Questions tagged [reference-works]

Reference works include encyclopedias, dictionaries, books of tables (which may include numerical tables, tables of integrals, series, and products, tables of Fourier transforms, tables of finite groups, tables of combinatorial designs, etc.).

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Adding Examples to Math Paper

I'm writing a paper on the Mandelbrot set and want to add some examples of iteration to it to show values that are members of the set and to show values that are not members of the set. What's the ...
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Where are the Optimal Tours of TSPLIB 95 Instances?

I am looking for the optimal tours of the TSPLIB 95 instances as downloadable files. I have checked several places, but all lists I could find contain gaps, despite the fact, that all instances have ...
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62 views

Forward-backward induction

I've seen the famous proof presented by Cauchy for the AM-GM inequality but what other neat proofs use forward-backward induction? Is it fundamentally inextricable from ordinary induction (are there ...
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1answer
196 views

Book about Lattices, Boolean algebra

I have a subject about Applied Algebra and the first part of it it's about lattices, distributive lattices, hasse diagram, etc.. Next day we are going to start with Boolean Algebra. My professor is ...
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1answer
55 views

Finnish-English Dictionary on Graph Theory and Reliability Engineering?

I need to translate an abstract to Finnish and I need to find a dictionary on Graph theory. Does there exist any canonical reference work in Finnish that could be used as a reference for finding the ...
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1answer
242 views

Collected works of Mathematicians

The collected work of any mathematician is, in my opinion, more than collection of his works. Since it is edited (collected) by some people which have passed through many papers of the mathematician, ...
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Regularity of a function by approximation by polynomials.

A standard argument says that a continous function is $ C^{k,\alpha} $ at zero if there exists a polinomial of degree k such that $$ | (u - P)(x)| \le C | x|^{k+\alpha}. $$ This is the way for ...
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110 views

What is the proper way to cite a math textbook when writing a paper?

For example, I see this written in a bibliography of a paper: W. Fulton and J. Harris, Representation Theory, A First Course, GTM-RIM 129, Springer, 1991. The general case isn't clear to me from ...
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28 views

Explain a statement in a proof

At a proof at ProofWiki it is proved that there is a neighborhood $U$ of $x_0$ such as $fU\subseteq(c..d)$. In the proof it is used $(a): \qquad x \in {U_r}^- \implies f \left({x}\right) \le r$ I ...
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Key reference book on toric ideals: normal or not? Which definition to follow?

I want to understand sum of binomials better in terms of ideals such as binomial ideals, normal ideals and so by toric ideals. Examples about toric ideals contain $$\sum x^\alpha+\sum x^\beta\in\...
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Null space and Matrix equations

http://studyguide.pk/Past%20Papers/CIE/International%20A%20And%20AS%20Level/9231%20-%20Further%20Mathematics/9231_s03_qp_1.pdf I would like to know the method to answer question 8. I have been having ...
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The leatest research regarding ergodic operators

I always ask myself the following question which states: Where might the leatest research regarding ergodic operators be found ? It is undoubtedly I am not asking for the books that illustrate the ...
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328 views

Equivalence between Brouwer fixed-point theorem and Borsuk-Ulam theorem. Is there a simple proof of equivalence between them?

I wonder if Brouwer's fixed-point theorem and Borsuk-Ulam's theorem are equivalent. Brouwer's fixed-point theorem (simple form). Let $B_{\mathbb{R}^{n}}[0,1]=\{x\in \mathbb{R}^n: \|x-0\|\leq 1\}$ ...
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Recommendation topic - Numerical Analysis and computational

I'm having a course about 'Numerical Analysis and computational' in my master's. The course is about : Systems of Linear Equations: direct methods (LU factorization and Cholesky decomposition), ...
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176 views

Camille Jordan : Treatise on substitutions and algebraic equations ??

