The terminology tag has no wiki summary.

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### Independent Generic Curves in the Projective Plane

I'm trying to read a paper by Masayoshi Nagata
(available here)
where he gives a counter-example to Hilbert's fourteenth prolem
and I've run into some trouble understanding the terminology he's using.
...

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60 views

### Terminology for set of infinite strings with a certain prefix

Let $\mathcal{A}$ be a finite alphabet, and let $C$ be the Cantor space $\mathcal{A}^\omega$ under the product topology.
Given a finite string $s \in \mathcal{A}^*$, let $C(s)$ be the set of all ...

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### Generalisation of “tangent space” to not-necessarily connected sets

I vaguely recall having read somewhere a definition similar to (but probably not exactly the same as) the following.
Definition (Blob) Let $S\subset \mathbb{R}^n$ be a set, and $p \in S$. The ...

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### Is there a name for the operation that stretches out an invertible series by a factor of $m$?

The question is whether there is an established word for the transformation that starts with an invertible formal power series over a field $k$, $u(x)=xg(x)=x(1+a_1x+a_2x^2+\cdots)$ and delivers the ...

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### Why the term “geometric” rough path?

A "geometric" rough path is a rough path such that $Sym(\mathbb{X}_{s,t})=\frac{1}{2}X_{s,t}\otimes X_{s,t}$. For example the Ito rough path is not geometric because ...

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### Why do people use “formal calculation” to describe informal calculations?

Many times, I see the word formal being used to describe a calculation that is not rigorous. I would think that such calculations should rather be termed informal than formal. What is the explanation ...

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### Variations on the Mellin and Dirichlet transforms

There are a number of variations on the Laplace transform that turn up all over math. Some examples:
$\int_{-\infty}^{\infty} f(t)e^{-st} dt$ - The Laplace transform
$\sum_{-\infty}^{\infty} ...

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763 views

### Describe the desired features of a “Mathematics Colloquium”?

I'm now a member of my department's colloquium committee. Our task is to make a great colloquium series. I thought that the first step would be to come up with an appropriate definition of ...

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165 views

### name for an intermediate notion between huge and 2-huge

I am employing a large cardinal notion that has been used explicitly before, and I am wondering if someone has given it a good succinct name.
A cardinal $\kappa$ is huge if there is an elementary $j ...

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256 views

### Is there a name for this space?

I'm just asking if there is a name for the space of functions on $\mathbb R^n$ whose norm is defined by
$$ \|f\|=\|\hat f\|_{L^p} $$
for $p\in [1,\infty]$. I find it handy to give it a name when ...

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### Products between metrics in a product of manifolds

In the "Einstein Manifold" book written by Arthur Besse, chapter 16, there is a notation of a manifold composed by the Cartesian product between two others:
$(M_1\times M_2, f^p(g_1 \times g_2))$
...

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339 views

### Terminology for metrics?

For some reason, I'm currently interested in the following relation - let $d,\delta$ be two metrics on some space $X$. We call the metrics _______ if there are some constants $C,E>0$ such that for ...

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### What is the name for the subring of the Grothendieck ring of a bialgebra spanned by one-dimensional representations?

Let $B$ be a finite dimensional bialgebra over a field $\Bbbk$. Let $\mathcal G_0(B)$ be the ring whose underlying additive group is generated by isomorphism classes $[V]$ of finite dimensional ...

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### Is there a name for the function on $TTM$ swapping the 2nd and 3rd coordinates?

I'm not so good on geometry, so I fear this is a relatively basic question.
For any $N \in \mathbb{N}$, let us identify the tangent bundle of $\mathbb{R}^N$ with $\mathbb{R}^{2N}$ in the obvious ...

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### Fixed area, largest mass — is there a name?

Let $x\in \mathbb{R}^n$ and let $s_k(x)$ denote the sum of the $k$ largest entries of $x$. The function $s_k(x)$ is well-known to be convex and is often used in optimization, such as
...

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### Who coined “mob” and “clan” and why these words?

A mob is a word used for a topological semigroup which is a Hausdorff space. A clan is a compact connected mob with a two-sided identity element.
Who used these words with these meanings first and ...

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### Is there a name for the level-sets of the signed distance function to a set in a metric space?

