# Questions tagged [terminology]

Questions of the kind "What's the name for a X that satisfies property Y?"

591
questions

**6**

votes

**2**answers

373 views

### The Floer Equation is Elliptic

Let $(M,\omega)$ be a symplectic manifold and $H \in C^\infty(M \times \mathbb{S}^1)$. Furthermore, let $J$ be an $\omega$-compatible almost complex structure on $M$. The Floer equation is the ...

**-1**

votes

**0**answers

137 views

### Is there a name for an algebraic structure determined by a finite propositional formula? [closed]

Let $r_0$, ..., $r_n$ be symbols denoting finitary relations, $f_0$, ..., $f_m$ be symbols denoting finitary functions.
Consider formulas consisting of free variables, $r_0$, ..., $r_n$, $f_0$, ..., $...

**2**

votes

**0**answers

217 views

### Which fields and schemes “have enough finite residue fields”?

I am looking for assumptions on the spectrum $S$ of a field $K$ that ensure the following: there exists an excellent noetherian finite dimensional (integral) scheme $S'$ such that $S$ is its generic ...

**8**

votes

**2**answers

396 views

### Notation for the set of all injections from $A$ into $B$

Is there a common notation for the set of all injections from $A$ into $B$?
Some set-theorists use $B^{(A)}$, e.g., A. Levy in his book Basic Set Theory.
But some combinatorists use $B^{\underline{A}...

**6**

votes

**2**answers

730 views

### Is there a name for this equivalence relation?

Let $M$ be an arbitrary set and let $\mathscr{F}$ be a family of subsets of $M$. Is there a known name for the following equivalence relation or its corresponding partition?
$\sim_{M,\mathscr{F}}\,=\...

**0**

votes

**0**answers

12 views

### Discrete time process with linear mixing and multiplicative noise

Consider a stochastic process $\vec{x}^t\in R^N$ in discrete time $t\in N$ which develops according to
$$\vec{x}^{t+1}_i=s_i^t \sum_j A_{ij}\vec{x}^t_j$$
where $A\in R^{N \times N}$ is some matrix ...

**6**

votes

**1**answer

265 views

### Why is the inertia stack of a smooth Deligne-Mumford stacks called inertia?

Let $\mathcal{X}$ be a smooth Deligne-Mumford stack. Then there is an associated stack $I\mathcal{X}$, called the inertia stack of $\mathcal{X}$.
Why is the inertia stack called "inertia"?
We can ...

**16**

votes

**2**answers

791 views

### Origin of the term “sinc” function

Is the sinc function defined here, really a short form of "sinus cardinalis" as proposed by Wikipedia? This information is deleted now but it existed some time ago. Even if we search Google Books for ...

**4**

votes

**3**answers

234 views

### Is there a name for this “stack” of graphs?

Let $G_1,\ldots,G_m$ be a sequence of graphs, all having the same number $n$ of vertices. For each pair $(G_i, G_{i+1})$ we add $n$ edges that connect the vertices of $G_i$ and $G_{i+1}$ bijectively. ...

**3**

votes

**1**answer

245 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

**1**answer

525 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

**2**answers

214 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

**0**answers

137 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

**1**answer

94 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

**1**answer

208 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

**1**answer

166 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

**1**answer

202 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

**0**answers

370 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

**1**answer

161 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

**1**answer

242 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

**0**answers

143 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

**0**answers

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

**3**answers

706 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

**1**answer

142 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

**0**answers

68 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

**1**answer

371 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

**2**answers

94 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

**1**answer

204 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

**7**answers

4k 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

**0**answers

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

**0**answers

48 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

**1**answer

169 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

**0**answers

29 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

**1**answer

214 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

**1**answer

193 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

**1**answer

141 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

**1**answer

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

**1**answer

396 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

**2**answers

957 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

**0**answers

89 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

**2**answers

418 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

**0**answers

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

**1**answer

99 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

**0**answers

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

**0**answers

275 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

**1**answer

417 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

**1**answer

115 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

**0**answers

114 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

**0**answers

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

**1**answer

66 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 ...