Questions tagged [terminology]
Questions of the kind "What's the name for a X that satisfies property Y?"
582
questions
3
votes
1answer
226 views
Problem Understanding Euclid Book 10 Proposition 1 [closed]
this is embarrassing, but I am having trouble reading through Proposition 1 of Book 10 of Euclid's elements. I'm struggling with Euclid's terminology and don't have a clear picture of what divisions ...
11
votes
1answer
499 views
Physicists misuse the term “Kac Moody algebra”. Does that bring problems?
In physics textbooks one frequently sees the name (affine) Kac Moody algebra used to describe the universal (one dimensional) central extension of the loop algebra of a semisimple algebra. But this is ...
0
votes
2answers
209 views
Naming convention: Adjective for linear operators that are endomorphisms
If a matrix has the same number of rows and columns, we call it a square matrix. The analogous concept for linear operators would be operators with the same domain and range, i.e., endomorphisms.
Is ...
2
votes
0answers
135 views
Name for matrices with vanishing row and column sums
Question:
is there a special name for matrices whose rows and columns sum to zero?
I actually need information about those matrices and thus a keyword for online search.
Edit:
as there ...
2
votes
1answer
89 views
Actions that become free after quotienting out their kernel
Let $H$ be the kernel of an action of a group $G$ on a space $X$. Is there a term for the actions with the property that the action of the quotient group $G/H$ on $X$ is free?
5
votes
1answer
205 views
Symmetric monoidal category with trivial switch morphisms
Is there a specific terminology for a symmetric monoidal category in which for any object $x$ the switch map $x\otimes x\to x\otimes x$ is the identity ? (Or alternatively the action of the symmetric ...
10
votes
1answer
161 views
Verbal description, or terminology, for the ${\mathcal L}_p$-spaces of Lindenstrauss and Pelczynski
This question is intended for Banach-space specialists and so I will not repeat all the definitions here. My aim is to find out how the Banach space community refers to such spaces in discussions, and ...
2
votes
1answer
197 views
The name of special 16-dimensional hypercomplex number
Let's consider the following number:
$n = n_0 + n_1\textbf{i} + n_2\textbf{j} + n_3\textbf{k}$
Where $\{1,\textbf{i},\textbf{j},\textbf{k}\}\subset\mathbb{H}$ and in turn each component can be written ...
4
votes
0answers
356 views
Why are algebraic schemes called algebraic?
In scheme theory, an algebraic scheme is the data of a scheme + a morphism of finite type to the spectrum of a field. Where does the term "algebraic scheme" come from? It does not seem intuitive to me ...
3
votes
1answer
150 views
Which complexes of coherent sheaves are dual to perfect ones?
Let $X$ be a Noetherian scheme that is not Gorenstein but possesses a dualizing complex $D$ of coherent sheaves. Then (if I understand these matters and the answer to the question Characterization of ...
8
votes
1answer
217 views
Terminology about G- simplicial complexes
For a simplicial complex $X$ with an action of a discrete group $G$, we can impose the following condition, namely that if $g\in G$ stabilizes a given simplex $\sigma\subseteq X$, then $g:\sigma\to\...
6
votes
0answers
137 views
What is the name for this type of families?
Is there a common name for a family $\mathscr{F}$ which satisfies the following condition?
For any infinite $X\subseteq\mathscr{F}$ there exists a finite $A\subseteq X$ such that $\bigcap A$ is ...
0
votes
0answers
55 views
Term for product of group homomorphisms and their inverses
Given
two groups $X$ and $Y$
(in general, non-abelian) and
homomorphisms $h_1,\dots,h_n\colon X\to Y$,
consider the map
$$
f\colon X\to Y,
\quad
x\mapsto h_1(x)^{k_1}\dots h_n(x)^{k_n},
$$
for some $...
10
votes
3answers
684 views
Name for abelian category in which every short exact sequence splits
What is the name of the class of abelian categories defined by the following property: every short exact sequence splits?
1
vote
1answer
131 views
Simulation of Itô integral processes where integrand depends on terminal (Volterra process)
I need to simulate a process of the form
$$X_t=\int_0^t f(s,t)\mathop{dW_s}$$
where $f$ is deterministic and the integral is an Itô integral. I know I can simply take finite Itô sums of discrete ...
1
vote
0answers
65 views
What exactly is and is not a concentration inequality?
Hoeffding's inequality is surely a concentration inequality. It can be written in the form:
$\Pr(\bar X + f(n,\delta) \geq \mu) \geq 1-\delta,$
for some function $f$, where $X$ is a set of i.i.d. ...
5
votes
1answer
368 views
Do matrices with only elements along the main and anti-diagonals have a name?
