Questions tagged [terminology]
Questions of the kind "What's the name for a X that satisfies property Y?"
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The name of the equianharmonic curve
I have found several references where the elliptic curve $y^2=x^3-1$ is called the equianharmonic curve, and, more often, where the half-period of this curve
$$ \omega_1 = \frac{\Gamma(1/3)^3}{4\pi} $$...
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3
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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.
...
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0
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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(...
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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 ...
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2
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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 ...
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1
answer
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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.
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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 ...
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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 ...
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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
...
3
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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2
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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) ...
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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 ...
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1
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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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0
answers
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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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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 ...
3
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1
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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 $Y$.
...
3
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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 =...
2
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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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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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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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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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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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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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1
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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)\...
3
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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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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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0
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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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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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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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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 ...
3
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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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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 ...
6
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1
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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?