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.

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0
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6 views

Metric on Heisenberg group arising from CR isomorphism to punctured odd-dimensional sphere

It is well known that odd-dimensional spheres $S^{2n+1} \subset \mathbb{C}^{n+1}$ are CR manifolds, and on removing a point we get a CR isomorphism to the (underlying manifold of the) Heisenberg group ...
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0answers
24 views

Is Nathanson's Elementary methods in number theory a good book? [on hold]

I found this book at my university's library and I have looked at some of the problems in Chapters I, II and III and I must say that most of them (maybe I am wrong) are not very difficult (even ...
0
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0answers
15 views

Universal Grobner basis

Can anyone give me a reference about the theorem " the universal Grobner basis of an ideal is finite set". Is there a proof in Sturmfels book ?
2
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0answers
20 views

How to understand the geometry of bilinear forms that are not positive-definite?

I simply cannot find a good resource that explains intuitively how to understand the geometry that is induced on a vector space when the bilinear form is not positive-definite. In the ordinary ...
4
votes
0answers
22 views

All tangential Stiefel-Whitney numbers of $\mathbb{R}P^q$ are zero iff $q$ is odd, reference?

Where can I find a reference to the proof of the following fact? All tangential Stiefel-Whitney numbers of $\mathbb{R}P^q$ are zero if and only if $q$ is odd. I made a quick search through ...
7
votes
3answers
268 views

Succinct Proof: All Pentagons Are Star Shaped

Question: What is a succinct proof that all pentagons are star shaped? In case the term star shaped (or star convex) is unfamiliar or forgotten: Definition Reminder: A subset $X$ of ...
0
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0answers
5 views

Prequisites for chemical reaction network theory

What are the prequisites for chemical reaction network theory? Furthermore, can anyone please suggest some introductory material into the field. I thank you in advance.
0
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0answers
43 views

Prerequisistes for P. May's A Concise Course in Algebraic Topology

I wonder what are the prerequisites for studying P. May's A Concise Course in Algebraic Topology. I understand basic point set topology and category theory are required. How much algebra does one need ...
4
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0answers
15 views

Can there be a Diaconis-Shahshahani Upper Bound Lemma for Compact Groups?

Let $G$ be a finite group and $\nu\in M_p(G)\subset \mathbb{C} G$ a probability measure on $G$ and let $\pi$ be the uniform distribution on $G$. Denote by $d_\rho$ the dimension of a non-trivial ...
1
vote
1answer
16 views

Binary Linear Codes of Minimum Distance 3

Let $B_n$ denote the maximum size of a binary linear code (a binary code that is closed under addition) whose codewords have length $n$ and whose minimum distance is $3$. I have been searching for the ...
0
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0answers
12 views

Legendre transformation

My question is about Legendre Transformation. I need some example and some practical theory. Can you help me please with some examples or papers? Thanks!
-5
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0answers
19 views

Where can i download a pdf version of barrett o'neill's semi-riemannian geometry with applications to relativity. [on hold]

I need this book for a course I'm doing at the local university but, it'll be a while before i get official status and am allowed to borrow books, but the thing is i have a test coming up and the ...
2
votes
1answer
26 views

$C^\alpha$-regularity of elliptic PDE when $f$ is only continuous

Consider $\Omega\subset\mathbb{R}^n$, open bounded, $$ Lu=f\text{ in }\Omega,\quad u=0\text{ on }{\partial\Omega}, $$ with $Lu=a^{ij}D_{ij}u+b^{i}(x)D_iu+c(x)u=f(x)$, $a^{ij}=a^{ji}$, $L$: strictly ...
0
votes
1answer
24 views

Which are the good books,resources,extensive question banks to learn real analysis,calculus

Which are the good books,resources,extensive question banks to learn real analysis,calculus(indefinite,definite,area under curves),differential equations for IIT plus plus level.Foreign authors are ...
-1
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0answers
39 views

The unit ball is not auto similar.

I want read a prove that the unit ball $B$ is not auto similar. I mean that there is not similarities $f_1,...,f_n$ with contracting constants <1, such that $$B=\bigcup_{i=1}^n f_i[B] $$ Anyone ...
3
votes
1answer
27 views

Was this arithmetic Möbius/Mangoldt function ever used for something?

