Questions tagged [terminology]

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

Filter by
Sorted by
Tagged with
23 votes
3 answers
4k views

What is Barr-Beck?

This is a question about a naming convention. The Barr-Beck theorem (or simply Barr-Beck) is used a lot in descent theory over the past 30 years, almost invariably without a reference, like folklore. ...
Friedrich Knop's user avatar
1 vote
0 answers
35 views

Term or reference for a set of integer edge weights to guarantee distinct weighted degrees

I am looking for a term or reference describing sets $S$ of $\binom{n}{2}$ non-negative integers such that, for every bijection $w: E(K_n)\to S$ and every pair of distinct vertices $u$ and $v$ in $V(...
subset's user avatar
  • 11
6 votes
0 answers
311 views

Does this plane geometry theorem have a name (well-known)?

Consider three circles $(O_1)$, $(O_2)$, $(O_3)$. Denote the homothetic center of $\{$$(O_1)$, $(O_2)$$\}$ by $A$, the homothetic center of $\{$$(O_2)$, $(O_3)$$\}$ by $B$. Let $C$, $D$ be two points ...
Đào Thanh Oai's user avatar
0 votes
2 answers
80 views

Name of distribution of the parameter of a Poissonian

Consider a Poisson process $\hat{n}$ with with parameter $t$ and distribution $$f_t(n) = e^{-t} \frac{t^n}{n!}$$ Now instead suppose to have a random variable $\hat{t} \in \mathbb{R}^+$ whose ...
tomate's user avatar
  • 503
2 votes
1 answer
735 views

Is there a term for a subgraph which includes all the edges of a graph?

A subgraph is called spanning when it includes all of the vertices of the given graph. Is there a term for a subgraph which includes all the edges of a graph? Thanks.
Tim's user avatar
  • 357
2 votes
0 answers
62 views

Name for a logarithmic ratio of roots

I'm trying to find a name for the following quantity that came up in my research. I've asked some people and looked around myself but can't find a name, yet it seems like something that has probably ...
Mark OSS's user avatar
  • 159
1 vote
0 answers
47 views

Term for the unit of grouping large numbers? [closed]

In English and probably most (if not all) western languages, we group numbers by powers of 1000. So we have: ones, tens, hundreds - then thousands, ten-thousands, hundred-thousands - and so on. We may ...
Elijah Madden's user avatar
7 votes
0 answers
425 views

Is there a name for these kinds of polynomials?

I've come across the following polynomials in my research and I am wondering if they have a name or if there is very much known about them: \begin{equation} F_{\chi}(T) = \sum_{a = 1}^{n-1} \chi(a)T^a ...
matt stokes's user avatar
3 votes
0 answers
122 views

Terminology for a generalization of the initial topology

This may be a simple piece of terminology, but I have not located it. For the initial topology, we are given a set of functions, indexed by $\alpha$, $f_{\alpha}:X\rightarrow Y_{\alpha}$, where each ...
Buzz's user avatar
  • 1,360
4 votes
1 answer
434 views

The maximum number of vertical independent vector fields on the tangent bundle

Let $M$ be a differentiable manifold. Is there a name for the maximum number of globally defined independent vector fields on $TM$ which are tangent to the fibers of $TM\to M$? Is there a name for ...
Ali Taghavi's user avatar
8 votes
0 answers
282 views

Name for an involution associated to a Coxeter element

Let $(W,S)$ be a finite Coxeter system, and $c \in W$ a Coxeter element. There is an involution $g\in W$ for which the involutive map $w \mapsto gw^{-1}g$ fixes $c$. Is there a standard name for this ...
Sam Hopkins's user avatar
  • 22.7k
0 votes
0 answers
54 views

Attached convex "hulls"

Let $\mathcal{P}$ a finite set of points of a Euclidean $\mathbb{E}^n$ and take the union $\mathrm{U}(\mathcal{P})$ of all closed half-spaces defined by $n$ elements of $\mathcal{P}$ that contain only ...
Manfred Weis's user avatar
  • 12.6k
0 votes
0 answers
69 views

Looking for a name for a generalization of geometry to graphs

I am pursuing generalizations of planar Euclidean geometry to complete symmetric and weighted graphs, the guiding principle being applicability to the TSP. The operations and tests that are available ...
Manfred Weis's user avatar
  • 12.6k
1 vote
0 answers
75 views

Is there a term for a linear operator on an $L^p$ space that "locally respects boundedness"?

