# All Questions

100,133 questions
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### William Thurston's quote?

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding. Is this from Thurston? If yes, where and when it has been said. I've checked "ON PROOF AND ...
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### Are complete minimal submanifolds closed?

Is it true that any complete minimal submanifold of some Riemannian manifold is closed as a subset? What about the case in which the ambient manifold is an euclidean space?
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### Explaining the consistency of PRA and ZF from predicative foundations

Recently I got interested in predicative foundations, mostly because of Laura Crosilla's work and because Agda employs a predicative type theory. From the point of view of a predicative foundation to ...
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### Chromatic polynomial and the circle

In https://arxiv.org/pdf/1208.5781.pdf It is proved that there is spectral sequence converging to $H^*(M^G,R)$ with the E1 page given by the graph cohomology complex $C_A(G)$ where $A:=H^*(M,R)$. My ...
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### Differential equations satisfied by quasi modular forms?

It is known that modular forms are solutions of differential equations. More precisely, let me cite the statement from the following question. Differential Equations Satisfied by Modular Forms ...
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### Infinite spectral norm of linear mapping

Suppose we have a linear mapping $A:\mathbb{R}^m\rightarrow \mathbb{R}^n$. We define its $k$-spectral norm as: $\sigma_k(A)=\sup_{x} \frac{||Ax||_k}{||x||_k}$. We know that when $k=2$, $\sigma_2(A)$ ...
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### Finding a curve through divisor

Let $k$ be a field. Is it true that for any smooth irreducible projective $k$-variety $X$ and a dense open set $U\subset X$, for any zero-cycle on $X$ one can find an irreducible curve containing its ...
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### Fundamentals of Networks and Graph theory: listing labelled graphs with given number of edges [on hold]

Under the assumption of simple graph, how it is possible to determine the list of all the labelled graph with order 4, and so vertex set {1,2,3,4} and three edges?
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### Quasimorphisms and Bounded Cohomology: Quantitative Version?

Consider maps from a discrete group $\Gamma$ to the additive group $\mathbb{R}$. A function $f:\Gamma \to \mathbb{R}$ is called a quasimorphism if it is locally close to being a group homomorphism. ...
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### Example coordinates for a dodecahedron in x, y, z? [on hold]

Good morning/afternoon/evening all, I'm working on some high-level Python simulations and wanted an example set of coordinates for the vertices of a regular dodecahedron in terms of x, y and z ...
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### Compact complex affine Kähler manifold is a torus

Before giving a motivation let me ask the precise question firstly. By a complex affine manifold I mean a complex manifold $M$ with the property that there exists an holomorphic atlas for which ...
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### Linear intersection number and chromatic number for infinite graphs

