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Questions tagged [reference-request]

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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References regarding Green's function on a square domain in 2D

I'm trying to obtain the Green's function on a square domain, i.e, I'm trying to solve the following BVP: \begin{cases} \Delta G(\bar x,\bar y) = \delta^2(\bar x - \bar y),& \bar x, \bar y\...
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Reference request: applications of topological quantum field theory to continuous-time dynamical systems.

From wikipedia: In dynamics, all continuous time dynamical systems, with and without noise, are Witten-type TQFTs and the phenomenon of the spontaneous breakdown of the corresponding topological ...
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1answer
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Expression of the dirichlet coefficient of an L-series in terms of the Satake parameters

Last year, I had found a pdf where the expression of the Dirichlet coefficient $\lambda_{\pi}(p^{\nu})$ in terms of the Satake parameters $\alpha_{p,i}(\pi)$ was given. Unfortunately I don't remember ...
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$s$-convexity implies $p$-convexity in Banach lattices

If $1<p<s<\infty$ and $E$ is a Banach lattice which is $s$-convex, is it also $p$-convex? If so, what would be a good reference for this?
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Parametric representation of the real branches $\operatorname{W_{0}},\operatorname{W_{-1}}$ of the Lambert W function

$\require{begingroup} \begingroup$ $\def\a{\alpha}\def\la{\ln{\a}}\def\e{\mathrm{e}}\def\W{\operatorname{W}}$ $\def\Wp{\operatorname{W_0}}\def\Wm{\operatorname{W_{-1}}}$ For $x\in(-\tfrac1{\mathrm{e}...
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LASSO's (or BPDN) parameter tuning

We have to solve the following problem : $$\min_x \|x\|_1 \text{ s.t. } \|Ax-y\| \le \sigma,$$ with $\sigma$ some positive real number, $A$ a complex rectangular matrix and $x,y$ complex vectors. ...
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47 views

Is there a reasonable one hour summary of Game Theory?

In his Topology and Geometry course on Youtube (http://www.youtube.com/watch?v=QzfZS3iopR0&t=10m7s), Tadashi Tokieda claims he can teach all of game theory in an hour. He seemed very sincere and ...
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Beach-ball like differential operators of a two-dimensional function

I'm looking for references, known names of, and other useful pointers and insight about (pairs of) differential operators that are "beach-ball like" because they sample a 2-dimensional function in ...
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Reference request for convergence question in probability and statistics

Recently I have asked question here on math.se Regression covergence No one answered it so I decided to try to solve it on my own, however I don't know where to start. I had undergraduate courses in ...
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1answer
28 views

It would be possible to define an uniform distribution on $\Bbb N$ using infinitesimals?

In standard analysis it is clear that it is impossible to define an uniform probability distribution on $\Bbb N$ because there is no constant $c\in\Bbb R$ such that $\sum_{k=1}^\infty c=1$. Using ...
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Reference request: Density of testfunctions in sobolev space $ W^{1}_{0}$

can someone help me out and name a good source where the following statement ist proven? $C^\infty_0(\Omega)$ is dense in $W^{1,p}_0(\Omega)$ with $\Omega \subset \mathbb{R}^n$ being an open, bounded ...
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1answer
27 views

Reference for homology of real projective space in a field.

I need a reference in a book for the computation of the homology of real projective space with coefficients in an arbitrary field. I do know how to do the computation, and I also found an online ...
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1answer
59 views

Categorical general topology — reference request

I am looking for literature describing general topology in terms of category theory. I would prefer literature which does not assume too much familiarity with category theory, but would appreciate any ...
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1answer
51 views
+100

Propagation of regularity for the heat equation

Let $\Omega$ be an open bounded subset of $\mathbb R^N$. Let $u_0 \in L^\infty(\Omega)$ and $f \in L^\infty((0,T)\times\Omega)$ and consider the following boundary value problem for the heat equation:...
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On the preimage of injective holomorphic map

I am hoping the following is true. Mention of related ideas/topics are appreciated. Suppose $F:\mathbb{C}^n \to \mathbb{C}^n$ is a injective holomorphic mapping such that $F(0)=0$ and $dF(0) = I_n$ ...
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References on Kähler Differentials

I'm working on an independent study project on Kähler differentials for my commutative algebra class. I'm looking for any references on these that might help me out. Any references to their use in ...
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2answers
25 views

