Questions tagged [terminology]
Questions of the kind "What's the name for a X that satisfies property Y?"
907
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Who coined "mob" and "clan" and why these words?
A mob is a word used for a topological semigroup which is a Hausdorff space. A clan is a compact connected mob with a two-sided identity element.
Who used these words with these meanings first and ...
2
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1
answer
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Is there a name for the level-sets of the signed distance function to a set in a metric space?
$\newcommand \X {\mathcal{X}}$
$\newcommand \sd {d_{\rm sign}}$
Let $(\X, d)$ be a metric space and define the distance between a point $x \in \X$ and a set $S \subset X$ by $d(x,S) = \inf_{y \in S} d(...
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2
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Why the 'S' in S-procedure/S-lemma?
The S-procedure (also called as S-lemma) is a technique from V. A. Yakubovich that is used to relax a system of quadratic inequalities to a linear matrix inequality problem. It is used largely in ...
19
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2
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Why is a matrix pencil called a pencil?
I'm trying to understand the historical context behind the word pencil in matrix pencils, or pencil of curves so on.
I am aware that even Gantmacher 1959 has this terminology however I don't know ...
0
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0
answers
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Terminology for conditions on the negation of relations.
Suppose you have a relation $R$ and you want to impose the condition upon the relation $\lnot R$ that it be (e.g.) transitive. What would be a good terminology in this case? Would $counter transitive$ ...
1
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0
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Intuitive meaning of benign subgroup
Disclaimer! This is a copy of a question I posted on M.SE!
I still think the question belongs there but I'm not getting any answers so I'm dublicating with slight changes:
I've been studying a proof ...
2
votes
2
answers
958
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Term for vertex connected to every other vertex in a graph
Do you know a good common term for the operation of connecting a new vertex v to every vertex in a graph G (or a term for such vertex v)?
The ones I know give me poor search results:
a nice word ...
2
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0
answers
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Does this symmetrization operator have a name? Any theory?
Consider a function $f(x_1,\ldots,x_n)$ of $n$ complex variables. Define
$$f_{\mathrm{symm}}(x_1,\ldots,x_n) =
2^{-n}\sum_{\varepsilon_1,\ldots,\varepsilon_n=\pm 1}
f(\varepsilon_1x_1,\ldots,\...
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2
answers
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Is there a standard notation for off-diagonal transpose?
Given a matrix $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$,
its transpose, obviously, is $A^T=\begin{pmatrix}a&c\\b&d\end{pmatrix}$.
But is there a conventional way of notating the matrix
...
14
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2
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Why is "The Higman Rope Trick" thus named?
I'm studiyng Higman's Embedding Theorem, and a fundamental part of the proof is the following lemma:
If R is a benign normal subgroup of finitely generated group F, then F/R can be embedded in a ...
11
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0
answers
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Who first talked about "holes" in homology?
The question Why do the homology groups capture holes in a space better than the homotopy groups? and many others here use the idea that homology counts the ``holes'' in a space. The comments on this ...
4
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1
answer
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Continuous-piecewise-linear versus piecewise-linear
Some authors use the term "continuous piecewise-linear" where other authors use the shorter term "piecewise-linear" (with continuity tacit).
I'd be interested in people's thoughts about this ...
4
votes
1
answer
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Why are they called ‘pernicious’ numbers?
A pernicious number is a positive integer such that the Hamming weight of its binary representation is prime.
[Wikipedia]
The meaning of ‘pernicious’:
pernicious (adj.): highly injurious or ...
8
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1
answer
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Why is this group called "The Holomorph of a group"
Many years ago I found in google the notation "Holomorph of group". It is the semi direct product of $G$ with $Aut(G)$. Why is the term "Holomorph" used here, while it is usually used for complex ...
4
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2
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Has this construction, which builds a symmetric multicategory from a commutative monoid, been described or studied anywhere, and if so, where?
Whenever $R$ is a commutative ring, write $R[x^{(n)}]$ for the set of all $p \in R[x]$ such that $p$ is a monic polynomial of degree $n$. Then $R[x^{(n)}]$ is not closed under sums, nor does it ...
5
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1
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Is there a standard name for this poset
I've run into the following poset and I would expect it has a standard name. Let $n\geq k\geq 0$. Then $P_{n,k}$ consists of all $k$-element subsets of $\{1,\ldots,n\}$ ordered by $X\leq Y$ if $X=\{...