Let $n=\prod_k p_k^{c_k}$, with $p_k \in \mathbb P$ and $$ A(n)=\sum_{d|n} \mu(d)\Lambda(d), $$ with the $\mu$ Möbius function, which has values in {−1, 0, 1} depending on the factorization of n ...
1
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2answers
33 views

Lucas's proof of a special case of Beal's conjecture

While studying the properties of a certain elliptic curve, I came across the equation $x^4+y^4=z^3$. There is no solution of this equation in relatively prime integers, and this is a special case of ...
2
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0answers
20 views

Measure-preserving map between a function and its symmetric rearrangement

Let $f \, \colon \mathbb{R}^d \rightarrow[0, \infty)$ be a function such that the sets $ \{ y \: \colon f(y) > \lambda \}$ are of finite Lebesgue-measure, for every $\lambda \geq 0$. Then, we can ...
2
votes
1answer
17 views

A certain zeta function; or, the determinant of the Laplacian plus a constant on the circle

I am interested in a certain "zeta function," a meromorphic function of $s \in \mathbb{C}$ that depends on a real parameter $\alpha \neq 0$. It's defined for the real part of $s$ large by $$ ...
-1
votes
1answer
28 views

Is there any practical use of $0^\circ angles$?

An angle is defined as two rays $\overrightarrow{YX}$, $\overrightarrow{YZ}$ sharing a midpoint $Y$; the angle formed is called $\angle XYZ$ or simply $\angle Y$. Then, the measure of $\angle Y$ is ...
0
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0answers
21 views

Guidelines on how to formalize mathematics from its foundations.

Let's say I wanted to understand mathematics in the most formally rigoruous way, meaning from the basic understanding of arithmetic, I'd want every operation I make to have a formal proof, and ...
0
votes
1answer
60 views

What are the prerequisites for Michael Spivak's monumental A Comprehensive Introduction to Differential Geometry?

What are the prerequisites for Michael Spivak's monumental A Comprehensive Introduction to Differential Geometry? In particular for volume 1? Are these 5 volumes self-consistent in the sense that a ...
0
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0answers
5 views

Reference for completely bounded homomorphisms between $L^p$ operator algebras or between general Banach algebras

I am not aware of work that has been done on completely bounded homomorphisms between $L^p$ operator algebras ($p\neq 2$) or between general Banach algebras. By $L^p$ operator algebra, I mean a Banach ...
3
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1answer
26 views

Discrete analogue of bounded variation

What kind of sequences $(a_n)\subset\mathbb{R}$ are expressible as the difference of two increasing sequences?
0
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0answers
20 views

Euler - Lagrange Equations proof

I have been searching on the internet about Euler - Lagrange Equations and I didn't find anywhere the proof for Euler - Lagrange Equations. I need to find a proof for this equations. From where can I ...
0
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0answers
6 views

References for involutive systems of vector fields?

Can anyone recommend me references dealing with involutive systems of vector fields? I'm taking a course which is using the book An Introduction to Involutive Structures (F. Berhanu, J. Hounie, P. ...
-1
votes
0answers
30 views

Is Tu's “Introduction To Manifolds” a good place to pick up diff-geo intuition for Vakil's notes?

So I want to study algebraic geometry from Ravi Vakil's notes. However, the only thing I seem to be missing -- I have all the official prerequisites like commutative algebra and point-set topology ...
0
votes
0answers
11 views

Boundary conditions for a radiative heat transfer problem

Consider the heat equation $$ \frac{\partial T}{\partial t} - a\Delta T + \mathbf v \cdot \nabla T = S $$ where $S$ is a source term dependent of the radiation intensity $I$ and the temperature $T$. ...
1
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0answers
30 views

References for methods for convergence analysis of discrete time dynamical systems with non lipschitz nonlinearity

Let a nonlinear dynamical system be described by the difference equations $$x(n+1)=f(n,x(n)),\ n\ge 0$$ with the function $f$ being nonlinear and non-lipschitz and bounded over a domain $D$. My ...
0
votes
0answers
18 views

GCD for real analytic functions

In the theory of real analytic functions of several variables, is there a concept of greatest common divisor. If so, does it also hold true that if the gcd of a collection of functions is $1$, then ...
0
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1answer
44 views

Books like Anold's Real Algebraic Geometry

I am looking for books on the topics covered in Arnold's Real Algebraic Geometry which doesn't have too many pre-requisites.I don't expect it to be written in the same style as Arnold's which is truly ...
4
votes
1answer
39 views

Gauss' original proof of quadratic reciprocity

Is the original proof of quadratic reciprocity due to Gauss available anywhere online? I've been looking for quite a while now, but with no results. Most papers seem not to include it because of it ...
0
votes
2answers
35 views

Why distribution of multiple recursive random number generators is uniform?

