Questions tagged [notation]

For questions about mathematical notation, i.e. the symbols used to represent mathematical objects and operations.

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Weighted random sampling notation [closed]

I'm a computer scientist, not a mathematician, so please excuse the lack of mathematical rigor. I'm currently writing a paper where I would like to express the following using equations: I have a ...
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62 views

Terminology and notation for generated subgroups

I would like to think about formation of the smallest subgroup (or monoid, or whatever) $H$ of $G$ containing two given subgroups $A$ and $B$ as an operation on subgroups, and I wonder if there is a ...
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Higher order Leibniz rule and ordered multiindex notation

Although I think this is probably known, I am making here a short exposition on the multiindex notations I am using to make this question self-contained. I note that there is at least two different ...
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121 views

What does square bracket superscript star mean in basic group theory typically?

I'm reading some paper where they haven't really defined their notation very well (or I've missed something). You can see the image below. What does the square bracket and star mean precisely? The ...
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1answer
102 views

Notation for H is isomorphic to a subgraph of G

Is there a notation for the statement $H$ is isomorphic to a subgraph of $G$? I was thinking of using $H<G$, but I'd like to use standard notation if possible.
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125 views

Can NBG be interpreted in this system that use new notation for class-abstractions?

We introduce a new symbol $\lambda$ to denote class-abstractions, and we add the following rule: if $\phi$ is a formula that use $``\mu"$, and in which the symbol $\sf y$ doesn't occur; then: $\lambda ...
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2answers
202 views

What is meant by this notation of the real forms of $E_6$?

There are five real forms of the exceptional Lie group, $E_6$. Four of them are notated as in the following: The split form as EI or $E_{6(6)}$ The quasi-split form as EII or $E_{6(2)}$ EIII or $E_{...
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135 views

Proof of Theorem 9.2 of the book Cubic Forms by Yu. I. Manin (end of page 37)

I warn that I first posted this question in Mathematics Stack Exchange but it got no attention at all. I think that it fits better there by its explanatory nature but maybe the book being reference is ...
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1answer
165 views

Finitely-generated conjugation action on a subgroup that is not normal… what is that?

If $H \lhd G$, then $G$ acts on $H$ by conjugation. I need to talk about this action but in a situation where $H$ is not (necessarily) normal. When $H \leq G$, there is a "partial action" of ...
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151 views

How to denote a partial derivative?

This question is related to Was Jacobi the first to notice the ambiguity in the partial derivatives notation? And did anyone object to his fix? and Suggestions for good notation . When there are two ...
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70 views

Good notation for finite partial functions from $\omega$ to 2

I'm working in computability theory and need to use partial functions with finite domain from $\omega$ to 2 as approximations in my current paper. Normally this is simply done using $2^{< \omega}$ ...
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1answer
113 views

Temporal generalization of graphs: density vs $n$ and $m$?

In short: we generalize graphs to the temporal case, but fail to fully preserve the usual relation between density, number of vertices, and number of edges; how to make better? Context. We propose a ...
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131 views

Confusing notation for sets of unordered vs ordered pairs

Given two finite sets $X$ and $Y$, one may consider the ordered pairs $(x,y)$ with $x\in X$ and $y \in Y$. Then, $(x,y) \not= (y,x)$, and $(x,x)$ exists if $x\in X$ and $x\in Y$. One may also consider ...
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166 views

Ideals with certain properties

I recently isolated the following definition, which I believe it should have appeared somewhere. Let $\kappa$ be a cardinal, and let $X$ be a set with $\kappa^+\leq |X|$. Definition: An ideal $\...
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1answer
162 views

Typesetting of symbols and “operators” denoting sets [closed]

Question: what are the conventions for typesetting sets of certain objects, especially the vertices and edges of a graph or those adjacent to an edge or vertex. For vectors and matrices there is the ...
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1answer
119 views

Explanation of a formula to calculate the zenith distance of sun and moon [closed]

I am studying tidal accelerations and referring to a well known paper by I M Longman : Formulas for computing.." J Geophys Research 64 (12) Dec 1959. At Eq 12 he writes a term "1336.rev"...
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1answer
541 views

Origin of the symbol for the tensor product

I have recently realised that the Paleo-Hebrew (and Phoenician) graph for the Hebrew letter ט (Teth) is $\otimes$. This made me wonder if there is any relation between the choice of the symbol and the ...
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142 views

Notation for the regular and the adjoint representation of a finite group, in particular the symmetric group

The (left) regular representation of a finite group $G$ is the action on itself by left multiplication, $g\cdot h = gh$. The adjoint representation of a finite group $G$ is the action on itself by ...
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223 views

Why are fundamental weights denoted by omega?