To expand upon the title, I am wondering if there is a specific name for square matrices of the form: $$M = \begin{bmatrix} a_{11} & 0 & \cdots & 0 & \cdots & & 0 & b_{1n} ...
3
votes
2answers
86 views
Is there a name for “splitting a probability distribution into independent components”?
Suppose I have a random variable $\theta=(\theta_1,\dotsc,\theta_n)$; where the $\theta_i$ might have pairwise correlations. I decompose it into $\theta=\hat\theta(\phi_1,\dotsc,\phi_k)$, where $\hat\...
5
votes
1answer
197 views
Smash product and the integers in a Grothendieck $(\infty, 1)$-topos
Let $\mathcal{H}$ be a Grothendieck $(\infty,1)$-topos. According to this page in nlab, for any $X \in \mathcal{H}$, the suspension object $\Sigma X$ is homotopy equivalent to the smash product $B \...
43
votes
7answers
3k views
What is an explicit bijection in combinatorics?
A standard way of demonstrating that two collections of combinatorial objects have the same cardinality is to exhibit a bijection between them. Browsing through some examples (here, there, yonder) ...
4
votes
0answers
71 views
Terminology for a foliation that is only tangentially smooth
I'd like to get some information and references, starting with a name, for the following quite common situation, for a smooth (i.e. $C^\infty$) $n$-manifold $M$. A partition $\mathcal{L}$ of $M$ is ...
2
votes
0answers
46 views
Is there a common framework for working with topological base spaces and manifolds?
There is the general construct of a fibre bundle induced by a topological group action. Yet, one of the distinctive differences between this notion and the notion of a vector bundle is that the base ...
3
votes
1answer
166 views
Cofibrations of functors
Let $\cal M$ and $\cal N$ be model categories, $S,T:\cal M\to N$ functors, and $\alpha:S\to T$ a natural transformation. Say that $\alpha$ is a <blank> cofibration if for any cofibration $i:A\to B$...
1
vote
0answers
28 views
Name for a Lower Bound on the Length of General TSPs and ATSPs
Let $G\left(\ V,\ E=V\times V\setminus\lbrace(v_i,v_i)\rbrace,\ \Omega: E\ni e_{ij}\mapsto\omega_{ij}\in\mathbb{R}\right)$ be a(n) (A)TSP instance.
Then
$$2*\ell(T_{\mathrm{opt}})\quad\ge\quad\sum_{...
9
votes
1answer
209 views
Intuition behind orthogonality in category theory, and origin of name
In category theory, two morphisms $e:A\to B$ and $m:C\to D$ are said to be orthogonal if for any $f:A\to C$ and $g:B\to D$ with $m\circ f=g\circ e$, there exists a unique morphism $d:B\to C$ such that ...
-3
votes
1answer
192 views
A common name for a functorial construction of Commutative Algebra?
I am interested whether the following construction naturally appearing in Commutative Algebra has some know and acceped name.
Given a commutative monoid $(M,+)$ and a set $X$, consider the family $F(...
7
votes
1answer
135 views
Name for topological spaces where “every point has a local base wellordered by reverse inclusion”?
There are many properties regarding local bases of a topological space, like first countable if every point has a countable local base.
Is there a similar name for a space where "every point has a ...
0
votes
1answer
85 views
Name for Directed Edges in Digraphs
Graph theory originated in German speaking countries and there directed edges are called "Pfeil" which translates to "arrow", which makes sense, because arrows have distinguishable front end and rear ...
1
vote
1answer
353 views
Why is the matrix of all 1's called “J”? [closed]
I've seen J referenced recently in some discussion about algebraic combinatorics, and it took me a while to figure out it was the matrix of all ones. It came up without definition, and I spent too ...
9
votes
2answers
936 views
Terminology about trees
In set theory, a tree is usually defined as a partial order such that the set of elements below any given one is well-ordered. I am interested in the class of partial orders $P$ such that for every $...
4
votes
0answers
85 views
Name for facet of a cone containing all but one edge
Let $C \subseteq \mathbb R^n$ be a polyhedral cone, so generated by its edges ($1$-dimensional faces) and $F \subseteq C$ a facet (codimension $1$ face) of it containing every edge except $e$. In ...
5
votes
2answers
415 views
Name of a group-like structure
The late Vladimir Arnold, in
Arnold, V., Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world, Bull. Braz. Math. Soc. (N.S.) 34, No. 1, ...
3
votes
0answers
72 views
Name for mappings that are “not quite projections”
Is there a known name for the following definition?
