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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1answer
14 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
votes
0answers
9 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
votes
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
0answers
16 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 ...
0
votes
0answers
31 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
vote
2answers
32 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
votes
0answers
15 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
votes
0answers
20 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
55 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
votes
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
votes
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
votes
0answers
19 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
votes
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. ...
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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
26 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. Assume that $f$ is linear and bounded ...
0
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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
votes
1answer
43 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
1answer
27 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 ...
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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 [on hold]

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
votes
1answer
12 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
votes
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.
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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
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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
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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
vote
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
33 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
16 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 ...
2
votes
1answer
32 views

What is a good book for learning Stochastic Calculus?

I am in search of a good book for learning Stochastic Calculus from a purely mathematical/statistical point of view. Almost all the books I see are based on Finance. Also, please specify the ...
2
votes
0answers
26 views

Abelian hypersurfaces

Is there any way to tell from its defining equation when an affine hypersurface has a group law? I am aware that all such groups are matrix groups; in that case I might want to ask when a variety over ...
0
votes
1answer
49 views

Estimate for partial sums of a series equivalent to the Riemann hypothesis

The sums $$S_N=\sum_{n=1}^N\frac{\mu(n)}{n},$$ where $\mu$ is the Moebius function, are known to tend to 0 as $N\to+\infty$. As far as I remember, there was an estimate on $S_N$ equivalent to the ...
2
votes
1answer
28 views

Multiplicative version of convex hull

The convex hull of a finite set of points, $(x_i,y_i) \in \mathbb{R_+}^2$ ($i=1,...,n$), is defined as: $$\left\{(\sum_{i=1}^{n} \alpha_i x_i,\sum_{i=1}^{n} \alpha_i y_i) \mathrel{\Bigg|} (\forall i: ...
6
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0answers
55 views
+50

Interval arithmetic with different definitions of intervals

Interval arithmetic normally deals with intervals defined as $[a,b]$ with rules like $$[a,b]\cdot[c,d]=[a+c,b+d]$$ I am interested in interval arithmetic with different interval definitions such as ...
0
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0answers
15 views

Geometrical Interpretation of Risk Ratio (RR) [closed]

Can anyone suggest any book or article on the topic "Geometrical Interpretation of Risk Ratio (RR)" ?
0
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0answers
32 views

do Carmo or Pressley as introduction to Differential Geometry? [on hold]

I'm choosing between these authors for self-studying Differential Geometry. The contents seem pretty similar for both books and I was wondering which book I should choose. The level of these books ...
0
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0answers
11 views

Reference needed: Chi-square goodness of fit test, independence test, …

I want to really understand what is a Chi-square test and how it works: when is it needed, what motivates its use, etc. The same thing is needed for "Independence tests" and analysis of variances. Is ...
1
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1answer
24 views

What are those variations of norms called?

Let $V$ be a vector space with a function $\|\cdot\|$ on it that satisfies all the axioms of norms except for scalability condition $\|\alpha \mathbf{x}\| = |\alpha| \|\mathbf{x}\|$ replaced with ...