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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Can't parse a statement in an article on coalgebras and umbral calculus

I am reading Nigel Ray's "Universal Constructions in Umbral Calculus" (1998, published in "Mathematical Essays in Honor of Gian-Carlo Rota", page 344). The article reads: We ...
Daigaku no Baku's user avatar
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Mathematical references for gauge theory in condensed matter physics

I am currently trying to go through some literature on the classification of symmetry protected topological phases. One shortcoming in my background is that I am unable to understand the physics-...
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Stronger version of proposition 1.1.8 in "Model theory" by Marker

In proposition 1.1.8 of "Model Theory: An Introduction" David Marker proves that: If $\cal M$ is an $\cal L$-substructure of $\cal N$, $\bar a \in M$, and $\phi(\bar v)$ is a quantifier-...
Eduardo Magalhães's user avatar
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1 answer
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How to express rotation direction mathematically?

In This question I tried to solve this problem Show that as $z$ traverses a small circle in the complex plane in the positive (counterclockwise) direction, the corresponding point $P$ on the sphere ...
pie's user avatar
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Questions on sequences and modular forms

Let me apologize ahead of time since I am not at all well versed in the theory of modular forms. I have seen some nice examples where modular forms are used to study certain interesting numbers. For ...
matt stokes's user avatar
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Background for Gross-Zagier paper

I have been reading the paper "Heegner points and derivatives of $L$-series" by Gross and Zagier. Link to the paper. In section III of the paper, they use intersection theory to express a ...
Joseph Harrison's user avatar
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1 answer
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Tubular neighborhood of compact set

Let $X \subset \mathbb{R}^n$ be a compact, connected non-empty subset. Does there exist an analogue to a tubular neighborhood for $X$, i.e. something like a smooth manifold with boundary that retracts ...
The_Rookie's user avatar
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Finding a subgroup of some order

Apart from a brute force search, is there any algorithm to find a subgroup of some order $k$ of a finite group or say if there is none ?
user221985's user avatar
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How does Fleming's Functions of Several Variables compare to other texts?

How does the book Functions of Several Variables by Wendell Fleming compare to texts like Spivak Calculus on Manifolds, Munkres Analysis on Manifolds, C.H Edwards Advanced Calculus of Several ...
user926356's user avatar
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3 votes
2 answers
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Existence of a kind of balanced tournament schedule

Recently I was confronted with another tournament design problem: Suppose we have a tournament with $2n$ teams ($n\in \mathbb{N}$). We have $n$ different types of games (say at $n$ distinct locations),...
5th decile's user avatar
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Bound on the amount of probability mass 'seen' from a sample.

I was thinking of the following puzzle out of the blue and I would like to know if it has already been studied (I would assume so due to the simplicity of the setup). Imagine you have some unknown ...
SammyH's user avatar
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1 answer
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"Subset" List Coloring for Graphs

I am interested in the following problem for research: we are given a graph $G$ and two integers $N, d$ with $N \ge d$. Say that $G$ is "$(N,d)$-subset-list colorable" if each vertex $v$ is ...
Ryan Dougherty's user avatar
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is there a set of great circles on a hypersphere analogous to Buckminster Fuller's 31 in 3 dimensions?

I am addressing points on a sphere using great circles, and am investigating using Buckminster Fuller's "31 great circles." I am considering the viability of doing the same on a 3-sphere (in ...
Travis Well's user avatar
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56 views

Bounding the average slope of a convex function by an average of the slopes.

For a convex function $f$, I am interested in bounds of the form $$\frac{f(y)-f(x)}{y-x}\geq (1-\lambda)f'(y)+\lambda f'(x),\quad x<y.$$ For $\lambda=1$, this becomes true of any convex function $f$...
Not Euler's user avatar
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Reference for the lemma in Nakagawa's article

In K.Nakagawa's article "On the orders of automorphisms of a closed Riemann surface" there is Lemma 3, that doesn't have any proof or reference. Specifically, let $S$ be a closed Riemann ...
NicStr's user avatar
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Can you recommend a good textbook for Algebraic geometry for a beginner?

I want to learn Algebraic geometry. My main focus will be on Varieties. Can you recommend a good textbook for Algebraic geometry for a beginner?
jasmine's user avatar
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Software for finding a closed formula from a list of triples of positive integers

Suppose we have a finite list of $n$ triples of positive integer numbers, as: $$ \mathcal{L}=\{(a_{i1},a_{i2},a_{i3}):a_{ij}\in \mathbf{N}\setminus\{0\}, \text{ for } j=1,2,3\}_{i=1,\dots,n}.\ $$ Is ...
Hola's user avatar
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How can I fix my understanding of Numerical Analysis?

I am an undergraduate student taking Numerical Analysis. I’m having a hard time understanding some of the material because it feels as though my instructor is jumping all over the place. When it comes ...
Dr. J's user avatar
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Differentiability and continuity of the value function of optimal stopping problem

This question arise from Lemma 4.14 of Kwon, H. D., & Palczewski, J. (2022). Exit game with private information. arXiv preprint arXiv:2210.01610. Let us consider the following optimal stopping ...
Probvis's user avatar
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2 votes
0 answers
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Optimal Stopping Problem as an $L^p$ function?

