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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3
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2answers
113 views

Proper axiomatization of Euclidean Geometry that Euclid would approve of

It is relatively common knowledge that Euclid's axiomatization is not sufficient to prove all the things that Euclid wants to, and that there are other axiomatizations out there that strengthen ...
1
vote
0answers
24 views

Learning about Markov Chains

I am trying to learn about how to use markov chains for complicated probability problems. I have been looking for different materials to learn these but haven't had much luck. Does anyone have any ...
2
votes
0answers
51 views

A question on (odd) perfect numbers

(Note: This has been cross-posted to MO.) Let $\sigma(x)$ be the (classical) sum of the divisors of $x$. A number $N \in \mathbb{N}$ is called perfect if $\sigma(N)=2N$. An even perfect number $U$ ...
17
votes
2answers
224 views

To whom do we owe this construction of angles and trigonometry?

I've come across what is, to me, the most precise, beautiful and thorough definition of what we know of as the angle between two vectors. I say this because most literature either skims over things ...
2
votes
0answers
49 views

20th century books on geometry

I've heard something about the fact of some old geometry textbooks, dated to the beginning of the 20th century approximately, have a structure composed by a problem, the solution and then something ...
0
votes
0answers
23 views

Table of Fourier series

I found that there are very good references on Fourier integral transform but none on Fourier series. Do you happen to know one?
0
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0answers
26 views

Identifying a sequence of numbers from an optimization problem in $L^1$

Question Does there exist general closed form solutions (or some sort of recurrence relation) to the system of equations: $$\begin{align} x_0 &= -1\\ x_{k+1} &= 1\\ \sum_{j = 0}^k (-1)^j ...
6
votes
1answer
172 views

Conjectured Primality Test for $N=8\cdot 3^n-1$

Definition Let $P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right)$ , where $m$ and $x$ are nonnegative integers . Conjecture Let $N=8\cdot 3^n-1$ ...
1
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1answer
20 views

Reference request: Right pseudo inverse

Suppose, I have a matrix $P\in\mathbb{R}^{m\times n}$ with $\text{rank}(P)=m$ and I'm searching for a right pseudo inverse $P^{+R}$. Since I'm working with symbolic matrices in a computer algebra ...
4
votes
1answer
92 views

Existence of bijection that reorders elements?

Suppose I have some function $f:\mathbb{R}\to[0,1]$. Does there necessarily exist a bijective mapping $g:\mathbb{R}\to\mathbb{R}$ such that $g(x)\leq g(y)$ implies $f(x)≤f(y)$? If not, does it help if ...
1
vote
2answers
84 views

How can we detect if a topological space has “holes”.

I realize that this question might seem ambiguous, is there a topological notion for what a Hole is? I think it has something to do with the fundamental groups of the topological space but I don't ...
0
votes
0answers
17 views

Domains whose Green functions is explicit or can be approximated explicitly?

The only examples I keep finding are upper half plane (and tilted) and sphere (eg. Evans). Can you suggest some other domains? If not, how about any good books or papers documenting the progress ...
0
votes
1answer
78 views

Help with an inequality in Cazenave's book “Semilinear Schrodinger equations”

I'm reading Cazenave's book "Semilinear Schrodinger equations" and I found this inequality at page 84 $$\vert\vert u_1\vert^\alpha u_1-\vert u_2\vert^\alpha u_2\vert\vert\leq C (\vert ...
3
votes
1answer
80 views

Affine variety and dimension

I'm working on a paper about representation of quivers and Gabriel's theorems. See this .pdf if you're interested ; but I guess you can answer my question without knowing anything about quivers, or at ...
1
vote
4answers
127 views

Calculus books recommendation (intermediate level)

:) I would like to ask for some intermediate level textbook for calculus (single variable), or, at least, some supplement to Spivak's Calculus for better understanding on how to approach and solve ...
1
vote
0answers
21 views

If $R$ is a noncommuative Noetherian ring, is it true that $R[[x]]$ is a Noetherian ring?

