Questions tagged [terminology]

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

Filter by
Sorted by
Tagged with
6
votes
2answers
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
0answers
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
0answers
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
2answers
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
2answers
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
0answers
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
1answer
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
2answers
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
3answers
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
1answer
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
1answer
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
2answers
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
0answers
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
1answer
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
1answer
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
1answer
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
1answer
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
0answers
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
1answer
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
1answer
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
0answers
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
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
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
1answer
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
0answers
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
1answer
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
2answers
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
1answer
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
7answers
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
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
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
1answer
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
0answers
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
1answer
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
1answer
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
1answer
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
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
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
2answers
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
0answers
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
2answers
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
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
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
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
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
1answer
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
1answer
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
0answers
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
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
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 ...