2
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1
answer
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Terminology question for maps between posets
Let $P$ and $Q$ be two poset (partially ordered sets) and $\phi : P \to Q$ an order-preserving function.
I would like to know whether there is a name and perhaps a different characterizations of such ...
2
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2
answers
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Polar Coordinate Systems on Manifolds [closed]
Is there agreement on how to interpret $r$ and $\varphi$ on a manifold if a reference point and a reference direction are given, or, put differently, does the definition of a reference point and, of a ...
4
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5
answers
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A generalized diagonal?
A simple question. Let $ f:X\to Y $ be a function and let $ E_f:=\{(x, y): f (x)=f (y)\}\subset X\times X $. What is the name of the set $ E(f) $? It would be nice to have some reference also. It ...
1
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0
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How would you call a variety that is locally a complete intersection up to defect c?
Let $X$ be an equidimensional variety of dimension $n$ over a field that can be covered by open subvarieties of certain intersections of $N-n$ hypersurfaces in $P^N$ (for a large enough $N$; we ...
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1
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Integrating factors and integrability of an ODE system
The following argument is from a paper about the Bendixson-Dulac Theorem.
Consider a smooth differential equation on the plane
$$
x'=g(x,y),\quad y'=h(x,y).
$$
Suppose there exists a function $...
2
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0
answers
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The Euler characteristic of Hilbert series
The Hilbert series of a graded vector space $V=\bigoplus_{n\mathbb Z}V_n$ is the (ordinary) generating function of the dimensions of its homogeneous components, $h_V(t)=\sum_{n\in\mathbb Z}t^n\dim V_n$...
4
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2
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What is the standard name of an edge-graph
Given a graph $G=(E,V)$, I construct a graph $G'$ where the vertices of $G'$ are given by the edges of $G$ and say that two edges of $G$ are neighbors in $G'$ if they have a common vertex.
Is there a ...
1
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0
answers
120
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Properties and name of some polynomials
I have encountered in a problem some polynomials given by $P_k(x) = \prod_{j=0}^{k-2} (kx-j)$. I need to understand if these polynomials are known, and if they have certain special properties, as ...
5
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1
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Intersection of nonzero prime ideals is zero -- does it have a name?
The Rabinowitch trick (in Eisenbud's Commutative Algebra with a view toward Algebraic Geometry, page 132) says that $R$ (commutative unital ring) is Jacobson if and only if for every prime ideal $P \...
32
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2
answers
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Term for "uncheckable constructions"
Is there a term for "uncheckable geometric constructions"?
Say, Angle Trisection and Doubling the Cube are checkable;
i.e., if the answer is given one can do finite Compass-and-straightedge ...
13
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1
answer
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Between compact and locally uniform: What is the name of this convergence?
Let $X$ be a topological space, $(Y,d)$ a metric space, $f\in Y^X$, and $(f_n)$ a sequence in $Y^X$ with the following property:
For every $x_0\in X$ and every $\varepsilon>0$, there exist a ...
2
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1
answer
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Standard names and methods for this type of fitting minimization
In material science research, we have come across the following type of problem.
Given a m by n matrix A, a m vector b, and error tolerance $\varepsilon$, we want to do this minimization
$$\eqalign{
...
1
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0
answers
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Name for generalization of bivariate weighted-homogeneous polynomials
A polynomial $f = \sum_j c_j X^{\alpha_j}Y^{\beta_j}\in\mathbb K[X,Y]$ is said weighted-homogeneous if there exist $p$, $q$ and $d$ (where $p$ and $q$ are not both $0$) such that $p\alpha_j+q\beta_j=d$...
2
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0
answers
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Combination of convex and multiplicative structures
Combination of linear and multiplicative structures gives an algebra. What if instead of a linear structure one has a convex one? Is there a term for this?
A natural example is provided, for ...
10
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1
answer
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Optimal definition of "paving by affine spaces"?
Cell decompositions have been used in topology for a long time as a tool in computing cohomology, but the notion in algebraic geometry and arithmetic geometry of paving by affine spaces (or "affine ...
3
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1
answer
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Characteristic Varieties and Associated Varieties
Two notions that occur often in representation theory seem to be that of a "characteristic variety" and that of an "associated variety". The former term seems exclusive to D-module theory while the ...
