Questions tagged [terminology]
Questions of the kind "What's the name for a X that satisfies property Y?"
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Why are free objects "free"?
What is the origin/motivation for the adjective "free" in the term "free object"?
Does it refer to them coming "for free" (as being constructed from a set in a straight-forward manner) or does it ...
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Graded rings with compatible S_n actions
Does the following mathematical gadget have a standard name? Let $R$ be an $\mathbb{N}$-graded ring together with an $S_n$ action on each $R_n$ which are compatible in the following sense. Let $i:...
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Tracing the word “form”
Today the word form can refer to (at least) three different kinds of mathematical object:
A homogeneous polynomial. This was apparently started by Gauss (1801), renaming what others had called ...
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Does this geometry theorem have a name?
Start with a circle and draw two tangent circles inside. The (black) inner tangent lines to the smaller circles intersect the large circle. The (red) lines through these intersection points are ...
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Origin of the terminology "trace operator" related to boundary-value problems for PDEs
Important results in the theory of PDEs regarding boundary-value problems are trace and extension theorems. Since the trace operator essentially acts by restriction to the boundary of the domain, I ...
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Is there a commonly used short name for "squared Euclidean distance"? [closed]
In an optimization program I pass around distance values quite often. In my case these are simple 2D Euclidean distances $\sqrt{\Delta x^2+\Delta y^2}$. Since I want to perform the square root ...
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Is there a name for these especially simple directed acyclic graphs, and are any decent characterizations known?
Define the notion of a "foo digraph" recursively as follows.
If we take any finite number of directed path graphs each of which has at least $2$ vertexes, and glue them at the start and end vertexes, ...
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What do you call a Markov kernel continuous w.r.t. the weak topology?
Let $X$ and $Y$ be Polish spaces and $K$ a Markov kernel from $X$ to $Y$. That is, $K$ is a mapping $X \times \mathcal{B}_Y \rightarrow [0,1]$ (where $\mathcal{B}_Y$ is the $\sigma$-algebra of Borel ...
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Is there a standard name for (non-square) matrices with orthonormal columns?
One encounters often in numerics non-square matrices with orthonormal columns, i.e., $U\in\mathbb{R}^{m\times n}$, with $m > n$, such that $U^TU=I$ (but, clearly, $UU^T \neq I$).
Is there a name ...
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Whence “homomorphism” and “homomorphic”?
Today homomorphism (resp. isomorphism) means what Jordan (1870) had called isomorphism (resp. holoedric isomorphism). How did the switch happen?
“Homomorphic” (and “homomorphism” as “property of ...
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What is graph canonisation?
In a paper I am working on, I come across a term called "graph canonisation "
According to math-world Wolfram:
A canonical labeling, also called a canonical form, of a graph $G$ is a graph $G^{'}...
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Category of concrete categories
Consider the following 2-category:
• It objects are concrete categories, i.e., categories equipped with a faithful functor to $Set$.
• A 1-morphism between $(C_1,U_1)$ and $(C_2,U_2)$ consist of a ...
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The number of permutations of a given cycle type that fix a string with a given histogram
Let $\lambda$ and $\mu$ be partitions of some integer $n \geq 1$. Let $d$ be the number of parts in $\mu$ and let $\bar{\mu} \in \{1,\dotsc,d\}^n$ denote the string $1^{\mu_1} 2^{\mu_2} \dotsb d^{\...
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The letter $\wp$; Name & origin?
Do you think the letter $\wp$ has a name? It may depend on community - the language, region, speciality, etc, so if you don't mind, please be specific about yours. (Mainly I'd like to know the English ...
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What Kind of Graph is This?
I am currently developing TSP heuristics that aim at symmetrically reducing the original, complete and undirected graph.
The overarching rationale is that the reduction is done via a sequence of ...
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Terminology: Lost in translation or multiple-meanings
I was reading Uniformization of Riemann Surfaces by Henri Paul de Saint Gervais (not a real person, but a group of French mathematicians), and the translator kindly points out that the name of "the ...
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Regarding a new algebraic structure
By "left semigroup-joined-semigroup" I mean an algebraic structures $(S,\cdot,*)$ such that both $\cdot,*$ are associative, and the following property holds (see this )
$$
x*(y\cdot z)=x*y*z\;\; ; \;...
