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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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
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1answer
55 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 ...
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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 ...
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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
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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 ...
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0answers
47 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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
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0answers
36 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 ...
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0answers
24 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" ...
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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.
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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". ...
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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 ...
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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
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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 ...
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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
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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
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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
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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.
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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 $n$ ...
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1answer
27 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 ...
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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
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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 ...
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35 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 ...
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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
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0answers
29 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 ...
0
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1answer
40 views

Jordan Canonical Forms: Different Approaches

Let $\dim(V)=n$ over the field $\mathbb{C}$. The Jordon canonical form of a linear transformation $T\colon V\rightarrow V$ can be obtained in the following way. 1) Let ...
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0answers
13 views

About inverse system definition

In the definition of an inverse system in the category of groups some authors ask for the index set to be a partially ordered set, others a directed set (and others both conditions). I am dealing ...
0
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1answer
50 views

What are some examples of unconventional fields?

We started talking about fields in my foundations of mathematics class, and since the symbols we are using are + and •, I keep catching myself giving them properties of multiplication and addition. ...
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0answers
48 views

Fact on Iwasawa module

The following fact falls under the category of Iwasawa modules. Let $M$ be a torsion free finitely generated module over the non commutative noetherian ring $\Bbb{Z}_p[[G]]$, (where $G$ is a p ...
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2answers
130 views

An analogous definition of Fourier transform $\hat f(u) = \int_{-\infty}^{+\infty} f(t) \exp(- i u t) dt$ for sinc-function.

We know the definition of Fourier transform $$\hat f(u) = \int_{-\infty}^{+\infty} f(t) \exp(- i u t) dt \ \ \ (*)$$ It is widely used in the analysis in the frequency of dynamical systems, in the ...
0
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1answer
18 views

Smallest integer $N(\epsilon)$ such that $K\subset \bigcup_{n=1}^{N(\epsilon)}B(x_i,\epsilon)$

In a metric space, a set $K$ is said to be totally bounded if for each $\epsilon>0$ there exist a finite number of balls $B_1,B_2\dots B_{N(\epsilon)}$ with radius $\epsilon$ which covers $K$. ...
1
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1answer
43 views

Lower bound on convexity radius in terms of injectivity radius (without using curvature)

Let $M$ 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 $p$ ...
3
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5answers
81 views

Can anyone suggest a book on Fourier Analysis containing many good problems

I am taking a basic course in Fourier Analysis in my undergrad Analysis class and I know the theory and related theorems. However, this is a relatively new zone for me and I would like a book that ...
2
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1answer
46 views

Does the Riemann tensor encode all information about the second derivatives of the metric?

In answer to this question I suggested the following as a motivation for the definition of the Riemann tensor: Let two $\mathcal M$ and $\mathcal N$ be two dim-$n$ Lorentzian manifolds with ...
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0answers
26 views

Angle condition for $a^2+c^2=nb^2$

Find a necessary and sufficient angle condition (independent of $a,b,c$ -- see under "what I have got so far" for examples) such that $a^2+c^2=nb^2$ where $n$ is a positive integer. Note: As usual ...
1
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1answer
59 views

Analogue of splitting field in several variables

Let $k$ be a field, and $P \in k[X]$. Consider the extensions $k \subset L \subset K$, where $L$ is a splitting field for $P$ over $k$ and $K$ is the algebraic closure of $k$. Then (by definition) all ...
3
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2answers
66 views

In triangle $ABC$, $a^2+c^2=3b^2$

In triangle $ABC$, we have $a=BC$, $b=CA$ and $c=AB$ as usual. What is a necessary and sufficient condition for $a^2+c^2=3b^2$ to hold? I created this problem as a generalization of $a^2+c^2=2b^2$ ...
3
votes
1answer
44 views

Triangle geometry: $BC^2+AC^2=n\cdot AB^2$.

I am looking for information regarding which triangles $ABC$ satisfy $BC^2+AC^2=n\cdot AB^2$ for $n=1,2,3,...$. I'm sure that work has already been done in this area since it is a fairly simple ...
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0answers
19 views

Manifolds from a “fiber bundle” viewpoint

I am starting to study fiber bundles and its relations with field theories in physics, and I would like to know some books in manifolds/differential geometry that are oriented for a complete study in ...
0
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1answer
22 views

Consequence of linear combination in matrix .

If a column of a matrix is linear combination of another column, what are the consequences ? Several terminology coming into my mind to relate with this such as Rank of the matrix ; Determinant ...
0
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0answers
20 views

Precalculus book recommendation (list provided)

Looking for a precalc book to brush up my knowledge before I start calculus. I know a bit about functions, trig identities/equations etc, but just a few bits here and there and would like a ...
2
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1answer
59 views

Chain rule in several complex variables: Wirtinger derivatives

Let $\Omega,\Omega'\subseteq\Bbb C^n$ open, $F:\Omega\to\Omega'$ holomorphic invertible function; it's a variable change, so let's call $F(z)=\tilde z$. Let $r:\Omega\to\Bbb R$ twice differentiable, ...
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0answers
14 views

Mathematical foundations of formal semantics in linguistic

I am looking for information on the mathematical foundations of formal semantics in linguistic. After some time, I found this book (Mathematical methods in linguistics / by Barbara H. Partee, Alice ...
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1answer
24 views

Rigorous pre-calc book with answers

I'm looking for a rigorous pre-calculus book so I can start learning Calc and beyond. I have taken some precalc topic, but have a 40%ish comprehension rate. I've done a few bits on limits, continuity, ...
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0answers
106 views

Topology and Planetary Nebulae

I apologize ahead of time if this receives any down-votes, but I was just reading a text on topology when the idea struck me: has any mathematician or, for that matter, any topologist, analyzed the ...
1
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1answer
52 views

Definition of a smooth complete integral pointed algebraic curve

Can anybody give me a reference to understand the definition of "a smooth complete integral pointed algebraic curve"? I'm beginning to study the paper "upper bounds for the dimension of moduli spaces ...