Questions tagged [notation]

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Are measures better thought of as densities than differentials?

The standard notation for integrating with respect to a measure $\mu$ is: $$\int f(x)\,d\mu(x).$$ But I've wondered if it could be better written as: $$\int f(x)\mu(x)\,dx$$ where $\mu(x)$ is now ...
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39 views

About the Notation $\int |d\mu|$ [migrated]

I see the notation $\int |d\mu|$ lots of times and I could not find the definition of this notation. I can guess what it means, but I want to know the mathematically precise meaning. Thank you!
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23 views

Clarification of second order condition on orthogonal optimization

In the paper A Feasible Method for Optimization with Orthogonality Constraints, the arthors write: where I am confused about the notation $\mathcal{D}(\mathcal{D}\mathcal{F}(X))[Z]$. My ...
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3answers
734 views

Examples of improved notation that impacted your research?

The intention of this question is to find practical examples of improved mathematical notation that enabled actual progress in someone's research work. I am aware that there is a related post ...
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1answer
246 views

Need help in understanding meaning of a notation and theorem used in research paper due to a reference being in German Language

I thought of utilizing this lockdown period to study research papers in number theory by myself. I began reading the research paper By T Estermann ->" On Goldbach Problem : Proof that Almost all ...
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1answer
220 views

Why are orthogonal matrices so often denoted $Q$?

I apologize for the stupid question in the title. Of course, we can baptize a particular given matrix as we want but, for example, the QR-decomposition has a fixed meaning. My humble guess is that ...
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2answers
414 views

QFT and its notations

I know hardly anything about quantum field theory (QFT) but I'm giving a try to understand some ideas of it. As far as I understand, in QFT one is interested in studying measures such as: \begin{...
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1answer
54 views

Is there a common notation to indicate the final form of a simplified definition? [closed]

I'm trying to become better with using proper terminologies and standard notation when taking notes, which lead me to think: Similar to the indication of a completed proof by use of the Q.E.D. mark, ...
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39 views

Notation of $P^+$-families - bibliography searching

have you ever met with notation of $P^+$-families in other papers than Iian B. Smythe "A local Ramsey theory for block sequences" and his phd? Thank you in advance
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1answer
49 views

Relative degree of a prime over a number field (notation from Algebraic Number Fields from Gerald J. Janusz) [closed]

I´m working with "Algebraic Number Fields" from Gerald J. Janusz (1. edition from 1973) and I have a question about his notation. In chapter IV proposition 4.5 he states if K is an algebraic number ...
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1answer
45 views

Name for matrix associated to smooth continuation

Is there an established name for the matrices that establish the conditions for a linear combination of $n$ functions $\lbrace f_1(x),\dots,f_n(x)\rbrace$ being the $n$-times smoothly differentiable ...
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2answers
896 views

Notation for “the” left adjoint functor

As far as I know, there is no "official" notation for the left adjoint of a functor $F : \mathcal{C} \to \mathcal{D}$ if it exists. I have seen the notation $F^*$ sometimes, but this looks only nice ...
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0answers
38 views

Notation for non-adjacency in graphs

I'm new here, so if the question is off topic here, please excuse. The most common notation in graph theory for the adjacency relation is $\sim$, and I've certainly seen the complementary relation ...
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0answers
99 views

Notation for the geometric quotient of a separated Deligne-Mumford stack?

Suppose that $X$ is a separated Deligne-Mumford stack, say over a base scheme. Is there some standard notation for the geometric quotient of $X$? I've tried using $[X]$ but have had complaints.
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0answers
79 views

Confusion optimal control abuse notation

I'm currently reading this paper describing a numerical scheme for the approximating optimal policy of a stochastic control problem. However, I run into a confusion directly on the first page where ...
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0answers
114 views

Arithmetization of Syntax: Can any semantic be encoded as syntax?

