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.

learn more… | top users | synonyms (3)

2
votes
0answers
29 views

Generalization to higher dimensions of a statement about plane triangles

Let $\Delta=\Delta ABC$ be a plane triangle with area $F_\Delta$ and let $P$ be a point in $\Delta$. Draw lines through $P$ parallel to the sides of $\Delta$; then $\Delta$ is decomposed into three ...
1
vote
0answers
11 views

Kac's Theorem about stationary stochastic processes

I've read that Mark Kac proved a very beautiful theorem which says that, for a stationary, discrete-valued stochastic process, the expected recurrence time of a finite trajectory is just the ...
3
votes
1answer
30 views

Vanishing of the first Chern class of a complex vector bundle

Suppose that $E\to M$ is a $\mathbb{C}^n$-bundle with a metric. This is equivalent to saying that there exists a chart $\{U_\alpha\}$ of $M$ and $\phi_{\alpha,\beta} \colon U_\alpha\cap U_\beta\to ...
3
votes
0answers
55 views

Transcendence of $\Gamma(1/3), \Gamma(1/4)$

Wikipedia mentions that the transcendence of $\Gamma(1/3), \Gamma(1/4)$ was proved by G. V. Chudnovsky. Does anyone have a reference to that proof? Or maybe some details on the essential ideas ...
0
votes
0answers
19 views

On stochastic process

What is a linear stochastic process ? is it different from a stationary process ? Can you give me an example of linear discrete stochastic process ? What are the title of good books so that i can ...
0
votes
1answer
63 views

Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height

Let $V_n$ be the volume on the set of polytopes in $\mathbb R^n$, defined axiomatically, i.e. a functional, that assigns to each polytope $P\subseteq\mathbb R^n$ a real number $V_n(P)\ge 0$ in such a ...
0
votes
0answers
35 views

What are “reciprocal radii/radiuses”?

in a novel I found the phrase "reciprocal radii". What exactly does this phrase mean? Can you explain it even for non-mathematicians, maybe in a more philosophical way (by connecting this phrase to a ...
1
vote
0answers
35 views

Existence of an homeomorphism between $X$ a complete separable metric space and a subspace of $[0,1]^{\mathbb{N}}$

Result: If $X$ is a complete separable metric space then there is a $E \subset [0,1]^{\mathbb{N}}$ such that $X$ is homeomorphic to $E$ ($E$ is a $G_\delta$ set - is the intersection of denumerable ...
4
votes
1answer
50 views

Methods for Finding Exact Solution For $e^{2x}+p(2x)$

I know there are ways using the Lambert W function, and have had answers to simpler examples, for example $$e^{2x}+1+2x=0\Rightarrow e^{2x}=-2x-1$$ has the solution ...
0
votes
1answer
16 views

chromatic polynomial of chordal graph

Let $G$ bei a chordal Graph. What is the chromatic polynomial of $G$? My own research on this lead me to a conference paper, "chromatic polynomials of chordal graphs" by Chandrasekharan, Madhavan and ...
0
votes
1answer
25 views

What does the notation $\mathcal{O}_{\mathbb{P}^n}(1)$ mean?

I have tried looking at my sheaves notes but couldn't find anything.
0
votes
0answers
23 views

Positive matrix perturbed by one with negative eigenvalues

This is firstly a reference request in order to understand and study the following problem. Consider the sum of matrices $$ \sum_{k=1}^mc_kA_k,\hspace{3cm} (1) $$ where each $A_k$ (they are $k$ ...
1
vote
1answer
50 views

Studying machine learning

I'm currently studying machine learning using Bishop's book "Pattern Recognition and Machine Learning". The main disadvantage of this book (for me) is a lack of practical applications. Also it seems ...
1
vote
1answer
53 views

Which ZFC axiom schemes are reducible to a single axiom?

It is a remarkable fact that the $\in$-induction scheme (i.e. the claim that $\phi(x)$ holds for any $x$, whenever $\phi(\emptyset)$ and $\forall x(\forall y\in x \phi(y)) \Rightarrow \phi(x)$) is ...
0
votes
0answers
6 views

State-of-Art library or a method for paralell matrix inversion?

Do you have reference to a computer library or a paper regarding a state-of-art method to obtain inverse of a matrix in parallel? Thanks, Mojo.
1
vote
0answers
18 views

ODE and PDE : Solving DE with constant coefficients using differential operators

I want to study the method of finding solution to Differential Equations with constant coefficients using method of operators (finding the particular integral to the equation using inverse operator). ...
1
vote
1answer
31 views

Positivity of Coulomb energy for gerenal measures

Suppose $\nu$ is a compactly supported signed measure in $\mathbb R^{n\geq 3}$. Is the Coulomb energy still positive? More precisely $$\iint \frac{1}{\|x-y\|^{n-2}}d\nu(x)d\nu(y)\geq 0?$$ This ...
2
votes
0answers
20 views

Closure of a Manifold is a Manifold with Corners?

