials: is it bijective? Let$\Lambda^d_n$the space of symmetric polynomials in$n$variables, with maximum 'partial degree' of each variable$d$. A basis for this space is the set of symmetrized monomials$m_\lambda$, where ... 1answer 9 views ### Pullback via flow as operator group Let$X$be a vector field on a manifold$M$that induces a complete flow$\Theta_t$. Then the operator family$\Theta_t^*$, $$\Theta_t^*u(x) = u(\Theta_t(x))$$ is a strongly continuous semigroup of ... 0answers 19 views ### Why have most maximal cliques of Paley graphs odd size? I ask this question mainly by curiosity. See here for definitions and a plot of the clique numbers of the Paley graphs for the primes$p\equiv 1 \pmod 4$up to$10000$. Is there an ... 0answers 34 views ### Constructing sums of squares identities Recall that a sum of squares formula for$[r,s,n]$over a field$F$is an identity of the form $$( x_{1}^{2} + \cdots + x_{r}^{2})( y_{1}^{2} + \cdots + y_{s}^{2}) = ( z_{1}^{2} + \cdots + ... 0answers 30 views ### Computing the maximum of a (Classic) function involving factorial I'm trying to compute the global maximum (or an upper bound that does not depends on x) for the expression$$1/x!\binom{x+n-1}{x},$$as a function of x. Where n in a positive integer parameter. An ... 2answers 30 views ### Numerical integration of legendre polynomials I hope that numerical questions are also permitted here. I want to expand a smooth functions f \in C^{\infty}in terms of Legendre polynomials. Thus I need to calculate integrals of the form ... 0answers 65 views ### Characterization of a subset of [0,1] II My question follows the previous one Characterization of a subset of [0,1] But I don't know whether it is correct to ask again with a new title. Thanks a lot for pointing the mistake and I ... 0answers 40 views ### An epimorphism into a profinite group Let p be an odd prime number, G a finitely generated nonabelian profinite group, L \lhd_o G a pro-p group with [G : L] = 2. Suppose that there is a continuous surjection from G onto a free ... 1answer 116 views ### Examples of non isometric surfaces having the same curvature function I think it is really natural to believe, after doing Riemannian geometry for a little time, that sectional curvature encodes the all local geometry of a Riemannian manifold. One of the first thing one ... 0answers 10 views ### relationship of SDE in Langevin equation form and Ito form A formal SDE can be written in a way as (ito form): dx(t)=ax(t)dt+dw(t) where w(t) is brownian motion. Another way is to write the SDE (Langevin equation form) is \frac{dx(t)}{dt}=ax(t)+w(t) ... 0answers 23 views ### How prove this numerical solution we parameterize the integral equations Let \Omega\subset R^2 be a simply connected bounded domain with inﬁnitely diﬀerentiable boundary \partial\Omegaand unit normal vector v directed into the exterior of \Omega ... 1answer 30 views ### query about quasi-simple algebraic groups over local fields Suppose that G is an absolutely quasi-simple algebraic group over a non-archimedean local field k (of either zero or positive characteristic). Is it known whether or not it is necessarily the case ... 1answer 50 views ### A question about minimal nonnilpotent groups Let G be a minimal nonnilpotent group with cyclic Sylow p-subgroup P and normal Sylow q-subgroup Q [see Huppert, Endlich Gruppen I]. If Q is abelian and q > 2, then can we get that ... 0answers 75 views ### The angular distribution of the (a,b) in p = a^2+b^2, and the distribution of the lattices corresponding to prime ideals Here is a really basic question which I wished I understood better about the primes of the Gaussian field \mathbb{Z}[i]. But I was curious about the possibility of generalizing it to other (real ... 1answer 34 views ### Complexity of Untwisting Polygons What is the complexity of the following task: given a sequence p_1, ..., p_n, p_1 that defines a closed polyline in the euclidean plane, what is the complexity of finding a reordering of the points, ... 0answers 26 views ### Mean squared error of a noisy random variable [on hold] Assume we have a distribution D, and a random variable X from this distribution. We want to estimate E(D) through X. Obv E(X) is an estimator for E(D). The question is that does the MSE (=mean ... 