I am looking for a reference in order to answer the following question: If $R$ is a noncommutative Noetherian ring, is it true that $R[[x]]$ is a Noetherian ring? The answer is well-known in the ...
1
vote
0answers
28 views

Reference request: extending tensor product of modules

I'm looking for a reference to a construction similar to the following. I have a right R-module, $A_{K'}$, and a left R-module, $_KB$, where $K$ and $K'$ are fields and $K'\subset K$. I want to take ...
0
votes
0answers
51 views

Calculus book with interesting examples

I need to prepare presentation about calculus, paying special attention for examination of function of one variable. I am not very advances in the topic, but I'm looking for book which contains ...
6
votes
1answer
116 views

Generalization of Minkowski inequality

I am wondering if the following is true: Suppose continuous function $g: [0, \infty) \to [0, \infty)$ satisfying $g(0)=0$ is increasing and strictly convex and (therefore) invertible. Let $||f ...
2
votes
1answer
49 views

Reference request: Derived category of category with sufficiently many injectives

I'm studying derived categories and have encountered problem with references I have. Namely, proof of the following theorem: Theorem: Let $\mathcal A$ be Abelian category and $\mathcal I$ full ...
0
votes
0answers
10 views

Finitely generated modules over completed group rings

Let G be a profinite group. Let $M$ be a finitely generated $\Bbb{Z}_p[[G]]$ (completed group ring). How to show the following facts: $M$ carries a unique Hausdorff topology(called its canonical ...
1
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0answers
19 views

Can anyone suggest a reference to learn about relative log-likelihood and likelihood intervals?

I want to understand how to calculate the 10% likelihood interval for a Poisson model of count data. It is an old assignment where they give you 20 counts, tell you it is a Poisson model and ask you ...
2
votes
1answer
57 views

Problem Books with Problems less “intense” than Putnam Problems

As the title indicates, I'm looking for a few suggestions on problem books. The problems should be a bit less demanding than Putnam problems. Like the Putnam, however, the prerequisites should be ...
0
votes
0answers
39 views

I need a good reference in topology [duplicate]

Can someone please give the title of a good topology book with exercises, preferably written by a master in the field Actually, i have basic notions like compactness, completeness, connectedness and ...
-1
votes
0answers
47 views

I need a reference in topology [duplicate]

Can someone please give the title of a good topology book with exercises, preferably written by a master in the field? Actually, I have basic notions like compactness, completeness, connectedness and ...
2
votes
1answer
40 views

Group generated by self-inverse elements

Given objects $x_1, \dotsc, x_n$, is there a name for the group generated by $x_1,\dotsc,x_n$ subject only to the relations $x_i^2 = 1$ for all $i \in \{1,\dotsc,n\}$? The dihedral group seems ...
4
votes
0answers
48 views

What is the automorphism group of the field of all constructible numbers?

Let $\Omega\subseteq \mathbb{C}$ be the field of all constructible numbers (i.e. $\Omega$ is the smallest subfield of $\mathbb{C}$ which is closed under taking square roots). What is known about the ...
0
votes
0answers
37 views

what are mathematical and scientific website & database?

I have seach mathematical website, which are http://scienceworld.wolfram.com or http://www.mathforum.com and many more which are given by http://www.tifr.res.in/~base/links/website.html. Can anybody ...
1
vote
0answers
30 views

Runge-Kutta methods for PDEs

How are RK methods for solving time-dependent PDEs implemented? I am trying to reproduce results of a thesis. It is a advection-diffusion unsteady equation. It is clearly mentioned that they have ...
1
vote
0answers
32 views

Sets that are convex in two different metrics

Let $(M,g)$ be a complete Riemannian manifold, and let $C$ be a subset of $M$. We will say $C$ is convex if for any points $p,q \in C$, there exists a unique normal minimal geodesic $\gamma$ joining ...
0
votes
0answers
29 views

Sobolev spaces on compact manifolds

Let us consider a self-adjoint elliptic pseudodifferential operator $P \in OPS^2$ on a compact manifold $M$ such that $spec(P) \subset (0, \infty)$. Is the norm $(Pu, u)^{1/2}$ on $H^1(M)$ equivalent ...
1
vote
1answer
25 views

Domain of square root of a self-adjoint positive operator

Let $A \geq 0$ be a densely defined self-adjoint positive operator on a Hilbert space $H$ obtained by Friedrichs extension, and let $Q$ be the densely defined quadratic form associated to $A$, that ...
2
votes
0answers
37 views

Is the analytic version of the Whitney Approximation Theorem true?