In my field (and many others, I believe) the absolutely standard notation for the fundamental weights of a root system is lowercase omega: $\omega$. Recently I was taken aback to receive a copyedited ...
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105 views

Question about the notation $N_{\chi}(\alpha, T)$, the number of zeroes of the $L(s, \chi)$ in a rectangle

I am confused with what seems to be a standard notation in analytic number theory and I'd appreciate any clarification. I am interested in the zero density estimates, for example link.springer.com/...
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83 views

What are Conway's orbifold notations for the conjugacy classes of the icosahedral group?

In MathWorld, the conjugacy classes for the icosahedral group are listed as $1, 12C_5, 12C_5^2, 20C_3, 15C_2, i, 12S_{10}, 12S_{10}^2, 20S_6$, and $15\sigma$. I should like to know what Conway's ...
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1answer
275 views

Name and properties of $\mathrm{lcm}(\{1,\,\cdots,\,n\})$ [closed]

one of the most prominent functions of the first $n$ natural numbers is the factorial $n!$ that denotes their product. Today however I wondered whether the least common multiple $\mathrm{lcm}(n):=\...
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94 views

What is the p-adic Plancherel measure?

What I know as the Plancherel measure for a group is a measure on the spectrum of $G$, aka the set of irreducible representations - at least for finite groups, this makes perfect sense. Now, this ...
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150 views

Who introduced the heart ($\mathcal{C}^\heartsuit$) notation in the context of $t$-structures on triangulated categories?

In the context of $t$-structures ([Wikipedia], [nLab], [Notes I], [Notes II], [HA, Definition 1.2.1.11)], [BBD, Définition 1.3.1]), one often writes $\mathcal{C}^\heartsuit$ for the heart of a ...
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104 views

Reference request: Dictionary of the Leibniz notation

Is there any published, somewhat comprehensive, list of (almost?) all the many ways in which the Leibniz notation ($dx,$ $P(dx),$ $d\mu(x),$ $du\wedge dv,$ etc., etc.) gets used in the various areas ...
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109 views

A question about chaining Vinogradov notation

This is not a research question, but I hope it is still legitimate to ask for this platform. Suppose $A(x)$, $B(x)$, $C(x)$, $D(x)$ are positive-valued functions of $x$, and $A(x) \ll B(x)$ and $ C(x) ...
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35 views

Terminology: Almost stable states

I have a question about fixed points which are almost stable. I have an increasing transition function $f:[0,1]\rightarrow[0,1]$ where $f(0)>0$ and $f(1)<1$ but I don't necessarily have ...
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53k views

What are the benefits of writing vector inner products as $\langle u, v\rangle$ as opposed to $u^T v$?

In a lot of computational math, operations research, such as algorithm design for optimization problems and the like, authors like to use $$\langle \cdot, \cdot \rangle$$ as opposed to $$(\cdot)^T (\...
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90 views

Notation question: bigraded direct sum of graded objects

In some work I'm doing I have two graded modules $M$ and $N$ (graded on $\mathbb Z$, say) and need to take, not the usual direct sum, but the bigraded sum consisting of all $M_p \oplus N_q$ (so graded ...
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79 views

Notation for induced subgraphs

For a graph $G=(V,E)$, is there a standard notation for the induced subgraph on $V \setminus \{v,w\}$ where $v,w$ are the endpoints of some edge $e$? I know $G[V \setminus \{v,w\}]$ is an option, but ...
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112 views

Marcinkiewicz-Mihlin-Hormander Fourier multiplier theorem

I'm trying to understand the hypothesis of the Marcinkiewicz-Mihlin-Hörmander multiplier theorem. See for instance Theorem A in this paper of Elias Stein. Theorem A: Assume that $m: (0, \infty)\to \...
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1answer
103 views

Unknown notation in “Boolean function complexity” by Stasys Jukna [closed]

I am currently reading Boolean Function Complexity - Advances and Frontiers by Stasys Jukna and on page 7 of the latest edition there is a paragraph titled Boolean functions as set systems with the ...
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477 views

Why did mathematical notation stay so hard to read? [closed]

One of the first things you learn in a programming 101 course is to write readable code, and to name your variables properly. This notion has seemingly never translated into mathematics. Everywhere ...
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161 views

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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Examples of improved notation that impacted 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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353 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
279 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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495 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
59 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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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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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
51 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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976 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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107 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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85 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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126 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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320 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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1answer
51 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
70 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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368 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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