Let $X$ be a Polish space, and $\mu$ a locally finite measure. Take any $p \in \{0\} \cup [1,\infty)$. We will say that a linear operator $T \colon L^p(\mu) \to L^p(\mu)$ has property $(\ast)$ if ...
Julian Newman's user avatar
1 vote
0 answers
75 views

Name for a directed acyclic graph with no skip-level edges?

I'm looking at a specific class of DAGs, namely those DAGs such that any path from $u$ to $v$ has the same length. Informally, we don't allow "skip-level" edges. I understand these graphs ...
Jan Westerdiep's user avatar
2 votes
2 answers
100 views

Solution to a matrix optimisation problem with a particular structure

Does a matrix of the form $A_{ij} = v_i + v_j$ for some arbitrary vector $v$ have a particular name? I am attempting to find the closed form solution (if it exists, although it looks like it might) ...
Nick555's user avatar
  • 31
0 votes
2 answers
929 views

Why are isotropic random vectors called isotropic if they aren't? [closed]

A random vector $X \in \mathbb{R}^n$ is isotropic if $\mathbb{E}XX^T = I_n$. However isotropic random vectors don't have the property of isotropy. See 1. So why are they called isotropic? Similarly a ...
lamlame's user avatar
  • 153
2 votes
1 answer
174 views

Trying to understand "moats"

According to the TSP Gallery moats provide lower bounds for the optimal solution of TSP instances. On the webpage they are depicted as blue rings around red disks, whose radii represent maximal vertex ...
Manfred Weis's user avatar
  • 12.6k
2 votes
0 answers
214 views

What is a hull in the most general mathematical sense?

I have implemented an algorithm that filters the edges of simple complete graph with weighted edges according to a criterion that is inspired by elementary planar geometry and, to my surprise, in the ...
Manfred Weis's user avatar
  • 12.6k
3 votes
0 answers
172 views

Probability terminology

This is strictly a low-level terminology question. If I have a probability space $\Omega$ and a measurable space $S$, then a random variable $X:\Omega\rightarrow S$ gives rise via pushforward to a ...
Steven Landsburg's user avatar
3 votes
1 answer
217 views

What is the name of this geometric structure, where we identify each sphere of vision with the sphere at infinity?

If you consider hyperbolic $n$-space $H^n$, modeled by the open unit ball $B^n \subset \mathbb{R}^n$, then given any two distinct points $x_1$, $x_2$ in $H^n$, there is a natural way of identifying ...
Malkoun's user avatar
  • 4,991
4 votes
0 answers
404 views

Dominant rational maps and compositions

According to many books (and also to Stack project, see https://stacks.math.columbia.edu/tag/01RI ), a morphism $f\colon X\to Y$ between schemes is said to be dominant if the image is dense in $Y$. ...
Jérémy Blanc's user avatar
3 votes
0 answers
130 views

Notions of "completeness" and "sufficiency" of a mathematical model

I'm modelling a real-world problem as having instances $i$ in a set $P$. As a very simple artificial example, consider the problem of choosing a meeting room given a certain number of people. Then $i =...
Peeyush Kushwaha's user avatar
2 votes
0 answers
73 views

Distorted elementary functions

Let $f(x)$ be an elementary function defined on $X\subseteq\mathbb{R}$ and $\xi(x), \eta(y)$ strictly monotone for $x\in X,\, y\in f(x)$. Questions: is there an established name for functions of the ...
Manfred Weis's user avatar
  • 12.6k
7 votes
1 answer
216 views

Terminology: "left homotopical"?