Polytopes with equal facets

My question is very simple though I was not able to find any related information. Is it true that if a convex polytope has combinatorially isomorphic facets then it is combinatorially isomorphic to ...
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1answer
33 views

Values of some “natural” sums over multiindices with a given absolut value

I'd like to know if there is a nice closed expression in terms of $j$ and $k$ of the sum $$ S_{j,k}:=\sum_{(i_1,\ldots,i_k)\in \mathbb{N}^k_0:\\i_1+\cdots+i_k=j}\frac{1}{i_1!\cdots i_k!}. $$ ...
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1answer
48 views

Tips for a dum-dum : Introduction to Analysis 1 and 2

First off let me say that math and I don’t get along. I want to be it’s friend, but it certainly doesn’t want to be mine. I have been out of high school for some time (decades) and recently returned ...
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Reference for elementary substructures of the standard model of analysis

Is there was any resource discussing or categorizing elementary substructures of the intended model of analysis? Analysis in this context is also known as second-order arithmetic. They will of course ...
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Answer sheet of Probability by Shiryaev, Albert N.

Do any of you have answer sheet for the questions of book "Probability" by Shiryaev ? I actually bought Probability-1 one of his newest books and questions seem similar to his older book Probability. ...
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Require guidance to proceed further in learning statistics

In my undergraduate course I learnt introductory level statistics and I really enjoyed it. With that background I decided to follow predictive analysis further and decided to take up this book . But I ...
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0answers
14 views

Reading material for Kähler geometry

I'd like to read and understand this paper on Kähler geometry. The most advanced math I've done is a read through Rudin's Principles of Mathematical Analysis which teaches analysis up to differential ...
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I need resources for elementary Number Theory, Theory of Equations (For KVPY exam), (details in post) [closed]

So I am currently starting 11th grade (in India). There's this KVPY scholarship exam that I am preparing for, and it needs pretty advanced concepts, like number theory (congruence modulo), theory of ...
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1answer
22 views

The derivative of the Delta function times another function

Good evening! I can't understand how to prove that $$\alpha(x)\delta'(x)=-\alpha'(0)\delta(x)+\alpha(0)\delta'(x).$$ I tried to use $$(Df,\phi)=-(f, D\phi),$$ also I used that $$(D(hf),\phi)=(h'f+hf',\...
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0answers
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Proof that the merit of a prime gap can become arbitary large?

If $p_n$ denotes the $n$-th prime number, we can define $$g_n:=p_{n+1}-p_n$$ as the gap after the $n$-th prime number. The merit of a prime gap is defined as $$m(p_n):=\frac{g_n}{\ln(p_n)}$$ It is ...
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0answers
19 views

If the frontier is a union of the orbits of a autonomous ODE then the set is invariant

I'm looking for a proof or reference proving this theorem which was written in my ODE class: Let $D \subseteq \mathbb{R}^d$ be open and $f:D \to \mathbb{R}^d$ continuous such that each IVP has a ...
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0answers
29 views

Exhibition where children were playing Tic Tac Toe against their parents

I recall that there was an exhibition, in some place in the US I believe, where children could play tic tac toe against their parents. The catch was the following: both were sitting in front of a ...
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0answers
76 views

Classifying the chains of orderable sets' power sets up to isomorphism

Recently, while trying to understand another result, I began to wonder about the following question: Given some orderable set $A,$ what (if anything) can we conclude about the order type or ...
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0answers
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reference on min/max rules

I am looking for some references to the basic algebra involving $\max()$ and $\min()$ functions. e.g: $$\max(x,y) = -\min(-x,-y)$$ $$\max(x-a,0)-\max(y-b,0) \le \max(x-y - (a-b), 0)$$ and the like....
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1answer
28 views

References on the Hugoniot locus of hyperbolic systems

I would like to get a good reference to study Hugoniot Locus in conservation laws, maybe videos or PDF's. Many thanks.
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0answers
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Reference Request: Proof of $\mathrm{H}(\mathrm{Prim}\,\mathcal{H}) \cong \mathrm{Prim}\,\mathrm{H}(\mathcal{H})$ for cocommutative dg-Hopf algebras

In Loday’s book Cyclic Homology the following theorem appears: A.9 Theorem. On a cocommutative differential graded Hopf algebra $\mathcal{H}$ over a characteristic zero field $k$ the homology and ...
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What are some of the best textbooks on multi-objective optimization?

