# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 $\pi_1(Y)$. ...
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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### 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 ...
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 \...