This tag is for questions where the poster seeks references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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18 views

Papers related to Tomography and compressive sensing.

Recently I studied about Radon transformation and its applications. I got to know that they are lots of application in tomography and am very much interest after reading that. Now I wanted to read ...
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0answers
73 views

Very challenging series

Find a closed form for $\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^{2^2}}+\frac{1}{2^{2^{2^2}}}+\cdots $ Since I've never encountered this type of series before I was hoping someone here could help me ...
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0answers
70 views

Transfinite composition and $\kappa$-categories

I wonder whether the following ideas make sense, and whether something in that direction has been written down somewhere; do you know a reference? The last definition is supposed to be a ...
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0answers
13 views

Problem in complexity class $P$ with highest known degree of a polynomial

Can someone help me find source where is listed complexity of most problems in complexity class $P$, particulary, I would like to know the one with the highest degree found so far. Somewhere I found ...
-2
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0answers
103 views

Solutions to do Carmo's Riemannian Geometry [closed]

I have lot difficult in solving problem in Riemannian Geometry by Manfredo do Carmo. Does anyone know solution book of those? I just want ask if anybody know so! Gracias!
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0answers
47 views

Classics on abstract algebra and real analysis

I am going through Apostol's calculus volume 1. What a wonderful creation from Apostol. Even I could not imagine that such a book introducing the basic concepts so informally but easy-to-understand ...
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2answers
22 views

Examples of dynamical systems over various spaces

Let's define a dynamical system as follow : ‎ A dynamical system is a triple‎ ‎$(T, X, ‎\varphi‎) $‎‎ where T is a time set, X is a state space, and‎ ‎$‎\varphi : T ‎\times X ‎‎\rightarrow X ...
0
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1answer
47 views

What is a squashed 3-sphere?

I have found the term "squashed 3-sphere" used in the literature but could not locate a precise definition of it. I suppose it is topologically a 3-sphere with a metric different from the round one. ...
5
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1answer
85 views

Top 10 math mnemonics

If you study undergraduate medicine, mnemonics are almost indispensable - there is so much factual material to learn. I was never given any mnemonics in my time as a maths undegraduate. But Robert ...
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0answers
10 views

Reference for this kind of exercice

I would like to know some reference to practice this kind of exercise with solution. Any (good) book or online resources will be fine. Thanks a lot for any help that can be offered. Algebra ...
1
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0answers
23 views

A Couple Formulas in Besse's “Einstein Manifolds”

In Besse's "Einstein Manifolds," Chapter 6D, there are 2 formulas which I am interested in, which apply to compact Riemannian $4$-manifolds: ...
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0answers
23 views

Locate proof of Second Fundamental Theorem of Asset Pricing

Where can I find a $\textbf{rigorous}$ proof of the Second Fundamental Theorem of Asset Pricing. That is, A market is complete if and only if it has a unique risk neutral measure. Please do not ...
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0answers
27 views

What is an open property?

From an academic paper, "the existence of elliptic or hyperbolic 2-periodic orbits is an open property". I have never seen the term "open property" used before, moreover the paper gives no ...
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0answers
11 views

Definiton of invariant curve

What is the definition(s) of an invariant curve? What book should i read to get a better idea of their use in dynamical systems. Are there any defining features i should be aware of especially with ...
1
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0answers
30 views

$C^0$ estimate for solutions of the Neumann problem

I am interested in a reference for (or counterexample to!) a particular $C^0$ estimate for solutions of the Laplace equation with Neumann boundary conditions. More precisely, let $(M,g)$ be a smooth, ...
2
votes
1answer
40 views

Representations of knot groups

Recently, I was studying the knot group and I want to learn some more material about it (e.g. its representations). "Knots" by Burde and Zieschang discusses some material but it is not entirely ...
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0answers
40 views

Who did first use the concept of “supremum”?

Is there one specific person, who first defined the concept of "supremum"? If so: In which work? In my textbooks or by a quick search on the internet, I did not find an answer to my question.
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0answers
32 views

Good coding theory books?