The Whitney Approximation Theorem states that any continuous map between smooth manifolds is homotopic to a smooth map. If the manifolds are real analytic, is every continuous map between them ...
0
votes
0answers
25 views

Books on Complex analysis and Probability

Any books exploring the connections between Complex analysis and Probability in the spirit of Dudley's book? In this forum I found Watanabe's "Algebraic Geometry and Statistical Learning Theory" ...
0
votes
0answers
11 views

Prime ideals in Iwahori-Hecke algebras

Results on the ideals (especially the prime, completely prime ones) of Iwahori-Hecke algebras (espcially the ones with finite order) is needed. Thank you very much.
1
vote
2answers
52 views

Sets of “Isolated” Cardinals

Let $C\neq\emptyset$ be a set of infinite cardinals with the property that NO member of $C$ occurs as the supremum of strictly smaller members of $C$. So the cardinals in $C$ are sort of "isolated". ...
0
votes
1answer
29 views

Distribution with density $x^2\operatorname{exp}\{-x^2/2\}$

I came across the probability distribution with density $$ f(x)=\sqrt{\frac{2}{\pi}}\,x^2\,\mathrm{e}^{-\frac{x^2}{2}},\quad x\geqslant 0. $$ Is this distribution known under a certain name? I only ...
1
vote
2answers
54 views

Are there any databases for PhD dissertations? [closed]

I just know ProQuest which supplies some PhD dissertations. However, it's hard to find some the dissertations of French and German. So are there any other good databases for dissertations of French, ...
6
votes
2answers
207 views

Prerequisits for Gauss-Green theorem

Consider the following theorem from the appendix C from Evans PDE book: I know about integration in $\mathbb{R}^n$ but not about how to make sense of the integrals on the right-hand side. As my ...
0
votes
0answers
16 views

Linear equations in non- commutative rings

Please any reference about general solutions of simple equations of the form $ax=b, xa=b, axb=c$ over non-commutative rings
0
votes
0answers
8 views

about a classic result from Han and Lin pde book

Let $A=a_{ij}$ an $n x n $ matrix where the coeficients are in $L^{\infty}(B_r(0))$ and satisfies $$ \lambda |\xi|² \leq a_{ij}(x)\xi_i\xi_j \leq \alpha |\xi|² x \in B_r(0), \xi \in R^n$$ for some ...
0
votes
0answers
26 views

References request: are there some references about simple modules of group algebras?

Are there some references about constructing the simples, determining the dimensions of simple modules and describing decompositions of tensor products of simple modules of group algebras? Thank you ...
1
vote
1answer
36 views

relations between a set of polynomials

I have a set of polynomials. Is there a computer algebra program that gives all the algebraic relations between them ? I will prefer singular if it has this component.
1
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0answers
20 views

Can Every Higher Order PDE be Written as a System of 1st Order PDEs?

Motivation A section on the Wikipedia page (here) of ordinary differential equations states the following. Reduction to a 1st Order System Any differential equation of order $n$ ...
1
vote
1answer
30 views

Notation in Reed/Simon Vol. IV (and possibly an earlier volume)

I'm wondering if there are any mathematical physicists/analysts out there that can help me with some notation I've seen in Reed and Simon's books on analysis. Unfortunately I don't have time to read ...
1
vote
2answers
195 views

(Updated) Geometric Illustration of Monotone and Maximal Monotone Maps

I am writing a note about the Monotone and Maximal Monotone maps from the following book http://link.springer.com/book/10.1007%2Fb97594 In this book we read a map ...
1
vote
1answer
43 views

FLATLAND's sphere intersection scenario, explored for four dimmensions

I recently finished this wonderful new vintage edition of FLATLAND. http://amzn.com/918775116X In 1884, Edwin Abbott wrote this strange and enchanting novella called FLATLAND, in which a square who ...
0
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0answers
36 views

Generalization of a class of sets

In topological space, we start with open set, which serves as fundamental set. We know that union of finite disjoint open sets is the smallest set amongst any kind of unions of open sets, so we have a ...
0
votes
0answers
9 views

Reference for proofs of the following facts concearning elliptic pseudo-differential operators on manifolds?

Throughout $M$ will be a $C^\infty$ compact $n$-manifold without boundary and $E$ will be an elliptic pseudo-differential operator on $M$. Can anyone recommend me a reference where I can find the ...
4
votes
0answers
30 views

What are Mumford's 'moduli topologies'?

I've been reading Mumford's Paper 'Picard Groups of Moduli Problems'. Stated in modern language, the most famous result from the paper is that the moduli stack of elliptic curves has Picard group ...