Given a hypergraph $H=(V,E)$ we let its intersection graph $I(H)$ be defined by $V(I(H)) = E$ and $E(I(H)) = \{\{e,e'\}: (e\neq e'\in E) \land (e\cap e'\neq \emptyset)\}$. A linear hypergraph is a ...
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Suppose that $X$ is a finite dimensional Hilbert space. Let $A_{1},\dots,A_{r}:X\rightarrow X$ be linear operators. Then define the multi-spectral radius of $(A_{1},\dots,A_{r})$ to be $$\limsup_{n\... 0answers 77 views ### Integral geometry for general closed smooth manifolds Let M be a closed smooth manifold of dimension 2n for some positive integer n. Let \mathit{Diff}(M) be the group of diffeomorphisms of M. Let L be a closed embedded n-dimensional ... 0answers 19 views ### Taylor series to give estimate for sin(pi/3 + 0.1) to 4d.p [on hold] Taylor series to give estimate for sin(pi/3 + 0.1) to 4d.p. I know how to do this for sin(x) about x = pi/3 but not sure how to do this specific problem 0answers 98 views ### Do we believe that the distribution of spacings of successive critical zeros of zeta is log-symmetric? Let \gamma^{+}(T) be the imaginary part of the critical zero of \zeta closest to 1/2+iT with \gamma^{+}(T)\ge T and define similarly \gamma^{-}(T) with a reversed inequality. Let g(T) be ... 0answers 41 views ### Global solution of second order ODE defined on riemannian manifold Consider the differential equation \nabla \dot X + \frac{3}{t} \dot X + gradf(X) =0, defined on a riemannian manifold (M,g) ( \nabla is the Levi-Civita connection and gradf(X) is the ... 0answers 37 views ### Are total graph of power of cycles homeomorphic to powers of cycles? Is the total graph associated to powers of cycles homeomorphic to powers of cycles themselves? I think yes, because the total graph associated to cycles is homeomorphic to cycles(i think?)So, does ... 0answers 207 views ### Comparing real topological K-theory and algebraic K-theory Does there exist an integer 0<i<8 with the following property: for any commutative unital ring R, there exists a compact Hausdorff space X such that KO^i(X)\approx K^i_{alg}(R)? P.S.: ... 1answer 90 views ### A totally geodesic triangulation Let M be a compact orientable n dimensional Riemannian manifold. Is there a triangulation of M such that every k dimensional face of each simplex is a totally geodesic submanifold, \forall k ... 0answers 48 views ### Why restrict to \Sigma_1^0 formulas in RCA_0 induction? I recently asked this question over on math.se, warmly welcomed by crickets. I hope it's appropriate here. I'm reading Stillwell's Reverse Mathematics, and the induction axiom was just introduced. ... 0answers 28 views ### Under which conditions the fixed points set is finite? Let M be a compact smooth manifold with an effective action by a Lie group G. Under which condition on the action and on M the set of fixed points by this action is finite? 0answers 48 views ### Joining metrics of positive Ricci curvature Let M be a smooth manifold such that there is a closed submanifold S\subset M with a Riemannian metric g_S given by the restriction of a Riemannian metric on M satisfying \mathrm{Ricci}_{g_S}(... 0answers 89 views ### Status of locality of perfectoidness for uniform rings Let k be a perfectoid field of zero characteristic. Recall that a Tate k-algebra is called uniform if the set of power-bounded elements is bounded. Let (A, A^+) be a uniform complete affinoid k... 0answers 59 views ### Solutions of a partial differential equations I'm looking for solutions of a PDE of the form :  P(t,x):[0,\infty]*[0,b]\rightarrow[0,1]$$ \partial_t P(t,x)= \partial_x [(1+2x) P(t,x)] P(0,x)=\delta_x (0)P(t,b)=g(t)$$Where b is a ... 0answers 39 views ### Regularity minimizer I am not an expert in calculus of variations and I am getting pretty lost in the vast literature. I've been studying the following functional$$ \int_\Omega (|\nabla f|+|\nabla g|)^2 dxdy $$where \... 0answers 54 views ### Regular intersecting family Let n=2k+1. When k=3, the set of lines of Fano plane is a regular intersecting family consisting of some k-subsets of [n]. Do anyone know such examples for general k? Thanks. 0answers 125 views ### Generalizing the formula between Wu class and the Steenrod square I know that on the tangent bundle of M^d, the corresponding Wu class and the Steenrod square satisfy$$ Sq^{d-j}(x_j)=u_{d-j} x_j, \text{ for any } x_j \in H^j(M^d;\mathbb Z_2) . \tag{eq.1}$$... 0answers 18 views ### Density of different types of critical points in an algebra of elementary embeddings Suppose that j,k:V_{\lambda}\rightarrow V_{\lambda} are elementary embeddings. Let \mathrm{crit}_{n}(j,k) denote the n-th element in \{\mathrm{crit}(\ell)\mid\ell\in\langle j,k\rangle\}. ... 0answers 55 views ### I need help about this math problem it seems i can't find answer [on hold] Jack chose 25 instead of 24, then he chose 4 instead of 5 and after that he chose 36 instead of 35. If he needs to choose again which of the following numbers will he select ? Given answers: a: 9 ... 0answers 69 views ### Condition on a Lie groupoid to be represented by manifold/group or an action groupoid Let \mathcal{G} be a Lie groupoid. I am thinking of following questions. When do we know \mathcal{G} is weakly/Morita equivalent to a Lie groupoid of the form (G\rightrightarrows *) for some ... 0answers 37 views ### The case of a redundant disjoint sum I'm trying to calculate \Sigma (\Gamma_{\sigma}) as discussed on p.230 of 'Structured meanings and reflexive domains' by Serge Lapierre. Use '\Sigma(\Gamma)' to indicate the disjoint sum of all ... 0answers 33 views ### Ellipticity-type condition An elliptic operator L=\mathrm{div}(A(x)\nabla u), is called uniformly elliptic if$$C^{-1}\mathrm{Id} \le A(x) \le C \mathrm{Id}$$If A depends also on u, what is the condition$$C^{-1} + C^...
I have been trying to solve the following Korteweg-de Vries (KdV) equation using NDSolve but nothing went right! The first equation is: $6 U_{t} + (9/2) U_{xxx}+ 9 U U_{x} - 6 a U_{x}=0$ and the ...