$\newcommand \X {\mathcal{X}}$
$\newcommand \sd {d_{\rm sign}}$
Let $(\X, d)$ be a metric space and define the distance between a point $x \in \X$ and a set $S \subset X$ by $d(x,S) = \inf_{y \in S} ...

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### Why the 'S' in S-procedure/S-lemma?

The S-procedure (also called as S-lemma) is a technique from V. A. Yakubovich that is used to relax a system of quadratic inequalities to a linear matrix inequality problem. It is used largely in ...

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285 views

### Why is a matrix pencil called a pencil?

I'm trying to understand the historical context behind the word pencil in matrix pencils, or pencil of curves so on.
I am aware that even Gantmacher 1959 has this terminology however I don't know ...

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### Definition of submaximal (group) topology

By [3] (or [2]), a submaximal group topology on a group is the infimum of all maximal group topologies on it.
By [4], a submaximal topological space is one with all dense subsets open.
By [1], a ...

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### Terminology for conditions on the negation of relations.

Suppose you have a relation $R$ and you want to impose the condition upon the relation $\lnot R$ that it be (e.g.) transitive. What would be a good terminology in this case? Would $counter transitive$ ...

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### Intuitive meaning of benign subgroup

Disclaimer! This is a copy of a question I posted on M.SE!
I still think the question belongs there but I'm not getting any answers so I'm dublicating with slight changes:
I've been studying a proof ...

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153 views

### Term for vertex connected to every other vertex in a graph

Do you know a good common term for the operation of connecting a new vertex v to every vertex in a graph G (or a term for such vertex v)?
The ones I know give me poor search results:
a nice word ...

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### Does this symmetrization operator have a name? Any theory?

Consider a function $f(x_1,\ldots,x_n)$ of $n$ complex variables. Define
$$f_{\mathrm{symm}}(x_1,\ldots,x_n) =
2^{-n}\sum_{\varepsilon_1,\ldots,\varepsilon_n=\pm 1}
...

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164 views

### Is there a standard notation for off-diagonal transpose?

Given a matrix $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$,
its transpose, obviously, is $A^T=\begin{pmatrix}a&c\\b&d\end{pmatrix}$.
But is there a conventional way of notating the matrix
...

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### Why is “The Higman Rope Trick” thus named?

I'm studiyng Higman's Embedding Theorem, and a fundamental part of the proof is the following lemma:
If R is a benign normal subgroup of finitely generated group F, then F/R can be embedded in a ...

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### Who first talked about “holes” in homology?

The question Why do the homology groups capture holes in a space better than the homotopy groups? and many others here use the idea that homology counts the ``holes'' in a space. The comments on this ...

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### Continuous-piecewise-linear versus piecewise-linear

Some authors use the term "continuous piecewise-linear" where other authors use the shorter term "piecewise-linear" (with continuity tacit).
I'd be interested in people's thoughts about this ...

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### Why are they called 'pernicious' numbers?

The definition of a pernicious number:
In number theory, a pernicious number is a positive integer where the Hamming weight (or digit sum) of its binary representation is prime.
The meaning of ...

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### Why is this group called “The Holomorph of a group”

Many years ago I found in google the notation "Holomorph of group". It is the semi direct product of $G$ with $Aut(G)$. Why is the term "Holomorph" used here, while it is usually used for complex ...

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### Has this construction, which builds a symmetric multicategory from a commutative monoid, been described or studied anywhere, and if so, where?

Whenever $R$ is a commutative ring, write $R[x^{(n)}]$ for the set of all $p \in R[x]$ such that $p$ is a monic polynomial of degree $n$. Then $R[x^{(n)}]$ is not closed under sums, nor does it ...

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### Is there a standard name for this poset

I've run into the following poset and I would expect it has a standard name. Let $n\geq k\geq 0$. Then $P_{n,k}$ consists of all $k$-element subsets of $\{1,\ldots,n\}$ ordered by $X\leq Y$ if ...

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### Terminology question for maps between posets

Let $P$ and $Q$ be two poset (partially ordered sets) and $\phi : P \to Q$ an order-preserving function.
I would like to know whether there is a name and perhaps a different characterizations of such ...

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### What is this graph property: number of vertices it takes to see every vertex?