Is there a general theorem that shows that if you have a manifold $S$ then its closure $\overline{S}$ is a manifold with corners? I am dealing with a specific set $S$ (I would rather not say which ...
1
vote
1answer
36 views

Fourier transform division theorem in $\mathbb R^n$

It is known that if $f \in L^1(\mathbb R)$, $\widehat f(\xi) \neq 0$ for any $\xi \in \mathbb R$, then for any $h \in L^1(\mathbb R)$ such that $\widehat h$ is compactly supported there exists $g \in ...
0
votes
1answer
45 views

Need resources for difficult Algebraic Identites.

Where can I find all the algebraic identities and their proofs of following types, $a^3+b^3+c^3–3abc≡(a+b+c)(a^2+b^2+c^2–ab–bc–ca)$ $a^3+b^3+c^3–3abc≡ \dfrac12 (a+b+c)((a-b)^2+(b-c)^2+(a-c)^2$ ...
1
vote
1answer
25 views

Limit(s) of a Sequence from the decimal expansion of $\pi$

I found a statement in a book concerning the decimal expansion of $\pi$ that I do not really understand. The statement is my problem number 2, where problem number 1 really looks like a reference ...
2
votes
1answer
86 views

Coordinate Geometry and Trigonometry book recommendation for GRE Math Subject Test

I am currently a math major at university and I plan to take GRE Math Subject Test in future (most probably next year). Can you please suggest any good book for revising and brushing up Coordinate ...
0
votes
0answers
33 views

Difference between Calculus $4$th edition and Calculus $3$rd edition by Michael Spivak?

I currently possess Calculus $3$rd edition by Michael Spivak in it's electronic form. However, I am considering buying a hard copy and have the option of buying either a used $3$rd edition or a new ...
0
votes
0answers
7 views

Table or diagram that classifies stochastic processes and summarizes their relationship?

I am looking for a diagram, table, graph, or something along those lines that classifies stochastic processes and summarizes how they relate to each other. Just to give an idea, I am interested in a ...
1
vote
2answers
25 views

A repository of constrained optimization test problems?

I am looking for a repository of constrained optimization problems with solutions. I want to find "benchmark" type problems to test my algorithm on and just trying to search for known problems ...
0
votes
0answers
30 views

Set Theory text with solutions to exercises [duplicate]

I'm looking for a set theory text that has solutions to the exercises. I will be studying on my own and want to be able to check my understanding. Thanks for the suggestions.
2
votes
0answers
21 views

Generalization of a Result Concerning Projective Planes

Let $\mathcal P$ denote the set of all possible orders of projective planes. For $q\in\mathcal P$, let $PG_2(q)$ denote the projective plane of order $q$. There is a theorem due to James Singler ...
0
votes
0answers
107 views

What to teach in Set Theory & Logic Course. [migrated]

I will be teaching a third-year introductory course on Set Theory and Logic soon and was hoping to get advice from this community. I would rate my students' proof abilities as weak and was hoping to ...
0
votes
1answer
13 views

How can I conclude this “gluing property” for these Sobolev functions?

Let $u \in W^{1,2}(\Omega) \cap C(\Omega)$, where $\Omega$ is an open bounded domain in $R^n$ with smooth boundary.Let $B(x,R) \subset \overline{B(x,R)} \subset \Omega $ a ball. Consider $u^{\star} ...
1
vote
2answers
73 views

Non-English-language graduate-level textbooks on differential geometry

I'm looking for modern graduate-level non-English-language differential geometry textbooks. I'm interested in original works by non-English-language speakers in their native languages, not ...
0
votes
0answers
12 views

$k$-vertex connected minimal Steiner network problem

Could any one suggest to me a paper related to the $k$-vertex connected minimal Steiner network problem? $k$-vertex connected minimal Steiner network problem is defined as: For an undirected and ...
1
vote
1answer
27 views

Permutation representations of finite abelian groups [closed]

What is a good source to study from about permutation representations of finite abelian groups, specifically $\mathbb{Z}_{p}$? If reference for the specific topic is not available, I would like to ...
2
votes
0answers
46 views

Find motivation for calculating $\int_{2}^{X} A^2(t) A(\alpha t)dt$

I read a thesis of Kong Kar Lun (student of Tsang K.M) about the some mean value theorems for certain errors terms in analytic number theory and in which he gave the asymptotic formulas of the ...
4
votes
0answers
171 views

Has this difference equation :$x_{n+1}=Ax^2_{n}-Bx^2_{n-1}$ been studied before?