It is my understanding that Gödel Encoding and "Arithmetization of Syntax" can be used to represent any logical system. This is exemplified by the encoding of a Universal Turing Machine. "According ...
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198 views

Conventions for Riemann curvature tensor

I am aware of two conventions for the Riemann curvature tensor, namely the expression $$\langle\nabla_X\nabla_YZ-\nabla_Y\nabla_XZ-\nabla_{[X,Y]}Z,W\rangle$$ is either declared to be $R(X,Y,Z,W)$ or $...
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21 views

Name for subset selecting matchings

Tutte and also Lovasz and Plummer reduce the calculation of (optimal) f-factors in graph to non-bipartite matching via replacing each vertex with a $K_{f,\delta}$, refered to as a 'gadget' whose ...
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1answer
49 views

Writing a set of all possible (symmetric) products condensely? [closed]

I have a set of elements $\{a_1, a_2, a_3...\}$ and $\{b_1, b_2, b_3...\}$ and I want to condensely formally write the set of all possible products of these elements, where the ordering does not ...
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1answer
69 views

Computability Theory Notation For Entering A Set At A Stage

Is there a standard (or at least common) symbol in computability theory used to indicate that $x$ enters the c.e. set $W_e$ at stage $s$, i.e., $x \in W_{e,s} - W_{e,s-1}$ (at least for $s \neq 0$)? ...
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0answers
314 views

Does the Polish character Ł have an established mathematical meaning

I was suggested to use the slashed letter $\L$ (the European character Ł, which looks like the English letter L with a small bar crossing its vertical part) to denote the left half-plane. To avoid ...
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1answer
3k views

Was Jacobi the first to notice the ambiguity in the partial derivatives notation? And did anyone object to his fix?

In his 1841 article De determinantibus, Jacobi remarked that the notation $\frac{\partial z}{\partial x}$ for partial derivatives is ambiguous. He observed that when $z$ is a function of $x,y$ as well ...
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0answers
76 views

Notation/definition for the state of a FIFO queue [closed]

A first-in first-out queue is filled up by tokens $t \in T$. The state of the queue $q \in Q$ is being changed by two operations, \begin{equation} \mathrm{push} : Q \times T \rightarrow Q \end{...
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1answer
123 views

Symbol for monotone relationship between two probability distributions

Motivation: At the present time it really isn't clear to me why this question might be inappropriate for the MathOverflow. However, it appears that some people are down-voting this question even if ...
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0answers
197 views

What does it mean for two natural numbers to be *approximately equal*?

This is related to this other question of mine about a paper of Colin and Honda. I'm trying to follow the proofs line by line. I found the following piece of notation that is not explained in the ...
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1answer
285 views

Question about interpretation of algebraic notation in differential geometry paper

I am unable to understand the notation of equations (1.1) and (1.6) in page 2 of Kowalski and Belger's paper "Riemannian metric with the prescribed curvature tensor and all its covariant derivatives ...
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0answers
225 views

Why are Thompson's groups called $F$, $T$ and $V$?

Why are Thompson's groups called $F$, $T$ and $V$? I never saw Thompson's unpublished notes, in which he introduces these groups; maybe an explanation can be found there?
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2answers
706 views

Who first discovered the concept corresponding to the symbol of class comprehension?

Who first discovered the concept corresponding to the symbol of class comprehension $\{x/\varphi\}$ used today in set theory ?
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0answers
79 views

Basic notation question involving Lie Groups and Lie algebras

I just started reading "On the functional equations satisfied by Eisentstein series" by Langlands http://publications.ias.edu/sites/default/files/Eisenstein-ps.pdf . I wasn't sure of some notation/...
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1answer
205 views

Is there any math notation for `be denoted by`? [closed]

The sentence s "In many supervised learning problems one has an output variable $y$ and a vector of input variables $x$ described via a joint probability distribution $P(x,y)$" from wiki Here ...
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0answers
111 views

Name for generalization of property: $f^n(x) \ne x$ for all $n > 0$

I am curious about how to specify with standard terminology that a certain function is non-periodic, in the following sense: In the simple case of a unary operation $f: X \to X$, this property would ...
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1answer
84 views

Name of a matrix with one column and row removed [closed]

I am looking for the exact name of a matrix where the i-th column and rows have been removed. I cannot remember how it is called in linear algebra, does anyone got an idea? Thanks!
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1answer
527 views

Whence “Durchschnitt” and “Vereinigung”?

Today the set-theoretic operations of intersection $\cap$ [German: Durchschnitt] and union $\cup$ [German: Vereinigung] are standard. The modern notations are present in the first edition of van der ...
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5answers
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Has incorrect notation ever led to a mistaken proof?