Consider topological spaces $X$, $Y$ and $f: X \rightarrow Y$ a continuous mapping. Then, $f$ is an "almost projection" if there is a topological ...
1
vote
1answer
88 views
Basis of cone lattice
I only want to know whether a construction that I use appears in literature and maybe has a name already.
Let $V$ be a $\mathbb Q$ vector space of dimension $d\in\mathbb N$.
A subset $C\subset V$ is ...
2
votes
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 ...
9
votes
0answers
273 views
Why does Loday call the permutohedra “zylchgons”?
Today I was reading Jean-Louis Loday's classic paper, "Realization of the Stasheff polytope", in which he produces a simple and very pretty realization of the associahedra as convex polytopes. He ...
5
votes
1answer
413 views
English translation of “Les aspects probabilistes du contrôle stochastique”
I am looking for an English translation of "Les aspects probabilistes du contrôle stochastique" written by Nicole El Karoui, or knowledge whether it exists.
Other references with similar content on ...
1
vote
1answer
107 views
Slow and fast forming singularities of the mean curvature flow
Let $M \times [0, T) \to \mathbb{R}^{n+1}$ be a mean curvature flow and let $T$ be a singular time. Let $A$ denote the second fundamental form.
We have a type I singularity if
$$
\max_{p \in M} |A(p,...
3
votes
0answers
104 views
How are the unit/counit of a Hopf algebra and of an categorical adjunction related?
For categories $\mathcal{C}$ and $\mathcal{D}$, a pair of functors $\mathcal{C} \xrightarrow{\;L\;} \mathcal{D}$ and $\mathcal{C} \xleftarrow{\;R\;} \mathcal{D}\,$ are an adjoint pair if we have ...
1
vote
0answers
56 views
Suppressing some but not all terms of a polynomial equation
(I'll ask the question over $\mathbb{R}$, but feel free to change fields if that makes the answer more straightforward or more interesting.)
Let $Q$ denote a bivariate quadratic:
$$Q(x,y) = Ax^2 + ...
1
vote
1answer
64 views
The Kronecker product of two bipartite graphs' biadjacency matrices: what's it called?
Here's two random $(0,1)$-matrices:
$$
A=
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 1 \\
\end{bmatrix}
\qquad
B=
\begin{bmatrix}
1 & 1 \\
0 & 1 \\
\end{bmatrix}.
$$
They can be ...
1
vote
0answers
44 views
What is the ring of functions on the open unit disc with polynomially bounded Maclaurin coefficients called?
Let $R$ be the the set of complex-valued (analytic) functions $f$ on the open unit disc $\mathrm D:=\{z\in\Bbb C:|z|<1\}$ for which there exist constants $a_0$, $a_1$, ... in $\Bbb C$ and $n$ in $\...
7
votes
0answers
316 views
Why are commutative diagrams called “commutative”?
Does anyone know the rationale behind the name of "commutative diagrams"? To be precise, what is(are) the reason(s) for calling those diagrams "commutative" and in what sense?
I have previously asked ...
0
votes
1answer
55 views
Standard names of two finitary properties of hypergraphs?
Now we are writing a paper on minimal covers and minimal vertex-covers in hypergraphs and would like to know if there are any standard names for the following two (dual) properties of a hypergraph $(V,...
2
votes
0answers
48 views
Probability Distribution on permutations with factor structure
Say I define a probability measure over the symmetric group $S_n$ as follows:
I specify $n$ positive `potential' functions $G_i : \{1, 2, \cdots, N\} \to (0,\infty)$
I then set
$$\mathbb{P}(\sigma) =...
28
votes
3answers
5k views
Naming in math: from red herrings to very long names
The are some parts of math in which you encounter easily new structures,
obtained by modifying or generalizing existing ones. Recent examples
can be tropical geometry, or the theory around the field ...
9
votes
1answer
508 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 ...
6
votes
1answer
154 views
Reference request: A collection of topologies on $\mathbb{N}$ formed via series
First, some quick notation: for any series $\sum_{n=1}^\infty a_n$ whose terms are positive real numbers, and for any subset $M = \{m_1, m_2,...\} \subseteq \mathbb{N}$, we write $\sum_M a_n$ to mean ...
3
votes
2answers
242 views
Non-probabilist term for conditional expectation?
When writing an article I encounter what is essentially a conditional expectation - function defined on a bounded interval (not necessarily of unit length) with Lebesgue measure, but information about ...
1
vote
2answers
113 views
Is there a standard name for this type of multidigraph?
A digraph (direct graph) consists of a set $V$ of vertices and a set $E$ of directed edges $v\to v'$. A multidigraph is a digraph in which $E$ is a multiset, so edges may appear multiple times in $E$, ...