I am wondering what the name is for the following graph property: given a graph $G$ what is the smallest cardinality of $A\subseteq G$ such that every $v\in G$ is connected to some vertex of $A$? I am ...

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### Polar Coordinate Systems on Manifolds [closed]

Is there agreement on how to interpret $r$ and $\varphi$ on a manifold if a reference point and a reference direction are given, or, put differently, does the definition of a reference point and, of a ...

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865 views

### A generalized diagonal?

A simple question. Let $ f:X\to Y $ be a function and let $ E_f:=\{(x, y): f (x)=f (y)\}\subset X\times X $. What is the name of the set $ E(f) $? It would be nice to have some reference also. It ...

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### How would you call a variety that is locally a complete intersection up to defect c?

Let $X$ be an equidimensional variety of dimension $n$ over a field that can be covered by open subvarieties of certain intersections of $N-n$ hypersurfaces in $P^N$ (for a large enough $N$; we ...

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### Integrating factors and integrability of an ODE system

The following argument is from a paper about the Bendixson-Dulac Theorem.
Consider a smooth differential equation on the plane
$$
x'=g(x,y),\quad y'=h(x,y).
$$
Suppose there exists a function ...

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### The Euler characteristic of Hilbert series

The Hilbert series of a graded vector space $V=\bigoplus_{n\mathbb Z}V_n$ is the (ordinary) generating function of the dimensions of its homogeneous components, $h_V(t)=\sum_{n\in\mathbb Z}t^n\dim ...

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### What is the standard name of an edge-graph

Given a graph $G=(E,V)$, I construct a graph $G'$ where the vertices of $G'$ are given by the edges of $G$ and say that two edges of $G$ are neighbors in $G'$ if they have a common vertex.
Is there a ...

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### Properties and name of some polynomials

I have encountered in a problem some polynomials given by $P_k(x) = \prod_{j=0}^{k-2} (kx-j)$. I need to understand if these polynomials are known, and if they have certain special properties, as ...

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### Intersection of nonzero prime ideals is zero — does it have a name?

The Rabinowitch trick (in Eisenbud's Commutative Algebra with a view toward Algebraic Geometry, page 132) says that $R$ (commutative unital ring) is Jacobson if and only if for every prime ideal $P ...

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### Term for “uncheckable constructions”

Is there a term for "uncheckable geometric constructions"?
Say, Angle Trisection and Doubling the Cube are checkable;
i.e., if the answer is given one can do finite Compass-and-straightedge ...

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### Between compact and locally uniform: What is the name of this convergence?

Let $X$ be a topological space, $(Y,d)$ a metric space, $f\in Y^X$, and $(f_n)$ a sequence in $Y^X$ with the following property:
For every $x_0\in X$ and every $\varepsilon>0$, there exist a ...

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### Standard names and methods for this type of fitting minimization

In material science research, we have come across the following type of problem.
Given a m by n matrix A, a m vector b, and error tolerance $\varepsilon$, we want to do this minimization
$$\eqalign{
...

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### Name for generalization of bivariate weighted-homogeneous polynomials

A polynomial $f = \sum_j c_j X^{\alpha_j}Y^{\beta_j}\in\mathbb K[X,Y]$ is said weighted-homogeneous if there exist $p$, $q$ and $d$ (where $p$ and $q$ are not both $0$) such that ...

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### Combination of convex and multiplicative structures

Combination of linear and multiplicative structures gives an algebra. What if instead of a linear structure one has a convex one? Is there a term for this?
A natural example is provided, for ...

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### Optimal definition of “paving by affine spaces”?

Cell decompositions have been used in topology for a long time as a tool in computing cohomology, but the notion in algebraic geometry and arithmetic geometry of paving by affine spaces (or "affine ...

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### Characteristic Varieties and Associated Varieties

Two notions that occur often in representation theory seem to be that of a "characteristic variety" and that of an "associated variety". The former term seems exclusive to D-module theory while the ...

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### Uniformizing a relation on ordered sets

Suppose $A$ and $B$ are (complete) ordered sets. Suppose $R\subseteq A\times B$, and
$f(a)=\inf\{b : (a,b)\in R\}$
$g(b)=\inf\{a : (a,b)\in R\}$
then what can we call $f$ and $g$? Perhaps there is ...