In mathematics we introduce many different kinds of notation, and sometimes even a single object or construction can be represented by many different notations. To take two very different examples, ...
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0answers
60 views

Question about Notation for Spaces of $n$-ary $k$-ic Forms

Define an $n$-ary $k$-ic form to be a polynomial over the integers of homogeneous degree $k$ in $n$ variables. In Section 1 of the paper "Higher Composition Laws I" (linked below), Bhargava writes $(\...
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1answer
122 views

Basic question regarding notation of summation over primitive characters

This seems like a very standard notation in analytic number theory, and I see it a lot. But I was confused with it and I would greatly appreciate any clarification. When one writes sum of the shape $$...
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8answers
2k views

Mathematical objects whose name is a single letter

(Not research-level, but perhaps not easily answered elsewhere — you decide if MO can afford the innocent fun. If so, it should likely be “community-wiki” i.e. one object per answer.) I am seeking ...
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1answer
259 views

Question about denoting/designating of algebraic structures

I saw this image on Wikipedia (Template:Group-like structures, current revision): Since there are five "properties" that we can have (in this context), namely: totality, associativity, identity, ...
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1answer
166 views

Notation for the restriction map in Galois cohomology

My coauthors and I are writing a paper based on MO questions and answers: Friedrich Knop's answer, my answer 1 and my answer 2. For a linear algebraic group $G$ over a perfect field $k$, I consider a ...
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0answers
404 views

Grothendieck construction and coends

In category theory, both the Grothendieck construction and coends are represented by a sort of "integral sign", respectively: $$ \int F $$ for a functor $F:C\to\mathbf{Cat}$, and: $$ \int^x G(x,x) $$ ...
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5answers
2k views

The letter $\wp$; Name & origin?

Do you think the letter $\wp$ has a name? It may depend on community - the language, region, speciality, etc, so if you don't mind, please be specific about yours. (Mainly I'd like to know the English ...
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2answers
206 views

Technical term for representing object of a presheaf determined by a left-adjoint?

If $\mathcal{D}$ is a locally-small category, then a functor $F\colon\mathcal{C}\rightarrow\mathcal{D}$ has a right-adjoint if and only if for each object $d$ of $D$, the presheaf $$\mathcal{C}^{\...
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0answers
230 views

What does the $\pi_1(\mathsf{C})$ really mean?

Assume that $\mathsf{C}$ is a small category (in my case with finitely many objects but this is probably irrelevant). In a paper I'm studying at the moment there is a notion used constantly, this of $\...
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0answers
79 views

Spectral multiplier and Littlewood-Paley projection

I am trying to understand this paper, and have some basic question, and hope this is OK for the MO. Let $f\in \mathcal{S}(\mathbb R^d)$ (Schwartz Space). We know that $\widehat{\nabla f}(\xi)= 2 \...
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0answers
118 views

Local system corresponding to induced representation

Let $p\colon Y\to X$ be a finite covering map of path-connected "good" spaces (e.g. manifolds), and let $L$ be a local system on $Y$, and let $V$ be the corresponding representation of $\pi_1(Y)$. ...
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1answer
552 views

Generalizing Big O notation to arbitrary vector spaces

I'm constructing a Coq library for Big-O notation. Naturally, I'd like it to be as general as possible. The Wikipedia page on Big-O notation says The generalization to functions taking values in ...
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Notation: Why Ω for the based loop functor?

This is just a question about notation - probably useless, but it's always baffled me: Why was $\Omega$ chosen to denote the based loop functor? I once heard someone speculate: "It's because $\Omega$...
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1answer
120 views

Typed Values in Formulas

Question: are there any "standard" ways of indicating the meaning of numerical values in formulas, resp. general mathematical texts (theorems, proofs, etc.)? I am especially looking for ...
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0answers
192 views

Is there standard notation for restriction partial functions?

Given a partial function $f : A \rightarrow B$, and a subset $S \subseteq A$, we get a new partial function $$f \restriction_S : A \rightarrow B$$ by restriction. However, I prefer to analyse $f \...
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3answers
1k views

History of the pullback corner notation

Where/when did the convention originate of marking pullback (and/or pushout) squares by that little right-angle symbol in the corner? The earliest instance I’ve been able to find is in Paul Taylor’s ...

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