0answers 40 views ### Explicit solution for a first order non-linear ODE [on hold] Is there any explicit solution to the following ODE? G'(z) =aG(z)+bG(z)^α-c G(0) = d_0 my range of \alpha is something like (0.2,9) 1answer 217 views ### Does the Pfaffian have a geometric meaning? While reviewing the proof of Gauss-Bonnet in John Lee's book, I noticed the following paragraph: " ...In a certain sense, this might be considered a very satisfactory generalization of Guass-Bonnet. ... 0answers 44 views ### Diophantine approximation in \mathbb{G}_m^r with approximants restricted to a finiteley generated subgroup Faltings, in the same paper (Diophantine approximation on abelian varieties, Ann. Math. 1991) in which he proved his famous big theorem,'' proved also that at any place v of a number field K and ... 1answer 120 views ### nonnegativity conditions for a polynomial in two variables Let$$P(X,Y)= c_{22}X^2Y^2 +c_{21}X^2Y +c_{12}XY^2 +c_{20}X^2 +c_{11}XY+c_{02}Y^2+c_{10}X+c_{01}Y+c_{00}$$be a polynomial of two variables X and Y with real coefficients c_{ij}. What are the ... 0answers 58 views ### Computing a projection of a p-adic plane curve Given a prime p and a polynomial equation f(x,y)=0 with rational coefficients, I would like to obtain a precise description of the set of all numbers y\in\mathbb Q_p such that the equation has a ... 0answers 31 views ### Binary motives in the decomposition of a minimal Pfister neighbor Let \alpha \in H^n(k,\mu_2) and X_\alpha be the respective Pfister quadric. Its well known due to Rost that the Motive M(X_\alpha) decomposes as a sum of twisted Rost motives R_\alpha such ... 3answers 124 views ### What do you call a fixed point theorem for a mapping from a subset of a space to the whole space? There are a number of fixed point theorems in which we have a map from some subset of a (metric, topological, ...) space to the whole space. (Usually, there is some condition regarding the behavior ... 1answer 94 views ### discriminant of smooth quartic del Pezzo surface in \mathbb{P}^4 I can't understand the proof of Lemma3.3 in Stability of genus 5 canonical curves. Let C be a complete intersection of three quadrics in \mathbb{P}^4 and let \Lambda be the net of quadrics ... 0answers 50 views ### question about the tightness of probability measures for a general topological space Let (E,\mathcal{X}) be a topological space and denote by \mathcal{F} its collection of Borel subsets referred to \mathcal{X}. Now let \mathcal{P} be the set of all probabilities on ... 0answers 30 views ### Bases for free pro-p groups Let p be a prime number, F a free nonabelian finitely generated pro-p group, L \lhd_o F and Y a basis for L with y \in Y. Is there a basis X for F such that y is in the abstract ... 1answer 131 views ### Variety of nilpotent Lie algebras or p-groups Here's a couple of analogous questions, one in terms of finite-dimensional complex Lie algebras and one in terms of finite p-groups; I'd be interested in an answer to either: 1) Let \mathcal{L} ... 1answer 83 views ### Differentiability of Nemytskii operator on Sobolev space I am trying to consider hypothesis on g such that the operator$$ H_0^1 (\Omega) \to L^2(\Omega), \qquad v \mapsto g(v) $$is \mathcal C^1. As additional hypothesis \Omega is bounded and g(0) = ... 2answers 372 views ### Random points on the unit sphere Suppose you have n points picked uniformly at random on the surface of \mathbb{S}^d, and let the volume of the convex hull of these points be V_{n, d}. Clearly, V_{n, d} converges to the ... 0answers 39 views ### The relationship between arc lengths and area of sectors [on hold] How are arc length and area of a sector related to proportionality? 0answers 21 views ### Feasibility of a linear program with linear single constraint [on hold] A linear program with a single constraint minimize z = c_{1}x_{1} + c_{2}x_{2} +· · ·+c_{n}x_{n} subject to a_{1}x_{1} + a_{2}x_{2} +· · ·+a_{n}x_{n} ≤ b, x_{1}, x_{2}, . . . , x_{n} ≥ 0. (a) ... 