I am looking for textbooks on non-linear multi-objective optimization that are rigorous. For instance, I am most comfortable with Arkadi Nemirovski style. I am looking for a book on nonlinear multi-...
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1answer
77 views

Difference between several books on complex geometry

I would like to learn some complex geometry, especially the interaction between algebraic geometry and complex geometry. I found that there are several famous books: Huybrechts, Complex Geometry; ...
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0answers
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A surprisingly simple smooth function, is it used as a sigmoid?

Consider the function $$f(x) = \frac{x}{1+|x|}$$ For what we can prove about it's derivative, it exists everywhere, is maximal at $x=0$ ($f'(0)=1$) and we can verify $$\forall x\in \mathbb R : f(x)\...
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Non-English papers in MathSciNet [closed]

Is there any way to find all papers in a specific language (for example German) in MathSciNet?
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0answers
25 views

Reference request on Combinatorics and set theory

I am thinking about teaching an introductory class in Combinatorics and Set Theory. My view on this is that much of the introductory part in combinatorics can be seen as finite set theory. The issue ...
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2answers
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Reference for some R.T. Curtis articles and thesis

I'm reading R.T. Curtis "Symmetric generation of groups", since interested in yet another way of seeing M12 and M24 construction. Actually this book refers to many seminal articles by the same author, ...
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Paper of Jacques Azéma [closed]

I am currently looking for J. Azéma's works translated in English such as Quelques applications de la théorie générale des processus I. Kindly leave a link if you have one. Thank you! P.S. I do not ...
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0answers
28 views

What is the largest composite fully factored repunit-number?

Here http://www.factordb.com/index.php?id=1100000000047111502 a huge number of the form $1.....1$ ($\ \frac{10^n-1}{9}\ $) is shown that is composite and fully factored (apart from the huge prime "...
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Combining rational interpolation and trigonometric interpolation?

My teacher mentioned that he never saw an article working out a theory of rational interpolation combined with trigonometric interpolation. (E. g. by using trigonometric polynomials instead of ...
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0answers
23 views

Cylindrical coordinates: history [closed]

Cylindrical coordinates $x=r \cos \theta$, $y=r\sin\theta$, $z=w$ seem to be a simple generalization of polar coordinates. When did they appear first? Also, who came up with the name?
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1answer
103 views

“Conditional distribution” of Brownian sample paths

I would like to consider the "conditional distribution" of the Brownian sample paths conditional on certain sample path functionals, in a similar way that one considers the Brownian bridge. For ...
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0answers
31 views

The origin of the term “Frobenius norm”

How did the name Frobenius get attached to "Frobenius norm" of a matrix? I could not find any work of his that uses the norm.
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1answer
897 views

Strange acknowledgment in Serge Lang's Linear Algebra

Recently I open this book to look up a certain theorem and saw something peculiar about the acknowledgments I've never notice before: Acknowledgments I thank Ron Infante and Peter Pappas for ...
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0answers
38 views

Have the reversed Smarandache numbers be checked already?

A Smarandache number emerges by concatenating the first $n$ positive integers in increasing order in base $\ 10\ $. The Smarandache numbers (See http://mathworld.wolfram.com/SmarandacheNumber.html) ...
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27 views

Proof of the Existence of Bayesian Nash Equilibria

I found the following two Theorems when studying games with incomplete information. "Consider a finite incomplete information (Bayesian) game. Then a mixed strategy Bayesian Nash equilibrium exists." ...
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1answer
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Does the limit of this sequence of operators have infinitely many eigenvalues?

Suppose that I have a sequence of compact, injective operators $\{T_\delta\}_{\delta>0}$ on a Hilbert space $H$ such that each operator $T_\delta$ has infinitely many eigenvalues. My question is ...
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1answer
45 views

Fibonacci numbers as weighted averages of powers of 5 — a bijective/combinatorial proof?

A straightforward use of the binomial formula shows that the nonrecursive formula for the Fibonacci numbers, $$ F_n=\frac{1}{\sqrt{5}}\left(\left(\frac{1+\sqrt{5}}{2}\right)^n-\left(\frac{1-\sqrt{5}}{...
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35 views

Smooth function zero at origin is x times smooth function

What’s the name (or reference) for the real-analytic lemma A $\mathrm C^\infty$ function $f:\mathbf R\to\mathbf R$ with $f(0) = 0$ is $f(x) = xg(x)$ with $g$ also $\mathrm C^\infty\,$ and the ...