Next week starts my coding theory course and i am really looking forward to it. Can anybody suggest me good coding theory books? I've already taken Cryptography class last semester and i studied it ...
1
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1answer
18 views

Loop spaces have the homotopy type of a topological groups

Every based loop space has the homotopy type of a topological group. I would like to understand this fact, and this is what this question is about : why is it true, and how does one prove it? I ...
1
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1answer
56 views

Analog of holomorphic Lefschetz fixed point theorem for smooth algebraic varieties

If $X$ is a compact complex manifold and $f: X \to X$ is a holomorphic map with isolated nondegenerate zeroes. Then there is a version of Lefschetz fixed point formula with traces on Dolbeaut ...
1
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1answer
35 views

Non-separable Hilbert spaces in duals

A topological space $X$ satisfies the countable chain condition if every family of pairwise disjoint open sets in $X$ is countable. I am looking for a reference to the following fact: Suppose that ...
4
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1answer
68 views
+50

Where can I learn more about the Galois connection induced by a graph on its own powerset?

Given a binary relation $R \subseteq X \times Y$, we get an antitone Galois connection $(F,U) : \mathcal{P}(X) \rightarrow \mathcal{P}(Y)$ in the usual way: The function $U : \mathcal{P}(X) ...
2
votes
1answer
39 views

Reference request: modern reference for Cantor's theorems of size of algebraic and transcendental numbers?

Cantor showed that the set of algebraic numbers is countable and the set of transcendental numbers is uncountable. Is there any (modern)book with the proof of these theorems?
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1answer
30 views

How are the essential upper and lower limits defined?

What means \begin{equation} \operatorname*{ess\,lim\,inf}_{x\to x^*} F(x) \end{equation} and \begin{equation} \operatorname*{ess\,lim\,sup}_{x\to x^*} F(x)? \end{equation} Sorry I also do not know in ...
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0answers
36 views

Where to find current literature, especially dissertations, on complex analysis?

Is there any public website or any other source which classify written master or doctoral thesis classify with respect to their content? Especially, I am going to make some research about complex ...
0
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1answer
15 views

Poisson Modeling/ Queue Theory - Reference Material

Can anyone reccomend some practical reference material related to building and implementing queueing theory models. using stochastic (prefferably Poisson) processes? We are looking to build out a few ...
1
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1answer
49 views

$\sin(x)$ is asymptotically equal to $x+5x^3$

Here is my question: I've never seen before this kind of fact underlined about asymptotic equalities (and why we keep only one term in these equalities) and I'm looking for reference. Here is an ...
0
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1answer
54 views

Book for probability theory

I need a good rigorous book to learn probability theory. So far, I've been suggested Gnedenko’s Theory of Probability, Shiyayev’s Probability and Feller’s An Introduction to Probability Theory and ...
3
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2answers
103 views

Motivating mathematics(particularly algebraic number theory) through historical problems.

Most mathematical textbooks start a subject by going backwards, historically. They will define the terms that were invented to solve a problem in their polished form and then use these definitions and ...
2
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0answers
20 views

Books on prime gaps?

I want to have a book on prime gaps, which includes both the theory of prime gaps and all the results obtained. The conditions may be harsh, but I hope I can have some recommendations that fit at ...
3
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0answers
27 views

Is there anywhere some explicit Bruhat decompositions are written down?

Question in title: most places I see Bruhat decompositions treated they're only briefly mentioned and no examples are given. Also, I calculated the following regarding the Bruhat decomposition of ...
3
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1answer
40 views

The periods of the Weierstrass function $\wp(z)$

Is it true that the periods $\omega_1$, $\omega_2$ of $\wp(z)$ are $\omega_1 = 4K$ and $\omega_2 = 4iK'$, respectively? Here, $K = K(k)$ is the complete elliptic integral of the first kind, and $K' = ...
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3answers
106 views

History of category theory

I am searching some information about the origins of the category theory. Anyone know where can I read about those topics? Thanks!
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2answers
80 views

Modified Hermite interpolation

I asked similar questions here and here, but I tried to formulate this one in a sharper way. Is anyone aware of some literature on polynomial interpolation where we sample the function and its ...
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2answers
81 views

Is there a theory of lie “rings”?

A Lie group is a group that is a differentiable manifold and addition and inversion are differentiable maps. Is there a theory for rings that are differential manifolds and have differentiable ...
0
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1answer
81 views

Who should I ask for Robin's paper? At any rate, I want to find out if a similar result to his can be achieved with 36 instead of 12.