I posted this problem before in MO but only I would like to know if this difference equation :$$x_{n+1}=Ax^2_{n}-Bx^2_{n-1}$$ where $A(\theta)= \cos(\theta)$ and $B(\theta) =\sin(\theta)$ are ...
1
vote
0answers
53 views

Ph.D thesis by Whitcomb

Does somebody has a link to Ph.D thesis by Whitcomb titled "The group ring problem" University of Chicago 1968. It was referred in a paper and I have some things to look up in that. I could not find ...
4
votes
1answer
37 views

Fractional powers of positive self-adjoint operators

Consider two positive unbounded operators $A$ and $B$ densely defined on a Hilbert space $H$ self-adjoint on a domain $\mathcal{D}(A) = \mathcal{D}(B) = H_1$. By the spectral theorem, we can define ...
0
votes
0answers
19 views

References for Dirichlet characters and L-functions

I am working on some exercises from my Analytic Number Theory course regarding Dirichlet characters, and I was wondering if someone could provide some references for this. Here's a problem that I'm ...
0
votes
1answer
31 views

Prerequisites for Random Graph Theory

I would dearly love to know the prerequisites for self-studying Random Graph Theory and Percolation Theory in Probability. My knowledge currently involves: Basic probability concepts: the axioms, ...
3
votes
0answers
24 views

What can be said about the space of vector fields for which a given, say $C^1$, function is a Lyapunov function?

I am learning Morse homology and I have been thinking about the following observation. One way of doing, say finite-dimensional, Morse theory is by fixing a Morse function $f\in C^{\infty}(M)$, where ...
1
vote
1answer
35 views

Is the Fourier Transform of the limit the limit of the Fourier Transform?

Assume you want to compute the Fourier transform of a function $f_\epsilon(x)$ given by \begin{align} \mathcal{F}(f_\epsilon)(k) = \int f_\epsilon(x) e^{-ikx}\, dx \end{align} Further assume, that ...
3
votes
1answer
78 views

Iterating until a diagram commutes

I'm coming across the following 'commuting' diagram a lot in my work, and I think it should have a neat categorical formulation. But I can't work it out for myself, and don't know what too google for. ...
1
vote
0answers
35 views

What is the connection between game theory and (modal) logic?

I'm interested in dynamic epistemic logic lately (reasoning about information and change in multi-agent systems). I also like game theory. I'm looking for some good resources about the connection ...
1
vote
2answers
57 views

suggest an elementary text in analysis

I have just completed my undergraduate course in mathematics but I don't feel better in analysis, there is a mugup of books in my book collection But don't know what to choose who will help me to ...
3
votes
1answer
57 views

Visual approach to abstract algebra

I'm currently finding abstract algebra to be very fascinating. However, one of the things that pulls me back is that I sometimes find it hard to understand something visually. For example, one could ...
3
votes
1answer
43 views

Differential Equations Lectures or books from a theoretical perspective?

I am looking for some differential equation lectures from a theoretical perspective, not a strictly computational one. I found the MIT 18.03 lectures which (as the professor says towards the end of ...
2
votes
1answer
44 views

Integral of the exponential of a homogeneous quartic - reference request

For a calculation I am doing, I have to calculate an integral of the form $$ I = \int_{\mathbf{R}^n} \exp[-Q(\mathbf{x})] d^n\mathbf{x} \text,$$ where $Q(\mathbf{x})$ is a homogenous, degree-4 ...
1
vote
0answers
14 views

Reference request: 2nd order Taylor expansion for functions between finite dimensional normed vector spaces using Fréchet derivatives

I'm looking for a reference of 2nd order Taylor expansion for functions between finite dimensional normed vector spaces using Fréchet derivatives. If this can't be found I think it would suffice for ...
6
votes
1answer
73 views

Applications of diagram lemmas

I'm currently reading Theo Bühler's survey on exact categories about which he says This article is written for the reader who wants to learn about exact categories and knows why. Very few ...
2
votes
2answers
176 views

Is the zero ring a domain?

Is the zero ring usually considered a domain or not? Wikipedia says: The zero ring is not an integral domain; this agrees with the fact that its zero ideal is not prime. Whether the zero ring ...
1
vote
1answer
75 views

Path to understand the maths behind contemporary Physics.

I am a physicist but I do really love maths and I would like to learn and have a deep understanding of the maths used in theoretical physics, just for leisure, in my free time. I know there is a ...