I first asked this on StackExchange, but no dice; so apologies in advance if this question really belongs there. Suppose a functor $F \colon \mathcal{C} \to \mathcal{D}$ between two model categories (...
prefix.crm114's user avatar
4 votes
1 answer
492 views

I want to know the name of or any references for a matrix in the book "The representation theory of the symmetric groups" by Gordon James

$\DeclareMathOperator{\Ind}{\operatorname{Ind}}$I'm reading "The representation theory of the symmetric groups" written by Gordon James. I found the matrix $B$ in the chapter 6 ("The ...
gualterio's user avatar
  • 1,043
1 vote
0 answers
145 views

Is there a name for a random variable that is the absolute value of the difference between two iid discrete uniform variables?

I'm working on a project and I needed to calculate the distribution of the difference between two iid discrete uniform variables (sorry for the long title). That is, let $I, J$ be two iid discrete ...
Simon's user avatar
  • 27
0 votes
1 answer
101 views

What is meant by basic figures of a graph?

In a theorem, there was mentioned that Let $P_G(λ) = |λI − A| = λ^n + a_1λ^{n−1} + \ldots + a_n$ be the characteristic polynomial of an arbitrary undirected multigraph $G$. Call an “elementary figure”...
Swarnakamal Barman's user avatar
6 votes
1 answer
325 views

What are these recursively defined sequences called?

Let $F(x,y)$ be a function of two variables, defined for all positive integers $x$ and $y$. Define a sequence $a_n$ recursively by setting $a_1 = 1$ and $$a_n = \sum_{k=1}^{n-1} F(k, n-k) \cdot a_k ...
Marty's user avatar
  • 13.1k
22 votes
3 answers
3k views

Cardioid-looking curve, does it have a name?

The curve, given in polar coordinates as $r(\theta)=\sin(\theta)/\theta$ is plotted below. This is similar to the classical cardioid, but it is not the same curve (the curve above is not even ...
Per Alexandersson's user avatar
1 vote
1 answer
71 views

Terminology: Co-completion of Met?

In main-stream mathematical literature, the term metric space is reserved for $(X,d)$ where $X$ is a set and $d:X\times X\rightarrow [0,\infty)$ satisfies the usual properties of a metric. However, ...
ABIM's user avatar
  • 5,019
0 votes
0 answers
56 views

What is the term for convoluting but scaling the time domain instead of shifting?

Given that the convolution definition as far as I am aware is: $(f*g)(t) = \int_{-\infty}^\infty f(\tau)g(t-\tau)d\tau$ Here I see that the functions f and ...
Saxpy's user avatar
  • 1
2 votes
0 answers
278 views

Is there a name for this "inner product" on projective space?

$\newcommand{\proj}{\mathbb{P}}\newcommand{\complex}{\mathbb{C}}\newcommand{\ip}[2]{\langle #1 , #2\rangle}\newcommand{\abs}[1]{\lvert #1 \rvert}$There is a natural bijection $\phi: \proj(\complex^n)\...
Ben's user avatar
  • 1,010
3 votes
1 answer
206 views

What is the name of this categorical construction?

If $\mathcal{C}$ is a skeletally small (i.e. it is equivalent to a small category) preadditive category, then we can make the following construction: First we form the additive category $\text{Mat} \...
user avatar
3 votes
1 answer
307 views

Name and properties of $\mathrm{lcm}(\{1,\,\cdots,\,n\})$ [closed]

one of the most prominent functions of the first $n$ natural numbers is the factorial $n!$ that denotes their product. Today however I wondered whether the least common multiple $\mathrm{lcm}(n):=\...
Manfred Weis's user avatar
  • 12.6k
1 vote
0 answers
21 views

Weakening s-unitality

Recall that a (non-unital, non-commutative) ring $R$ is left s-unital if for every $r\in R$, we have $r\in Rr$. Consider the following conditions: There is a nonzero integer $m$ such that for all $r\...
tomasz's user avatar
  • 1,214
3 votes
0 answers
97 views

Every partial isometry extends

I am interested in metric spaces $X$ where every isometry between two subsets of the space extends to a full isometry $X \to X$. Is there a name for this kind of space? Is there some paper which ...
James's user avatar
  • 31
7 votes
0 answers
74 views

Graphs all of whose cuts are positive

Let $(V, E, w)$ a weighted graph, with vertices $V$, edges $E$, and signed weight $w:E\to \mathbb R$. I am interested to know other popular properties that are known to imply, or are equivalent to, ...
Mircea's user avatar
  • 2,031
1 vote
1 answer
99 views

How do I fit flow values to connections in a known network?