Robin proved unconditionally that for $\ n \ge 3$ , $$ \sigma(n)<\left(e^\gamma+{\log\log12\left({\frac73}-e^\gamma \log\log12\right)\over (\log \log n)^2}\right)n \log \log n. $$ I need a similar ...
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0answers
104 views

Have these (extremely simple) classes of algebraic structures been considered in the literature? If so, what are they called?

Questions. Have the following kinds algebraic structures been considered in the abstract algebra literature etc.? If so, what are they really called? (I have used made-up terminology for the sake ...
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0answers
17 views

KAM theory in dynamical systems

What is the best text/lecture notes to read if you want to learn KAM theory in Hamiltonian dynamical systems?
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0answers
19 views

Reference for packing-covering of the sphere.

I suspect the following to be true and well known. I am looking for a reference. About the notations: $d$ is the dimension, $S^{d-1}$ is the unit euclidean sphere in $\mathbb{R}^d$, $d(x,y)$ is the ...
2
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0answers
43 views

Reference request for the proof of the Brodskii–Milman fixed point theroem for isometries

Can any one help me to access the paper M.S Brodskii and D.P Milman, On the center of a convex set, Dokl. Akad. Nauk SSSR 59 (1948) 837–840 in Russian? or to prove the theorem If $K$ is a ...
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0answers
32 views

recommend me some texts on the history of the non-western mathematics

I would like to self study the detailed history of the non-western mathematics. I have started the literature of Barton (7th Ed.) but it primarily concentrated on Western and American Mathematics. ...
1
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1answer
40 views

How many points does it take to identify a low-order polynomial in $\mathbb{Z}_N$?

I want to split the Bush's Baked Beans recipe into $M$ parts so that any set of $N<M$ people can reconstruct the recipe, but with the following constraints: Each person knows only a yes or no ...
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0answers
10 views

When the sum of coefficients of two linear combinations are equal.

I recently was looking a set of polynomials (the Legendre polynomials up to degree $n$) that form a basis for the space of polynomials $\{a_{0} + a_{1}x + \dots + a_{n}x^{n}: a_{i} \in \mathbb{R}\}$ ...
5
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1answer
205 views

A question about a mathematical analysis book

I am a newcomer to Analysis. All knowledge I know about "Analysis" are differentials,limit and integration (basically, what we have been taught in high school) I am studying Principles of ...
1
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3answers
82 views

Defining finite unions of intervals with algebraic endpoints on the reals

I'm currently working a bit on Enderton's logic textbook (2nd ed), and, on the second chapter, he marks the following exercise on definability with an asterisk. Let $(\mathbb{R}; +, \cdot)$ be the ...
4
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1answer
23 views

BMO functions are $L^p$ Loc for all $1<p<\infty$

In order to motivate my question, I'd like to remember that if $\Omega$ is a bounded domain and $f \in L^q(\Omega)$ for some $q>1$, by Hölder inequality $f \in L^p(\Omega)$ for $p \in (1,q]$ with ...
4
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2answers
204 views

Curiosity about a simple identity

Consider the well known formula $$1^3 + 2^3 +\cdots+ n^3 = (1+\cdots+n)^2 , n \in N$$ Now suppose that for all $n \in N$ the identity is true : $$1^k + 2^k +\cdots+ n^k = (1+\cdots+n)^{k-1} $$ ...
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0answers
27 views

A generalization of Clausen's formula

Clausen's formula, $${}_{2}F_{1}(a, b; c; x)^2 = {}_{3}F_{2}(2a, 2b, a + b; 2a + 2b, c; x), \quad c = a + b + \frac{1}{2},$$ is well known. Does anyone know if this formula has been generalized for an ...
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2answers
63 views

Books/subjects for proof practice

So I want to practice writing proofs. I've studied general proof-writing but now I want to learn how to apply that to mathematics. From what I understand, the best and most accessible subjects for ...
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0answers
70 views

Any Computational Number Theory Book, include software programs for key steps of the proofs of major theorem?

All: Can anyone recommend some Computational Number Theory Books, which include software programs for key steps of the proofs of major theorem ? Some computational number theory books only include ...