This might be a fairly silly question, but here it goes. I'm initiating my study of optimal stopping problems (OSP), and I was wondering if an OSP can be seen as a function in some $L^p$ space. ...
Oscar's user avatar
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3 votes
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Some questions on derived pull-back and push-forward functors of proper birational morphism of Noetherian quasi-separated schemes

Let $f: X \to Y$ be a proper birational morphism of Noetherian quasi-separated schemes. We have the derived pull-back $Lf^*: D(QCoh(Y))\to D(QCoh(X))$ (https://stacks.math.columbia.edu/tag/06YI) and ...
strat's user avatar
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0 answers
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Tensor product of $n$ modules with minimal assumptions

Let $R_1,\ldots, R_n$ be (commutative) rings, and $M_1 , \ldots, M_n$ be modules. What are the minimal assumpsions about the rings and modules needed in order to define a tensor product $M_1 \otimes_{...
Robert's user avatar
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Linear algebra text that covers Hamming codes

I'm teaching linear algebra next year and need to choose a text. It's an introductory course, with mostly sophomores. Many years ago, I taught such a course from a text that I remember liking a lot, ...
Barry Smith's user avatar
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3 votes
0 answers
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Fermat's (hypothetical) erroneous proof

Until Wiles' proof of Fermat's last theorem all proposed proofs have been erroneous. It is not known which proof Fermat himself had in mind - but it is assumed that it was erroneous, too. Have there ...
Hans-Peter Stricker's user avatar
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Does there exist a hadamard style transform over bits of digital numbers? Perhaps possible to be interpreted as $\mathbb Z^2$?

The Hadamard transform is well known in the information theory and signal processing communities and can be viewed in some sense as a discrete step version of the Discrete Fourier Transform. There ...
mathreadler's user avatar
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Looking for Solution to < An Introduction to the Theory of Point Processes> [closed]

I am currently reading the textbook < An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods, Second Edition >. May I ask if someone knows where I can find the ...
Qinling Wang's user avatar
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0 answers
58 views

Give algorithm for finding bidiagonal matrix similar to triangular matrix

Is there an algorithm that takes an upper triangular matrix $T$ over the complex numbers as input, and outputs a bidiagonal matrix $B$ which $T$ is similar to? We may assume that $T$ is invertible. ...
wlad's user avatar
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Modeling and Predicting Squirrel Territory [closed]

I am interested in modeling the growth of the Eastern Fox squirrel population in Los Angeles, not only in terms of numbers but also in overall territory. The site iNaturalist has a wonderful database ...
JoanGi's user avatar
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2 votes
2 answers
248 views

Overview of basic results in Stochastic Calculus

Are there some good overviews of basic facts about Stochastic Integrals and Stochastic Calculus? These can be in the form of resources (preferably accessible online) as well as directly writing out ...
FD_bfa's user avatar
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1 vote
0 answers
24 views

Quadrature of a random function

I would like to numerically compute the following integral $$ \int_a^b f(x) p(x) \mathrm{d} x $$ for some known smooth function $f(x)$ and unknown smooth function $p(x)$. I can estimate $p(x)$ by ...
Radost's user avatar
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0 votes
0 answers
25 views

Reference Request Separation of variables for PDEs

I was wondering if anyone knew good references for exercises, examples, theory for Separation of Variables for various PDE. Shearer and Levy has a chapter on it (chapter 6) but there are only a few ...
Math_Day's user avatar
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2 votes
1 answer
112 views

Ramanujan-Type Double Sum Infinite Series for $1/\pi$

$$\sum_{n,m=0}^{\infty}\binom{2n}{n}\binom{2m}{m}\binom{2n+2m}{n+m}^3\left(\frac{1+6n+6m}{2^{10n+10m}}\right)=\frac{4}{\pi}$$ These are Ramanujan-Type Series for $1/\pi$ but based on a Double Sum ...
Miracle Invoker's user avatar
3 votes
0 answers
167 views

Gradient estimates of linear elliptic PDE

Let $\Omega \subset \mathbb{R}^n$ be a bounded smooth domain. Assume that $u(x)$ is the classical solution solving $$a_{ij}(x)\partial_{ij}u(x)+b_i(x)\partial_iu(x)+c(x)u(x)=f(x)$$ $$u(x)\Big|_{\...
mnmn1993's user avatar
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2 votes
0 answers
38 views

Mathieu Functions References

I came across the Mathieu functions when solving a PDE with Mathematica. My solution was of the form $f=C_1Mat_C + C_2 Mat_S$ AFAIK those are the non periodical Mathieu functions, which are different ...
LolloBoldo's user avatar
0 votes
2 answers
53 views

Reference for: Every element of a finite field is the sum of two squares.

