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.).

59 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
6
votes
0answers
82 views

Is there an equivalent of differential geometry for infinite dimensional spaces?

Differential and (Semi/Pseudo-)Riemannian geometry provide a framework for doing calculus on finite dimensional manifolds and have applications in physics (general relativity) and dynamical systems ...
4
votes
0answers
75 views

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 ...
3
votes
0answers
73 views

Catalog of Categories

Could someone please indicate a website, book or PDF that contains a catalog of categories? I am looking for a place that contains descriptions and properties of the best known categories. I am ...
3
votes
0answers
86 views

About the research papers which led to beginning of Sieve Theory

I am an undergraduate and during these uncertain times due to covid -19 i have got a lot of spare time. I have a good background in Analytic number theory, Abstract Algebra, Real/Complex /Functional ...
3
votes
0answers
516 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 $B_{\mathbb{R}^{n}}[0,1]=\{x\in \mathbb{R}^n: \|x-0\|\leq 1\}$ ...
2
votes
0answers
19 views

Is there a bibliography of Lebesgue’s publications (with translations)?

I’m reading in the history of measure and integration and can’t find a complete list of Lebesgue’s publications, which I understand comprise his PhD thesis, some 50 papers, and two monographs. (...
2
votes
0answers
72 views

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), ...
2
votes
1answer
160 views

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 ...
2
votes
0answers
303 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 ...
2
votes
0answers
28 views

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 ...
2
votes
0answers
150 views

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 ...
2
votes
0answers
158 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 ...
2
votes
0answers
88 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 ...
1
vote
0answers
49 views

Reference to an elementary result of mathematical analysis.

Can anyone suggest a mathematical analysis textbook that contains proof of this Proposition below? I have already sought proof of this result in classic textbooks of mathematical analysis such as ...
1
vote
0answers
80 views

Hermite interpolation and basis functions.

I am using piecewise quintic Hermite interpolation at the joint level for a robot (1000 Hz) from a more time-sparse, but smooth trajectory (100 Hz). I have tested this according to the elegant ...
1
vote
0answers
31 views

Reference request on the Schwartz class on integers

It's a well known fact that the Schwartz class over integers defined by $$S(\mathbb{Z}^n)=\{\{a_m\}_{m\in\mathbb{Z^n}}\mid \sup_{m\in\mathbb{Z}^n}|m^\alpha a_m|<\infty, \forall \alpha\in\mathbb{N}^...
1
vote
0answers
23 views

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?
1
vote
0answers
41 views

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 ...
1
vote
1answer
497 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 ...
1
vote
0answers
89 views

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 ...
1
vote
0answers
39 views

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 ...
1
vote
0answers
38 views

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. ...
1
vote
0answers
110 views

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 ...
1
vote
0answers
275 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 ...
1
vote
0answers
136 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?
1
vote
0answers
26 views

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, ...
1
vote
0answers
360 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 ...
1
vote
0answers
138 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 $f\colon U\to\mathbb{R}^n$...
1
vote
0answers
61 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. ...
1
vote
0answers
253 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) : = \...
1
vote
0answers
41 views

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 $...
1
vote
1answer
276 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, ...
1
vote
0answers
36 views

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/...
1
vote
0answers
26 views

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 ...
1
vote
0answers
68 views

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 ...
1
vote
0answers
78 views

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 ...
1
vote
0answers
14 views

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, ...
0
votes
0answers
18 views

Schwarz-Christoffel transformation French references

It might be a weird question but I am looking for a good reference written in French on Schwarz-Christoffel transformation https://en.m.wikipedia.org/wiki/Schwarz%E2%80%93Christoffel_mapping I would ...
0
votes
0answers
23 views

Looking for references: in PDEs

This is not a technical mathematical question. I came across some PDEs with no references nor their names. $$-\Delta u + \int_\Omega udx = f\qquad \hbox{in $\Omega$} \tag{Eq1}$$ The above equation can ...
0
votes
0answers
35 views

Why work with p-divisible group over a field k?

In Michel Demazure's book "Lectures on $p$-divisible groups". He works particularly over a field $k$: For example is the definition of formal schemes, he began with base field $k$. Most ...
0
votes
0answers
23 views

Where to find known bounds on expressions?

Example. In a problem I was working on, I had an expression of the form $(1-e^{-\alpha n})^{e^{\beta n }}$. I wanted to find an upper bound $f(\alpha, \beta, n)$ on this that makes it easier to see ...
0
votes
0answers
21 views

Table of potential function for field

I know there is books that has table of common integrals, and I was wonder if there is a book that contain a table of common potential functions of fields.
0
votes
0answers
15 views

AMS Reference Style - No date

When including a reference in your bibliography, and the source has no date on it, how should this be indicated in the AMS reference style? Is it "n.d." or should the date simply be omitted?
0
votes
0answers
76 views

Book recommendation : Olympiad Algebra Book

I was searching for a book for olympiad algebra, I coudn't find good books. Can someone please help me with this? It will be much appreciated!
0
votes
0answers
18 views

Find this reference

I need this reference, but I couldn't find it online as a $\text{PDF}.$ Any help please? J. Sun, X, Zhang, The fixed point theorem of convex-power condensing operator and applications to abstract ...
0
votes
0answers
13 views

Are there pre-computed tables for values of the “sum-of-divisors” function?

Let $\sigma$ denote the "sum-of-divisors" function, i.e., $${\displaystyle \sigma _{}(n)=\sum _{d\mid n}d^{}\,\!.}$$ Note that the sequence $\sigma(n)$, for $n\geq1$ is in the OEIS as entry ...
0
votes
0answers
24 views

Reference for idempotent rings

In the wiki page of algebraic ring without multiplicative identity appears the definition of idempotent ring as a weakening of unital ring. Does any have a reference of where or why this concept ...
0
votes
0answers
61 views

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 ...
0
votes
0answers
33 views

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 ...
0
votes
0answers
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\}=\{\...