Questions tagged [terminology]

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

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

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 ...
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49 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 ...
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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 ...
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61 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 ...
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1answer
190 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 ...
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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 $Y$. ...
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What is the name for a functor preserving open maps? Quotient maps? Effective epimorphisms?

How does one call an endofunctor of the category of topological spaces which preserves open maps? Quotient maps? More generally, how does one call a functor that preserves effective epimorphisms?
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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 =...
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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 ...
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192 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 (...
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1answer
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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 ...
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82 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 ...
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49 views

Terminology: base affine space or basic affine space?

Let $U$ be the maximal unipotent subgroup of the special linear group $\mathrm{SL}_k$. In the book, on the top of page 14, $\mathrm{SL}_k/U$ is called a basic affine space. In some other place, it is ...
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1answer
81 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”...
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Liouville metric or Liouville line element

In the literature, the following is known as Liouville line element: $$ ds^2 = (U(u) + V(v))(du^2 + dv^2) \tag{1}\label{iso} $$ In my research I stumbled upon a generalization of this Liouville line ...
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283 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 ...
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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 ...
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1answer
66 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, ...
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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 ...
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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)\...
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1answer
126 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} \...
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271 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):=\...
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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\...
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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 ...
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Properties of semi-regular simple digraphs

Let semi-regular simple digraph denote graphs $G(V,E)\ $ with $\ E\subset V\times V\ \land\ e_{ij}\in E\implies e_{ji}\notin E\ $ and $\ \mathrm{card}(\lbrace e_{ij}\in adj(v_i)\rbrace)=\mathrm{const}\...
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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, ...
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1answer
46 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 ...
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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 ...
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99 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 ...
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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 \...
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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 ...
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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. ...
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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, ...
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1answer
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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 \...
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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'...
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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 ...
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1answer
241 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?
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2answers
271 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 ...
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Terminology: Existence + Representation

I'm looking to describe a result in a recent paper of mine, but I don't know if there is a term used for a result which is both an existence theorem and a representation theorem. Specifically, the ...
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Why the name `Lipschitz-Free Banach spaces'?

There are many names for the same objects that is known as the Arens--Eells spaces, transportation cost spaces, free Banach spaces over a (pointed) metric space, and Lipschitz-free Banach spaces. The ...
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Reference request for linear matrix inequality with PSD matrices

In literature, people say a spectrahedron is the following set $$\left\{x \in \mathbb{R}^d : x_1 A_1 + \cdots + x_d A_d \geq B \right\}$$ where $\geq$ is in the positive semidefinite sense. Is there a ...
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Is there a name for and/or reasonably nice characterisation of “mixingly physical” measures?

Let $M$ be a Riemannian manifold with volume measure $\lambda$, let $f \colon M \to M$ be a diffeomorphism, and let $\mu$ be a probability measure on $M$ with compact support. As stated in the ...
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What is a bipartite hypergraph?

Bipartite graphs are very useful, and I am looking for a generalization of this concept to hypergraphs. I found two different definitions of bipartite hypergraphs: In the Wikipedia page Hypergraph, a ...
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1answer
197 views

Why aren't $B_n$ and $C_n$ the other way around?

In the classification of complex simple Lie algebras/groups, I have always been vaguely puzzled why $B_n$ and $C_n$ are labeled the way they are. I always instinctively want to put the special ...
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Emergence of the orthogonal group

Do we know what mathematician first considered, and perhaps named, what we call the group $\mathrm O(n)$, or $\mathrm{SO}(n)$, for some $n>3$? I mean it specifically as group (not Lie algebra) ...
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Terminology: “transformed Brownian motion”

I cam across this article studies Markov processes which are functions of a Brownian motion. I general, if we relax the markov requirement, are such processes studied? If so do they have a name? To ...
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1answer
122 views

Is there a name for $f(M, x) = x^\top M x$? [closed]

I often encounter things of the form $x^\top M x$, where $M$ is symmetric positive (semi-)definite. Is there a term for that? I know related terms: We can say $M$ is a bilinear form, $M(x,y) = x^\top ...
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4answers
964 views

The name for an assumption made for the sake of contradiction

What is the name (or adjective) for an assumption made for the sake of contradiction? To be clear, I'm in search of an expression in the form "a(n) $\underline{\quad \quad \quad \quad}$ ...
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1answer
75 views

Is there a proper name for those 'shifted moments'?

Suppose that we have a random variable $X$, $i \in \mathbb N$, and a scalar $t$. Is there a proper name for these integrals, that I for the moment call 'shifted moments' ? $$I_{i}^{t} = \mathbb{E}\...
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133 views

Is there a name for commutative algebras over a field $k$ whose residue class fields have finite dimension over $k$?

Let $k$ be a field and let $A$ be a (commutative) $k$-algebra. Assume that for every maximal ideal $P \subseteq A$ the residue class field $A/P$ has finite dimension as a $k$-vector space. Is ...

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