Questions tagged [reference-request]
This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.
22,190 questions
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Reference for classical action of the standard height function on the two-torus written as sum of elementary and elliptic integrals?
The height function of the two torus $\mathbb{T}^2$ is a standard example. It has $2$ hyperbolic points and $2$ elliptic points. I was wondering if there exists a reference that computes the classical ...
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Proof on the Li -Yau Inequality
The standard Li Yau Estimate with a curvature term states that:
Let $(M^n,g)$ be a complete Riemannian manifold with $\text{Ric}\ge -(n-1)Hg, \space H\ge0$ , and let $u(x,t)>0$ solve the heat ...
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The name of an algebraic structure satisfying $y*(y*x)=x=(x*y)*y$
This is an abstract algebra exercise. See also here.
Let $(X,*)$ be an algebraic structure with $*$ a binary operation. If
$$ (x*y)*y=x=y*(y*x),\qquad \forall x,y\in X$$
show that $*$ is commutative.
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Reference Request: Non-trivial finite group can't act freely on contractible manifold
In the answers to this question here it was stated that:
"A nontrivial finite group cannot act freely on a contractible manifold."
This seems to be a straightforward result from group ...
- 3,657
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Books that cover multilinear algebra [duplicate]
We are currently following a course on multilinear algebra: tensor product and tensor - symmetric - exterior algebras.
The textbook for our course mainly deals with "mono"-linear algebra, ...
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Exercise I.3.19 in Hartshorne — still an open problem?
For completion, I here state what Exercise I.3.19 in Hartshorne's Algebraic Geometry (1977) says
3.19. Automorphisms of $\mathbb{A}^n$. Let $\varphi:\mathbb{A}^n \to \mathbb{A}^n$ be a morphism of $\...
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Fekete's lemma for Banach lattice sequences
Recall that a real sequence $(a_n)$ is sub-additive if
$$\forall n, m \in\mathbb{N}^*, ~ a_{n + m} \leq a_n + a_m$$
Fekete's lemma states that if $(a_n)_{n\in\mathbb{N}^*} \in \mathbb{R}^{\mathbb{N}^*}...
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problems or equations related to $x^2(x+1)^2 = 2y(y+1)$
In one of my sketchbooks, I found the Diophantine equation
$$x^2(x+1)^2 = 2y(y+1)$$
and a solution I apparently came up with at the time. The problem is, I can’t figure out where I found this equation,...
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Riemann Surfaces to Graphs
In the paper Riemann-Roch and Abel-Jacobi Theory on a Finite Graph by Matthew Baker and Serguei Norine, it is mentioned that 'It is well-known that a finite graph can be viewed, in
many respects, as a ...
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Which books I have to read to understand this articles? [closed]
A professor gave me these to study and find a problem or work around some but i have no background in crypto but i know noncommmutative and group rings really well. so i need suggestions of some books ...
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Justifying the Robbins-Monro procedure using Dvoretzky's theorem on stochastic approximation
[I asked this question on MathOverflow a little while ago and didn't get any response, so I thought I'd see if anyone on MSE could help.]
A colleague and I are trying to understand some results in ...
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Reference Request: Normal extension of minimal tensor product of homomorphisms
I am trying to find a reference (if the result is even true at all) to the following claims:
If $A,B$ are $C*$-algebras such that the enveloping von Neumann algebra of the minimal tensor product $(A \...
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Reference Request: Karush-Kuhn-Tucker conditions for convex optimization with generalized inequality constraints.
I'm reading the book Convex optimization by Stephen Boyd . In Section 5.9.2 he states (without proof) the Karush-Kuhn-Tucker conditions for an optimization problem with generalized inequality ...
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Almost all graphs only have adjacency eigenvalues of multiplicity 1
To me it seems like the following could hold.
Asymptotically almost all graphs only have adjacency eigenvalues (equivalently, Laplacian eigenvalues, see [1, Theorem 3]) of multiplicity $1$. I.e. the ...
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Explicit bounds for polytope integral
In Theorem 1.1 of this paper a constant is defined by a massive polytope integral, which is subsequently evaluated for certain values of $r$ using a computer algebra system. My question is whether ...
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