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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5 views

Short-sighted modifications of queueing processes

I am looking for any general results related to the context below. Situation Consider a general queueing system $\mathscr{S}$, whose customer arrival times are independent, and whose service times ...
1
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0answers
12 views

English translation of Minkowski's Geometry of Numbers

Is there an English translation of Minkowski's Geometry of Numbers? I have searched it but have found nothing.
1
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0answers
25 views

What is the relation between the length of period of simple continued fraction expansion of quadratic algebraic numbers and the integer

As we know,$\sqrt{2} = [1;2,2,2,2,…]$; while $\sqrt{14}= [3;1,2,1,6,1,2,1,6…]$,let $L$ the length of period of simple continued fraction expansion of quadratic algebraic numbers be the number of ...
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3answers
39 views

Collected works of David Hilbert?

1) Is there a collected works of D. Hilbert? 2) If 1) is affirmative, is there an English translation of the collected works of D. Hilbert?
3
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0answers
20 views

probability that two randomly selected integers of an imaginary quadratic field of class number 1 are coprime

Given an imaginary quadratic field $\mathbb{Q}(\sqrt{-D})$, where $D$ is a Heegner number (1, 2, 3, 7, 11, 19, 43, 67, 163), what is the probability that two randomly selected elements of that fields' ...
3
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0answers
22 views

Reference for understanding coalgebra

I am trying to read this paper, but I have no knowledge of coalgebra and have just started to learn Category Theory so I am struggling to understand it. Are there any references that can explain ...
4
votes
2answers
92 views

An axiomatic treatment of hyperbolic trigonometry?

I would like to see results derived in hyperbolic trigonometry synthetically, i.e. just by working from axioms, for example the ones given by Hilbert (or even Tarski). Most authors seem to discuss ...
4
votes
1answer
184 views

Book on advanced topics of Network Flows

I am taking linear optimization class. Could you suggest me good fundamental textbook on advanced topics of network flows. To be more specific I am interested in: Multicommodity flow and multicut, the ...
2
votes
1answer
39 views

Reference for $F$-algebras and induction?

I've been learning about $F$-coalgebras and coinduction from this fantastic paper, which has really helped me get a feel with its many examples. I'm starting to struggle with reconciling the ...
5
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1answer
344 views

Krivine Machine

Can someone please point out online resources to learn about Krivine Machine? My professor briefly touched it while teaching a course in Computer logic. google did not turn up much except some papers ...
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2answers
298 views
+100

What is the Coxeter diagram for?

I understand that Coxeter diagrams are supposed to communicate something about the structure of symmetry groups of polyhedra, but I am baffled about what that something is, or why the Coxeter ...
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0answers
22 views

Solutions to problems in the ODE book by Gerald Teschl

I am self learning ODE by the book: Ordinary Differential Equations and Dynamical Systems by Gerald Teschl. Anyone knows where I can solutions to the problems given in this book? Thank you.
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5answers
261 views
+50

I need help finding a rigorous Pre-calculus textbook

I dislike modern textbooks; their cookie-cutter approach and appearance, over reliance on breaking things down into little boxes, the general spoon-feeding they engender and most of all the poor ...
2
votes
2answers
65 views

Which book is appropriate for a Chemistry student that needs to learn basics about integrals?

A friend of me who is not studying mathematics now needs to deal with integrals, double integrals and triple integrals within his study of chemistry. He asked me to give him a suggestion for a basic ...
6
votes
2answers
93 views

Push forward of the structure sheaf along covering

Let $f: X \to Y$ be a covering (proper, surjective, finite regular map) of smooth projective varieties of degree $d$. How one can show that in this case $f_* \mathcal{O}_X$ is a locally free sheaf of ...
0
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0answers
25 views

Updating the LU Factorization

I am looking for a way to update the $LU$ factorization of a general $m \times n$ matrix after adding a column to the matrix. I have to iterate this procedure so I will begin with a matrix that is $m ...
2
votes
0answers
17 views

Relations between Eisenstein series and hypergeometric series

It is known that $$E_4(\tau) = {}_{2}F_{1}\left(\frac{1}{12}, \frac{5}{12}; 1; \frac{1}{J(\tau)}\right)^4$$ and $$E_6(\tau) = {}_{2}F_{1}\left(\frac{1}{12}, \frac{7}{12}; 1; \frac{1}{1 - ...
2
votes
2answers
75 views
+100

Which statements are equivalent to the parallel postulate?