I was reading the article of L'Ecuyer on random number generation. The title of this article is "Uniform Random Number Generation". One of the proposed PRNGs there, is multiple recursive random ...
2
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0answers
36 views

Reference request: Tubular neighborhood theorem for non-closed manifolds via the exponential map.

Let $M\subset N$ be a submanifold. (Both $M$ and $N$ have no boundary, but $M\subset N$ need not to be closed as a subspace and none of them need to be compact) Choose a Riemannian metric on $N$ and ...
0
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0answers
37 views

Regularity of elliptic PDE in terms of weighted Sobolev space

There seems to be a whole industry of weighted ver. of the Poincaré's inequality (Weighted Poincare Inequality) I wonder if there are results like, weighted $L^2$ equivalent of (interior/boundary) ...
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votes
1answer
58 views

I need this book by Michael Weinstein, Between nilpotent and solvable [closed]

I need this book by Michael Weinstein, Between nilpotent and solvable. I live in iran and i can't find this book. Please help me.
1
vote
1answer
28 views

Introductory Reference for Mathematical Physics

I'm a senior undergraduate student studying differential geometry. I have experience with smooth manifolds, some elementary theory of Lie groups, and a little multi-linear algebra. I understand this ...
0
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1answer
13 views

Proof for the fact that the method of characteristic equations is a valid method to solve recurrence relations

Could someone kindly point me to a proof of the fact that the method is characteristic equations is a valid way of solving recurrence relations? It seems fairly arbitrary to me. I would be grateful ...
0
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0answers
6 views

Property of locally cyclic groups

I am having difficulty proving that: A group $G$ is locally cyclic if and only if $G$ is isomorphic to a subgroup of $\mathbb{Q}$ or $\mathbb{Q/Z}$. Is there any easy way to prove it? Thanks.
0
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0answers
13 views

Automorphism group of a locally cyclic group

I am having difficulty proving that: The automorphism group of a locally cyclic group is commutative. Is there any easy way to prove it? Thanks.
0
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0answers
48 views

Differentiability of parameter-dependent integrals when derivative exists only almost everywhere

This unanswered question asked in 2013 Differentiation under the Integral Sign (let's call this Q-zero) seems to be taken from this (or pdf ver.). The result on differentiation under the integral ...
1
vote
1answer
45 views

About a matrix identity.

In a document named as "The Matrix Cook-Book" I saw two expressions of which I do not get any clue how they are derived. For $n = 3:$ $\det(I + A) = 1 + \det(A) + Tr(A) + 1/2\ Tr(A)^2 − 1/2\ ...
0
votes
0answers
9 views

Is there a solid reference work that covers optimization for discrete and for continuous domains?

I am looking for a good, comprehensive reference on optimization. Currently, I have Lundberg's "Linear and Nonlinear Programming, 3rd Ed", but this completely omits integer programming, except in the ...
0
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0answers
16 views

Study materials for Differential equations and Fourier analysis

In two days, on Monday, a new course called Introduction to differential equations starts, and when that ends in one month another called Fourier analysis and its application starts (Both are actually ...
0
votes
1answer
36 views

What's a somewhat fast introduction to (differential) geometry and algebraic topology for someone who knows a lot of analysis but little else?

I never got to learn much about geometry beyond curves and surfaces in Calculus III, and point set topology. So what is a fast introduction to differential geometry (specifically, differential ...
1
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3answers
97 views

Good algebra book to cover these topics?

I will be studying two algebra modules next year and I am looking for a comprehensive book that will cover both of them, however due to having very minmal exprience with algebra I am looking for your ...
3
votes
1answer
34 views

Double integral definition of periodic Sobolev spaces

Preliminaries: For $s \geq 0$ define the periodic Sobolev spaces $H^s(\mathbb T)$ with norm $$ \| f \|_{H^s(\mathbb T)}^2 = \sum_{k \in \mathbb Z} \big(1 + |k|^2 \big)^s \, \big|\widehat{f}_k \big|^2, ...
0
votes
1answer
43 views

What are some easier papers/books I can read? [closed]

I'm trying to improve my ability in reading mathematics papers. My field is more related to biological sciences, but there are a lot of interesting papers I'd like to read that use more mathematical ...
0
votes
0answers
17 views

Combinatorial Convex Optimization: Russian paper

I'm looking for an electronic version of the paper: David Yudin and Arkadi Nemirovski. Informational complexity and effective methods of solution of convex extremal problems. Economics and ...
0
votes
0answers
14 views

Application of Multivariate Analysis on Straight Lines [closed]

Can anyone suggest to me a reference on the Application of Multivariate Analysis on Straight Lines? The reference should contain the part where we use the concept of orthogonality to formulate ...