0answers 29 views ### Relationships between different properties and parts of a circle [on hold] What are the relationships among radii, chords, tangents, and inscribed and circumscribed angles of a circle? 0answers 23 views ### numerical method (implicit , backward difference or forward difference) for nonlinear pde \newcommand{\lbar}{\underline{\lambda}} In this linear PDE: \begin{cases} B_t+b^Q(r,t)B_r+\frac{1}{2}d^2(r,t)B_{rr}+(\mu(\lambda,t)+\alpha \sigma (t))(\lambda -\lbar)B_{\lambda} \\ ... 0answers 132 views ### Non-trivial bounds for polynomials at a fixed point Let f be a polynomial of degree d. Of course |f(z)|\sim C|z|^d as |z|\rightarrow\infty but also, since any polynomial is completely determined by its values at any d+1 points, we may ask how ... 0answers 30 views ### What does mean the exact value of derivative [migrated] i'm starting my calculus's journey and i have a question. What does mean the exact value of a derivative Take an easy example we have a derivative of f(x)=x^2, that is f'(x)=2x. Someone would ... 0answers 44 views ### Estimate of a Sobolev norm of p-form [on hold] \underline{\mathrm{NOTATIONS}} Let (M,g) be a compact connected Riemannian malifold of d dimensional. A^p(M) denotes the set of p-forms on M. g_{\wedge^p} denotes the fiber metric on ... 0answers 57 views ### Proving, that closure off set is equal this set iff set is closed [on hold] I've started intorduction to topology course and I need help with one of the problems: Let A \subset(X,T). Prove that cl(A) = A\iff A is closed. It may looks trivial, but I had a little ... 1answer 168 views ### If every nonseparable metric space contains a sequence of subsets with no convergent subsequence, does the Continuum Hypothesis hold? If every nonseparable metric space contains a sequence of subsets with no convergent subsequence, does the Continuum Hypothesis hold? This question is submerged in the discussion of Fedor Petrov's ... 1answer 148 views ### On a weak tree property for inaccessible cardinals Suppose that \kappa is inaccessible and consider a tree of height \kappa whose levels have size strictly below some cardinal \gamma < \kappa. Does this type of tree always have a ... 0answers 173 views ### Two questions on canonical line bundle over \mathbb{C}P^{n} The canonical line bundle over \mathbb{C}P^{n} is denoted by \ell_{n}. It is well known that:$$(\ell_{1}\otimes \ell_{1})\oplus1 \simeq\ell_{1}\oplus\ell_{1}$$Both sides are isomorphic ... 0answers 65 views ### Dense free subgroups Let$F$be a free pro-$p$group (for a prime number$p$) on a finite set$X$,$\Phi$the abstract subgroup generated by$X$,$\{1\} \neq N \lhd_c F$. Is it possible that$\Phi \cap N = \{1\}$? 0answers 24 views ### Try to prove that a discrete distribution function is a singular distribution function [on hold] actually it is the 6th question in the section 3 of chapter 1 in the book named by The course in probability theory, author:Chun Kai Lai. someone asserts that the derivate of the discrete function on ... 0answers 71 views ### Compact elements of$\mathrm{GL}_n(F)$, where$F$is a nonarchimedean local field Let$F$be a nonarchimedean local field and let$\mathcal{O}$be its ring of integers. An element$g$of$\mathrm{GL}_n(F)$is called compact if the cyclic subgroup that it generates has compact ... 3answers 173 views ### Contractibility of space of embeddings of a disc I'm pretty sure that both of the following spaces are contractible. However, I can't seem to find a proof or a reference. Can anyone provide one? Let$D^2$be the unit disc in$\mathbb{R}^2$. The ... 0answers 134 views ### Connes on Integers / Primes and Quantum Field Theory / Elementary Particles [on hold] I was browsing Matthew Watkins' Number Theory and Physics archive, and came across the following quote by Alain Connes (without context, aside from the fact that it was in a popular book called Dr. ... 1answer 2k views ### Did Leibniz really get the Leibniz rule wrong? A couple of posts ([1], [2]) on matheducators.SE seem to suggest that Leibniz originally got the wrong form for the product rule, perhaps thinking that$(fg)'=f'g'\$. Is there any actual historical ...

15 30 50 per page