2
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1
answer
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Uniformizing a relation on ordered sets
Suppose $A$ and $B$ are (complete) ordered sets. Suppose $R\subseteq A\times B$, and
$f(a)=\inf\{b : (a,b)\in R\}$
$g(b)=\inf\{a : (a,b)\in R\}$
then what can we call $f$ and $g$? Perhaps there is ...
8
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2
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Partial inverse of a matrix - or does it have its own name?
In my calculations I need to use something which is "between" a matrix and its inverse. That is, I invert only some dimensions. I am interested if it has an established name.
That is, a matrix (here ...
1
vote
1
answer
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Name for (function, set) pairs?
Right now I'm working on a topological graph theory problem. To prove a theorem I introduced some objects. Has anyone heard of something similar before? I would like to call them by the right name.
...
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1
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terminology: "complex" and "sequence" in homological algebra
It appears that the terms "complex" and "sequence" are used synonymously in homological algebra.
But there seem to be collocations (in the linguistic sense) that prefer one of those words. For ...
1
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1
answer
255
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Name for series $\sum f_n x^n / (n! (n+k)!)$
Let $(f_n)_{n\ge0}$ be a real sequence. Then $\sum f_n {x^n \over n!}$ is called the exponential generating function of $(f_n)$.
Let $k\ge0$ be a nonnegative integer. If we add another factorial $(n+...
2
votes
1
answer
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Reference request for generalization of groups with out identity element?
In other words what do we call a magma which is associative and has divisibility property but not existence of identity? Or a groupoid when it loses the identity property?
A reference on such ...
2
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0
answers
108
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Name of a difference of continuants
I am getting ready to publish the manuscript
http://arxiv.org/pdf/1408.4631v2.pdf
and I am trying to do due diligence on a quantity I study before it gets published. (This is cross-posted from Name/...
3
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2
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What do you call a fixed point theorem for a mapping from a subset of a space to the whole space?
There are a number of fixed point theorems in which we have a map from some subset of a (metric, topological, ...) space to the whole space. (Usually, there is some condition regarding the behavior ...
1
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0
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Proving identity involving delta-functions
Lately I came across the following identity:
$lim_{\eta\rightarrow0}\lim_{\delta\rightarrow0}2\eta\frac{1}{\omega-z_1-i\eta}\frac{1}{\omega-z_2+i\eta}\frac{1}{z_3-\epsilon-i\delta}\frac{1}{z_2+z_3-...
5
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1
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Decomposition vs filtration vs stratification
Are there accepted/standard definitions of "decomposition", "filtration", and "stratification" of a topological space (or of a manifold, or of an algebraic variety) $X$?
I tend to understand "...
6
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3
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Does this property of a first-order structure imply categoricity?
Let $\mathfrak{A}$ be a first-order structure over a relational language and let $\kappa$ be an infinite cardinal. Lets say that $\mathfrak{A}$ has the $\kappa$-property if for every structure $\...
5
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0
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Star shaped sets with a midpoint
Suppose $U$ is an open subset of $\mathbb{R}^n$ which is star shaped with respect to $p\in U$. I'll call $p$ a midpoint of $U$ if for any line $\ell$ through $p$, the point $p$ is the midpoint of the ...
6
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1
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The ten martini problem - reason for name
Why is the problem called the ten martini problem? Sounds like an interesting name for people who drink.
6
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2
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Morphisms every pushout of which is a weak equivalence
Let $M$ be a category equipped with a class of weak equivalences $W$. Is there a name for a morphism $f$ such that every pushout of $f$ (including, of course, $f$ itself) is a weak equivalence?
For ...
49
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9
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What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do they tend to succeed or fail?
I think we all occasionally come across terminology that we'd like to see supplanted (e.g. by something more systematic). What I'd like to know is, under what circumstances is it reasonable to believe ...
4
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3
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825
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"countable" topology
Given universal set $U$. Is there any name of the collection of subsets of $U$ (call them quasi-open) satisfying the following axioms:
i) $\emptyset$ and $U$ are quasi-open;
ii) finite intersections ...
50
votes
3
answers
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How did "normal" come to mean "perpendicular"?
How and when did the word "normal" acquire this meaning? When I first thought of this, I couldn't really come up with any explanation that wasn't complete speculation -- pretty much all I ...
11
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2
answers
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Origin of the term "generic" in set theory
In set theory, in particular the context of forcing, if $M$ is a model of $\sf ZFC$ and $P\in M$ is a partial order, we say that $G\subseteq P$ is a generic filter (or $M$-generic or generic over $M$) ...