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Terminology question- Antihermitian elements
Let $V$ be a vector-space over a field $F$, and let $B$ be a non-degenerate bilinear form on $V$.
Question: Is there a common term to call an operator $x\in End(V)$ satisfying $$B(xu,v)+B(u,xv)=0\...
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"Unimodality" of the positive eigenvector of a non-negative irreducible matrix?
Consider an eigenvalue / eigenvector problem for a matrix $A$ that is known to be non-negative and irreducible (so the Perron-Frobenius theorem applies):
$$\sum_j A_{ij} x_j = \lambda x_i$$
Here $\...
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$c$-coarsely connected space for every $c>0$
A metric space $(X,d)$ is called $c$-coarsely connected if for every two points $x,y\in X$ there exists a sequence $x=x_0,x_1,\ldots,x_n=y$ of points in $X$ such that $d(x_{i-1},x_i)\leq c$.
Question:...
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Terminology for this notion of "$\sigma$-algebra" in a topos
Let $\mathcal{E}$ be a Grothendieck topos. I want to define a sort of "$\sigma$-algebra" for it, and I'm asking about what it should be—or already is—called. I know from nlab that Cheng spaces are an ...
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Monads which are monoidal and opmonoidal
Do monads which are monoidal and opmonoidal have a name? (Bimonoidal?) In case they have already been studied, who can point me to a reference?
More in detail. Let $(C,\otimes)$ be a symmetric (or ...
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A functional on paths in a symplectic vector space
I'm running into a functional associated to a piecewise smooth curve $\gamma: [0,1] \to V$, where $V$ is a real vector space with a symplectic form $\omega$:
$$ \int_{0 \leq x \leq y \leq 1} \omega(\...
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What are transport, diffusion, dispersion, dissipation, and viscosity terms in a PDE exactly?
Consider the PDE
$$\partial_t u + au + b\partial_x u + c\partial^2_{xx} u + d\partial^3_{xxx} u + e\partial^4_{xxxx} u + f\partial^5_{xxxxx} u + \dots= 0.$$
in $(0,\infty) \times \mathbb{R}$, with $a,...
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What does $\pi$ in the term $\pi$-system stand for?
In measure theory, what does the $\pi$ in $\pi$-system stand for? Also, what about the $\lambda$ in $\lambda$-system? I want to know why Dynkin chosen these names, and why these names make sense.
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Name of area between two parallel lines [closed]
Assume that there are two distinct parallel lines on a Euclidean plane. Is there a name for the zone between these two lines?
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Open pushout stability
If a scheme $X$ (or any reasonable geometric object) is covered by two open subschemes $X_1$ and $X_2$, then we know how to describe morphisms with domain $X$. But we can also describe morphisms with ...
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Is Hilbert–Schmidt and Frobenius norm the same?
From the definition on $\Bbb R$ those two norm are the same:
the Frobenius norm,
the Hilbert-Schmidt norm.
Is there some difference (on $\Bbb C$) or historical reason for two names for the same ...
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Local system corresponding to induced representation
Let $p\colon Y\to X$ be a finite covering map of path-connected "good" spaces (e.g. manifolds), and let $L$ be a local system on $Y$, and let $V$ be the corresponding representation of $\pi_1(Y)$. ...
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Name for a Property of Certain Polylines
Question:
Is there already a name for polylines in the euclidean plane, that have the property, that no interior of none the triangles, defined by one of the polyline's endpoints and a non-...
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What is the definition of "geometric analysis"? [closed]
Recently it has been brought to my attention that the subject "geometric analysis" is not even well-defined (unlike the subject partial differential equations, algebraic geometry, etc). Can someone ...
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Is there a name for Lie superalgebras which are generated by the odd subspace?
Every Lie superalgebra $\mathfrak{g} = \mathfrak{g}_{\bar 0} \oplus \mathfrak{g}_{\bar 1}$ has a canonical ideal $\mathfrak{k} = [\mathfrak{g}_{\bar 1}, \mathfrak{g}_{\bar 1}] \oplus \mathfrak{g}_{\...