This is not my area and I'm new to its terminology, and am posting my problem in the hope that someone will be able to direct me to where it has been solved, or who has written about it. I have a flow ...
hmkc's user avatar
  • 11
1 vote
0 answers
35 views

Name for vertex of a digraph reachable from a directed cycle

I'm wondering if there is an established name for vertices of a finite directed graph that are reachable from a directed cycle. These also can be described as endpoints of arbitratily long directed ...
Benjamin Steinberg's user avatar
0 votes
0 answers
114 views

What is the name of the following root system?

The Dynkin diagram of the root system of affine $D_4$ is $$ \circ \quad \circ \quad \circ \quad \circ \\ \circ $$ where all of the four vertices in the first row connects to the vertex in the second ...
Jianrong Li's user avatar
  • 6,101
8 votes
0 answers
171 views

Does the "coproduct-elimination transform" have an accepted name, and where can I learn more about it?

Suppose we're in a bicartesian closed category. Then given a morphism $$f : X \rightarrow Y_1 + \ldots + Y_n$$ and a test object $T$, we get a corresponding morphism $$T^f : X \times [Y_1,T] \times \...
goblin GONE's user avatar
  • 3,693
0 votes
0 answers
36 views

Terminology: Almost stable states

I have a question about fixed points which are almost stable. I have an increasing transition function $f:[0,1]\rightarrow[0,1]$ where $f(0)>0$ and $f(1)<1$ but I don't necessarily have ...
MDR's user avatar
  • 188
3 votes
0 answers
71 views

Equivalence relation induced by Kolmogorov quotients

Recall: given a (possibly non-$T_0$) topological space $X$, its Kolmogorov quotient $KX$ is the $T_0$ topological space formed by $X/\sim$ where $x\sim y$ if they are topologically indistinguishable. ...
Willie Wong's user avatar
  • 37.4k
6 votes
3 answers
3k views

What is an "exact solution" to a PDE?

Wolfram MathWorld says As used in physics, the term “exact” generally refers to a solution that captures the entire physics and mathematics of a problem as opposed to one that is approximate, ...
Colin McLarty's user avatar
6 votes
1 answer
413 views

Name for a class of almost symplectic manifolds

A $2n$-dimensional manifold $M$ is said to be almost symplectic if it possesses a non-degenerate two-form $\omega \in \Omega^2(M)$. Equivalently, an almost symplectic structure is a $G$-subbundle $P \...
José Figueroa-O'Farrill's user avatar
0 votes
1 answer
659 views

Infinite composition of continuous functions

Let $f_n:\mathbb{R}\rightarrow \mathbb{R}$ be a sequence of functions and define $F_n:= f_n\circ \dots\circ f_1$. Then $F_n$ is continuous. However, the pointwise limit need not be (consider Mateusz'...
ABIM's user avatar
  • 5,019
4 votes
0 answers
55 views

How are these "Voronoi-dual" configurations called?

If $\mathscr P\subset \mathbb R^d$ is a discrete point configuration, take the Voronoi diagram of $\mathscr P$ and call $\mathscr P'$ the vertices of that diagram. I would like to know if ...
Mircea's user avatar
  • 2,031
6 votes
1 answer
258 views

Name for a matrices having a specific property

is there an established name for the property that a square matrix can be made symmetric by permutation of its columns? Is it possible to recognize those kind of matrices efficiently?
Manfred Weis's user avatar
  • 12.6k
2 votes
2 answers
488 views

Is there a name for order-preserving functions $f$ where “$a\le b$ if and only if $f(a) \le f(b)$”? [closed]

This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I’m not sure if there is a standard name for this in order ...
Mitchell Buckley's user avatar

1
3 4
5
6 7
19