Is there english translation available of the monograph by Camille Jordan, titled: Traité des substitutions et des équations algébriques, which is available easily online in french. The reason for ...
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List of 2D definite integrals not reducible to products of 1D integrals

I'm writing numerical integration routines for 2D surface integrals. To test it, I'm looking for a list of definite integrals which have analytic forms. I need Integrals in polar coordinates over the ...
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228 views

Up-to-date Matrix Cookbook

My copy of the Matrix cookbook is dated November 15, 2012, and is the newest copy I've been able to find. Identities may not change overtime, but the approach to an error-free presentation can be ...
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Which probability measure book is more comprehensive?

I have read Rudin's Principles of Mathematical Analysis. I am now choosing one of the 2 books: Probability and Measure by Patrick Billingsley OR Probability and Measure Theory by Robert Ash I ...
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124 views

Laplace-Beltrami operator

I'm interesting in the Laplace-Beltrami operator on a sphere, more precisely its spectral properties including the spectral function, etc. So if someone can give me some references that treats this ...
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83 views

List of theorems by number of proofs

Has anyone ever attempted a list of theorems ranked by the number of published proofs? Maybe such a table could have a column listing the number of known proofs (although it may be optimistic to ...
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36 views

Search for a paper?

I'm going to work on this paper: An existence theorem for weak solutions of differential equations in Banach spaces..I searched for it by internet, but I found it nowhere Can you help me find it? I ...
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Errata in Convex Analysis and Minimization Algorithms by Hiriart-Urruty and Lemaréchal.

Hiriart-Urruty and Lemaréchal have written Convex Analysis and Minimization Algorithms I and II. Is there an errata list for these books?
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reference request: visualizing ideal structures in CRing

In a basic algebra course last year, I learned some of how rings are taxonomized by properties such as "all the elements have unique factorization", or "all the ideals are principal ideals". Studying ...
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Sets with a time dynamic?

I am looking for advice regarding if there is any literature wrt set theory that also has a inter temporal aspect to the set theory notation. E.g. an element can exist in one set at t=1, but move to ...
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Is it possible to study Differential Geometry from Spivak's books starting with the second volume without reading the first one?

Is it possible to study Differential Geometry from Spivak's books starting with the second volume without reading the first one ? The content of Differential Geometry course that is taught in the ...
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Research in the Discrete Logarithm Problem

I have already taken a course on Abstract algebra and tis implementation in the criprography, among other topics the course focused on the discrete logarithm problem in finite fields. Now, I would ...
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Causality Theory of Space-Time.

I'm looking for some books about causality theory in physics from mathematical point of view. I'm already using Global Lorentzian Geometry by John Beem and Semi-riemannian Geometry by Barret O'Neill. ...
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Book of support for reading the Fulton book.

I would like to know about some support reference that could help me in reading the Fulton (Algebraic Curves). Sometimes, some definitions I find in Fulton's book are not clear to me. So maybe with ...
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114 views

Nets with no convergent subnets in Banach spaces

Is there a characterization of nets with no convergent subnets in a Banach space? Does someone know some survey or book's chapter that deals with this kind of stuff?
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Practice questions

I would like to know if there are any good textbooks/online resources that include plenty of practice problems with solutions for the following topics: Triple integrals in cylindrical coordinates, ...
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300 views

How to prove that an integer linear program is infeasible?

I have an ILP which I would like to show as infeasible. The naive idea I had was to try to show that the relaxed LP is also infeasible. Unfortunately, I know that the LP is feasible. I want to know ...
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114 views

Reference. Recession cone and max-min of a function.

I am looking for some bibliographic references where I can find a relationship between recession cone of a set $U\subset\mathbb{R}^n$ and the minimum / maximum of a function $f\colon U\to\mathbb{R}^n$...
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59 views

Geometry were points are squares or hexagons (have an area and shape)

I am looking for a book that goes deep into the geometry where points have area preferably were points are hexagons but a good introduction of the geometry where points are squares is also welcome. ...
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188 views

Green's function and strong Markov property for stopped Brownian motion

Let $X(t)$ be a Brownian motion in $\mathbb{R}^n$, stopped at some fixed time $T$. Is there a notion of Green's function for such a Brownian motion? I am guessing that there is, and $G(x, y) : = \...
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Spectral bands of periodic differential operators

I am reading the book "Multidimensional Periodic Schrödinger Operator" (O. Veliev, 2015) which says on page 11: It is well-known the following statements about the spectral properties of $L_{t}(q)$ ...
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What is Multi-bump solutions for a PDE?