I would like to have a long-ish list of statements that are equivalent to the parallel postulate. If a line segment intersects two straight lines forming two interior angles on the same side that ...
0
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0answers
7 views

about a barrier argument involving p-harmonic functios

Consider the lemma 2.2 and lemma 2.3 of this paper : http://www.ams.org/journals/tran/2002-354-06/S0002-9947-02-02892-1/S0002-9947-02-02892-1.pdf Lemma2.2: Let $D $ a convex domain in $R^n$ and ...
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0answers
13 views

References to papers/books that uses a kernel to smooth a discrete distribution

Since a kernel, such as Gaussian, is often used to smooth out the distribution of discrete points in 1D, 2D or 3D, I believe there must be some study materials or research work that have used this, ...
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0answers
6 views

References to papers/books that uses a kernel to smooth a discrete distribution

Since a kernel, such as Gaussian, is often used to smooth out the distribution of discrete points in 1D, 2D or 3D, I believe there must be some study materials or research work that have used this, ...
7
votes
1answer
527 views

If I know the probability of something happening after n trials is X, how can I estimate the probability of it happening for each individual trial.

This is assuming each trial has an independent probability. In other words, lets say that I perform $50$ trials a $100$ times. I know that the event happened only in $5\%$ of those hundred $50$-trial ...
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0answers
17 views

3-Point Shoot using Quadratic Equation [on hold]

This is my assignment. The question is "In what part of the three-point line can a player do best the three-point shoot to gain 3 point but using quadratic equation." There are no data given but we ...
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0answers
31 views

Reference Request: Matrix of a composition(sum) of two operators is the Kronecker product (sum) of the matrices of each operator

Here is link to an example: http://en.wikipedia.org/wiki/Kronecker_sum_of_discrete_Laplacians, but it provides no references. Hoffman and Kunze(Linear Algebra) develop linear algebra with explicit ...
6
votes
1answer
685 views

Difference between Gilbert Strang's “Introduction to Linear Algebra” and his “Linear Algebra and Its Applications”?

Could someone please explain the difference between Gilbert Strang's "Introduction to Linear Algebra" and his "Linear Algebra and Its Applications"? Thank you.
1
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0answers
38 views

Absolute continuity and convolution

Suppose that $\mu$ is a finite Borel measure on the real line, $f, g\in L^1(\mu)$. Define $\nu=\mu\ast\mu$. Do I understand correctly that the convolution $f\mu\ast g\mu$ is absolutely continuous wrt ...
4
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2answers
84 views

How to prove that all smooth vector bundles on a given vector bundle are the pull back of a vector bundle on the base

Recently, during a conversation, I heard about the result (previously mentioned also here on MO), whose statement is reported below. Not having the specific background necessary to reconstruct a proof ...
0
votes
1answer
30 views

Main theorem of Pythagorean plane

The theorem states: Any Pythagorean plane is isomorphic to the Cartesian plane $F^2$ over its field $F$ of segments. Can anyone give me a reference for this theorem?
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0answers
14 views

Hölder continuity for parabolic equations

What is a good and modern reference for hölder regularity for non-degenerate parabolic equations? To be a bit more precise, I have a degenerate parabolic equation, exhibiting two degeneracies, and can ...
5
votes
2answers
205 views

Characterization of primary ideals in a principal ideal domain

On the commutative algebra wiki, a table of properties lists that "for a PID, the primary ideals coincide with the powers of prime ideals." I played around with it, couldn't produce a proof, ...
6
votes
2answers
489 views

Elementary proof of Zsigmondy's theorem

I've been writing a not-so-short introduction to elementary number theory, supplying proofs for all theorems. When coming across Zsigmondy's theorem, it seemed difficult to find a proof available on ...
0
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0answers
13 views

Geometric dual graph

It is well known the notion of geometric dual graph. Let $G^*$ be the geometric dual of a planar graph $G$. I need the proof that $(G^*)^* \cong G$ , where can I find it ?
2
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2answers
347 views

Expected state of a Markov chain

Let's start with a slightly trivial Markov chain defined as follows: the beginning state is called $1$ and the set of states is $\mathbb{N}$. At each step, when the current state is $n$, the ...
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0answers
34 views

Building a function $p : \mathcal{D} \rightarrow \mathbf{Ord}$ from a faithful functor $U : \mathcal{C} \rightarrow \mathcal{D}.$

For simplicity, I will ignore size issues in this question. Let $\mathcal{D}$ and $\mathcal{O}$ denote categories. By a function $\mathcal{D} \rightarrow \mathcal{O},$ let us mean a functor from the ...
5
votes
1answer
233 views

What is “Approximation Theory”?