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Name for functions with local=global minimum
I have a simple question. We know that functions where every stationary point is a global minimum are invex functions. Is there a name for functions where every local minimum is a global minimum?
And ...
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Hopf algebroids without antipode
A cogroupoid object in $\mathsf{CAlg}_R$ is called a Hopf algebroid over $R$. How are cocategory objects in $\mathsf{CAlg}_R$ called? (Unfortunately, bialgebroid is already taken, which seems to mean ...
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"Pointwise" defintions in category theory
In category theory it is often said that certain operations are defined "pointwise". For example, limits in a functor category $[\mathcal{C},\mathcal{D}]$ can be defined "pointwise" (if $\mathcal{D}$ ...
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Terminology for "global sections" when sheaf is valued in general category
Let $\mathcal F$ be a sheaf (say on a topological space $X$) valued in some category $\mathcal C$.
What do we call $\mathcal F(X)$?
When $\mathcal C$ is some vaguely linear category (e.g. the ...
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Polyhedra names question [closed]
So I've been playing around with polyhedra for my own amusement, but I ended up with some that I couldn't find names for. I have been trying to find them on my own by Googling for polyhedra with these ...
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Is there any accepted single-word that means "partial function"?
When I'm explaining things involving partial functions, I usually end up stumbling over my words, like so: "Suppose $f : A \rightarrow B$ is a function, uhh, sorry I mean a partial function, and ...
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Terminology for "approximately convex" sequence of integers
I have a sequence of integers meeting the following inequality:
$u_n \leq \frac{u_{n-1}+u_{n+1}}{2} + \frac{1}{2}$. In other words, the sequence is "approximately convex", and the difference comes ...
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English language and Mathematics
I have a question maybe more relevant to an English language section of StackExchange, but I doubt that anybody but a Mathematician could properly answer my question.
Let $\mathcal M$ be a smooth ...
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What is the term for this type of matrix?
Is there an established term for the following type of square matrices?
$\begin{pmatrix}
c & c & c & c & \cdots & c & c \\
c & a & b & b & \cdots & b & ...
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What is the term for a matrix whose columns are orthogonal?
What is the term for a matrix whose columns are mutually orthogonal, but not necessarily othonormal?
I can't name such a matrix "orthogonal" because that would imply that all columns are unit vectors....
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name generalized invariant tensors
When $V$ is the defining representation of a matrix group $G$, it is common to refer to $Hom_G(\mathbb C, \otimes^r V)$ as the space of invariant tensors.
Is there a similar (well established) name ...
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Is there a well-established terminology for polyhedra/polytopes?
I got confused lately. It seems like in the metric context a polyhedron tends to mean an intersection of a finite number of half-spaces, while a polytope is a convex hull of a finite set of points. At ...
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What is a "scholium"? [closed]
In a paper I'm working on, I'm tempted to write something like:
Note that the argument above also proves the following result:
Scholium. bla bla
Is this ok? Is it correct to say that a "...
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Terminology for filtered $\infty$-categories
Often to prove that the Kanification of a simplicial set $X_\bullet$ is contractible, we instead prove that $X_\bullet$ is a contractible Kan complex (i.e. satisfies the extension property for ...
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"quotient" function for a specific system of representatives
Let $X$ and $Y$ be two sets and $f: X \to Y$. Let $\sim$ be an equivalence relation on $X$. Please note that $f$ is not assumed to be compatible with $\sim$. Let $p: X \to X/\sim$ be the canonical ...
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What do we call functions satisfying $[a[b]c] = [abc]$?
Let $M$ denote a monoid and suppose we're given a function $[-] : M \rightarrow M$ satisfying $[a[b]c] = [abc].$ Then:
Proposition 0. $[-]$ is idempotent.
Proof. Take $a=c=1$).
Proposition 1. ...
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Does the following class of functions have a name?
Consider the functions $\mathbb{Z}\to\mathbb{C}$ that can be expressed as $\mathbb{C}$-linear combinations of functions of the form $g(n)=n^d\zeta^n$, where $d\geq 0$ is an integer and $\zeta$ is a ...
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Why are affine functions called "affine" functions? [closed]
I am learning about affine functions and I do not understand why a certain type of function (functions that are in the form of $f(x)=ax+b$) are called affine functions. I read about the word "affine" ...
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