In the papers: http://www.sciencedirect.com/science/article/pii/S0294144905000041; http://www.sciencedirect.com/science/article/pii/S0022123609000597; http://www.sciencedirect.com/science/article/pii/...
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Lemmas, theorems to make non-sp graph into sp graph by addition of vertices?

The left graph is not sp graph because of edges crossing. The middle is a sp graph and the right is a sp graph. Notice that the left can be made into sp graph by addition of the vertex g. So does ...
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References on Inverse Problems, Approximation theory and Algebraic geometry

For example, you approximate structure functions of finite simple graphs in cases where only cut sets of the systems are known. The inverse problem means to build possible scenarios in underdetermined ...
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3-Book series on 'Set theory' 'Algebra' and 'Geometry'

I just read book on: 'Set theory and the Structure of Arithmetic by Hamilton and Landig' This book mentioned 'This is first book in a series of 3 books' Where 2nd and 3rd book are on algebra and ...
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References to papers/books that uses a kernel to smooth a discrete distribution

Since a kernel, such as Gaussian, is often used to smooth out the distribution of discrete points in 1D, 2D or 3D, I believe there must be some study materials or research work that have used this, ...
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*Reference Request* - Monograph on Triangular Numbers

Does anybody here know of a good monograph on triangular numbers, which preferably covers the basic number theory stuff and connections with other number-theoretic concepts? I tried searching MSE to ...
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How to get a math textbook that's out of publication?

I recently decided I wanted to learn more about the Dehn invariant, so I did what I always do and went on MSE and MO to get recommendations. I found this link, which suggested a book called "Theory ...
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Sinusoidal decomposition of signal

I have some data of periodic nature. The curve seems to be slightly irregular, and it makes sense to consider it as the sum of two or more different sinusoidals. I'm asking for a source or tools ...
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24 views

Is there a name for this defined element?

If $\Theta \in \mathbb{R}^d$ compact, $\rho(x,\theta): \mathbb{R}^p\times\Theta\rightarrow\mathbb{R}^+$ continuous in $\theta \in \Theta$ for all $x$, then $B=\{\rho(x,\theta), \theta \in \Theta\}=\{\...
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147 views

Proof of Coppel's Inequality for the matrix “measure”.

I am trying to understand the matrix measured proposed by W. Coppel in "Stability and Asymptotic Behavior of Differential Equations" in 1965, but I cannot find a pdf of this paper online, so if anyone ...
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Ideal generated by a set of polynomials $X^{a/b}$ where each monomial having $a$ and not having $b$

Let $$\mathcal R=\mathbb Z_2[x_1,\dots,x_n]/\langle x_1^2-x_1,\dots,x_n^2-x_n\rangle.$$ I want to learn ideal arithmetics to deal with polynomials of the forms such as Consider a set of ...
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About asymptotic expansion of parabolic cylinder functions

Let's have the parabolic cylinder function $U(a,z)$. I'm interested in its asymptotics for large argument $z$. Here I've found it, but I'm a bit confuzed now because of expressions $(12.9.1)$ and $(12....
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Fundamental solution of the Poisson equation with variable exponent

Let the variable exponent $p(x)$, where $p(x) \in C(\overline{\Omega})$, I want to know the fundamental solution of $$-(\Delta u)^{p(x)}=\delta_0.$$
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Sum of the reciprocals topology

Let's define this topology in $\Bbb N$ (here $\Bbb N$ begins at $1$): $$K\subset\Bbb N\text{ is closed }\iff K=\Bbb N\;\text{ or }\;\sum_{n\in K}\frac1n\text{ converges}$$ I have worked some on it. ...
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curves in Poincare half space (3 dimensional hyperbolic geometry)

Okay maybe I am going a bit ahead of my self The Poincare half plane still has many mysteries for me But still I was puzzeling about the 3 dimensional variant of it. So lets assume an hyperbolic 3 ...