What exactly is "Approximation Theory"? If I read the wikipedia-article I doesn't get much clearer. Why are "pure" mathematicians interested in it? I see a lot of people that do harmonic analysis also ...
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0answers
31 views

Are there any linkage or transformation between some period transcendental numbers and algebraic irrational numbers?

Are there any linkage or transformation by combination of integral and algebraic function like in the definition of period number between some period transcendental numbers and algebraic irrational ...
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0answers
16 views

Non-standard extensions of $p$-adic fields

Does there exist a non-standard extension of a non-Archimedean field (such as the construction $*\mathbb{R}$ out of $\mathbb{R}$ or the surreals $\mathbb{S}_\mathbb{R}$, not to mention their ...
1
vote
1answer
93 views

Miller's Construction, Partition Principle and Failure of Axiom of Choice

Partition Principle ($PP$) is the following statement: For all sets $a$, $b$ there is an injection $f:a\rightarrow b$ iff there is a surjection $g:b\rightarrow a$ It is known that $ZF\vdash ...
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0answers
57 views

Hypervolume of expanded $n$-simplex

The hypervolume of the expanded $n$-simplex with side $\sqrt{2}$ appears to be $$\displaystyle\frac{\sqrt{\;n+1\;}\;(2n)!}{n!^3}$$ Does anyone know of a published reference to this result? An ...
0
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0answers
82 views

Proof that $G(3)\le 7$

Let $G(k)$ be the minimal $n$ s.t. every sufficiently large integer is the sum of $n$ nonnegative $k$th powers. Does anybody know where I can find Vaughan's proof that $G(3)\le 7$? I can't find a ...
6
votes
1answer
303 views

Automata theory on infinite words: any video lectures?

I am fun of automata theory. Can you suggest good video lectures on the subject? (there is a good one here, but it is accessible from RWTH University only)
17
votes
4answers
694 views

Book ref. request: “…starting from a mathematically amorphous problem and combining ideas from sources to produce new mathematics…”

I couldn't find Charles Radin's Miles of Tiles at the local university library or the public library, and cannot afford its Amazon price right now. Thus, while sorely disappointed for the moment, I ...
2
votes
1answer
57 views

Math required for medical statistics

I have never been good with Math. I talk to many of my medical colleagues and it seems to me that most of them have a poor understanding of statistics. Many of them claim to understand it but actually ...
11
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3answers
705 views

History of notation: “!”

Does anyone know where the factorial "!" symbol came from? I can't decide if it is my favorite or least favorite notation in mathematics...
0
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0answers
24 views

Is logistic regression unbiased and efficient?

Seeing how in social sciences the Cramér-Rao lower bound is used as variances of the found parameters it would seem that the parameters are both unbiased and efficient, but what is the proof for this? ...
8
votes
3answers
120 views

The category of theorems and proofs

On a philosophy website, it said that you could have a category with theorems as objects and proofs as arrows. This sounds awesome, but I couldn't find anything on the web that has both "category" and ...
2
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0answers
28 views

Elliptic PDE on the Whole Space

Can anyone suggest a reference for elliptic PDE on the all of $\mathbb{R}^d$, as opposed to some bounded domain $\Omega$, covering the standard topics of existence, uniqueness, and regularity. I ...
2
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0answers
40 views

Entrance exam preparation suggestions.

I will be giving my Entrance Exam for (MS in Computer Science) and this is the Syllabus. Syllabus Screenshot : http://i.imgur.com/9KUDCt3.png I am worried about the maths and reasoning part. It's ...
1
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0answers
38 views

Hyperbolic vs Euclidean Brownian Motion

In this article, page 4 of the linked pdf file, Lalley and Sellke claim that a hyperbolic Brownian motion can be obtained by time-changing a 2-dimensional Euclidean Brownian motion, conditioned to ...
4
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0answers
37 views

What is known about the eigenvectors of random matrices?

Let $A$ be a real asymmetric $n \times n$ matrix with i.i.d. random, zero-mean elements. What results, if any, are there for the eigenvectors of $A$? In particular: How are the elements of the ...