Note: This is a reference-request question. It doesn't require the usual level of context. I am not asking for a proof. It is well known that Theorem: Let $x\in F$ for a finite field $F$. Then there ...
Shaun's user avatar
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1 vote
0 answers
42 views

Chirality and Colored Jones Polynomial

It is well understood that the usual Jones polynomial of a knot or link can be related to the Jones polynomial of the mirror image of the knot/link by changing the variable $V_L(t) \to V_L(t^{-1})$. ...
hopftype's user avatar
1 vote
0 answers
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Books on co-Heyting algebras (with a view to their logics).

I would like to know more about co-Heyting algebras, particularly from the perspective of their logics (like paraconsistent logics). What books are available out there on the topic? It might be that ...
Shaun's user avatar
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3 votes
1 answer
93 views

Minimal elements under division in a ring

Let $p$ be an element of a commutative ring with unity. The following definition is natural: $p$ is minimal under division if its only divisors (up to equivalence) are $1$ and itself. That is, for ...
Caleb Stanford's user avatar
0 votes
1 answer
64 views

About the two step centralizer

Let $G$ be a finite group. Define $\gamma_2(G)=[G,G]$ and $\gamma_{i+1}(G)=[\gamma_i(G),G]$ for all $i≥2$. Let $G$ be a finite $p$-group of order $p^n$ and maximal class. For each $i$ with $2≤i≤n−2$, ...
Fouad El's user avatar
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1 vote
0 answers
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Reference request for a subfamily of regular graphs

I'm looking for literature on the following "nice" family of graphs: Call a regular graph $G=(V,E)$ (of regularity degree $d$) nice if there exists a coloring $C:V\to \{ 1,\dots,d \}$ such ...
jojo's user avatar
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-4 votes
1 answer
35 views

Which distribution is most similar to a Gaussian but with $[0,\infty)$ support?

Which distribution $p$ is most similar to a Gaussian but with $[0,\infty)$ support (i.e., $p(0)=0$)?
Geremia's user avatar
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1 vote
0 answers
43 views

Techniques to Place a Lower Bound on the Real Zeros of a Polynomial

I am working with a family of polynomials with some particularly nasty coefficients. Unfortunately, I cannot give very many details as to what these polynomials look like, but, suffice it to say that ...
peabody's user avatar
  • 590
0 votes
1 answer
47 views

Minimal set of condition for the Feynmann-Kac formula to hold

The Feynmann Kac formula tell us that the solution of the PDE $$ \frac{\partial u}{\partial t}(x,t) + \mu(x,t) \frac{\partial u}{\partial x}(x,t) + \tfrac{1}{2} \sigma^2(x,t) \frac{\partial^2 u}{\...
Marco's user avatar
  • 1,900
7 votes
1 answer
132 views

Trace Class Operators On Manifolds With Boundary

Let $X$ be an $n$-dimensional manifold with nonempty boundary $\partial X$ and $n\geq 2$. Proposition 4.1 of this paper by Schrohe states that it is "not very difficult" to show: Proposition:...
RSpeciel's user avatar
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0 votes
1 answer
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Prove that $\sum_{d=1}^{n} M(\lfloor n/d \rfloor) = 1$

In Wikipedia entry for Mertens function it says that From [Lehman, R.S. (1960). "On Liouville's Function". Math. Comput. 14: 311–320.] we have that $$\sum_{d=1}^{n} M(\lfloor n/d \rfloor) = ...
Juan Moreno's user avatar
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-1 votes
0 answers
85 views

What book do you recommend for set theory? [duplicate]

This will be my first course on set theory, and I would like to buy a book that will help me at this beginning and also for a more advanced course on set theory
Jerson's user avatar
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0 answers
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What are some good learning materials for Affine Algebras

I am looking for resources - courses or books - that graduate students can take to learn Affine Algebras, preferably along with their generalizations and applications to physics. This post is inspired ...
Mahammad Yusifov's user avatar
2 votes
1 answer
52 views

Term for a product of groups that is neither direct, nor semi-direct, but generalises semi-direct ones

Suppose $H$ and $K$ are subgroups of a group $G$ such that every element $g\in G$ can be uniquely written as $g = hk$ with $h\in H$ and $k\in K$. (It follows then that every element $g\in G$ can also ...
Alexey's user avatar
  • 2,106
2 votes
0 answers
49 views

Universal Turing Machines with Simple Encodings of Their Tape.

I am seeking a small $2$-symbol Universal Turing machine $U$ such that if $T$ is a Turing machine written to the tape of $U$ somehow, and I wish for $U$ to simulate $T$ with its tape initialized to $n$...
Matthew Bolan's user avatar
2 votes
0 answers
34 views

Reference Request: Visual Approach to Symmetric Groups

The symmetric group is a factor of the braid group (see e.g. Surjective Group Homomorphism From Braid Group Into Symmetric Group, Symmetric group, Braid Groups, and related groups). Consequently one ...
Alp Uzman's user avatar
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