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

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votes

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63 views

### Name for the variety of preimages of a finite morphism

If $f:X\to Y$ is a finite morphism of degree $d$ between two varieties, you get a closed subset of the symmetric product $X^{(d)}$ (or perhaps rather the Hilbert scheme $X^{[d]}$), defined as the ...

**11**

votes

**1**answer

561 views

### Where did the term “additive energy” originate?

A fundamental object in modern additive combinatorics and harmonic analysis is additive energy. Given a subset $A$ of (say) an abelian group $G$ the additive energy of $A$ is defined to be the ...

**-3**

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**0**answers

47 views

### Mathematical notations [closed]

Please i have some questions about mathematical symbols and their explanations
Could you give please some examples to illustrate
-equivalent to
-similar to
Are there any relation between equivalent ...

**3**

votes

**1**answer

230 views

### Is there a name for this fast growing functions?

Define $F(n,i)=\prod_{j=1}^nj^{j^i}$.
$F(n,0)=n!$.
$F(n,1)$ is hyperfactorial.
Is there a term for $F(n,i)$? How fast do these grow? Is growth rate $2^{\frac{c_in^{i+1}\log_2n}{i+1}}$ with some ...

**0**

votes

**1**answer

97 views

### Node-edge coloring of graphs

There must be work on this concept, but I am not finding it through
searches, perhaps using the wrong terminology.
Define a node-edge coloring of a graph ...

**3**

votes

**3**answers

206 views

### Semantic reflection

Let $\ulcorner \cdot \urcorner$ be a fixed encoding of formulas by numbers, e.g.
let $\ulcorner \varphi \urcorner$ denote the Godel number of $\varphi$.
Let $T$ be a first-order arithmetic theory, ...

**1**

vote

**0**answers

86 views

### Notions of singularity for symmetric bilinear maps

Given a symmetric, bilinear map $B : \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}^m$, a common notion of nondegeneracy is the following:
$$
\mbox{If } B(x,y) = 0 \mbox{ for all } y, \mbox{then } ...

**2**

votes

**1**answer

88 views

### Does Gaussian Quadrature actually refer to Gauss-Legendre Quadrature？

When the term Gaussian Quadrature appears in most Literatures, does it actually refer to Gauss-Legendre Quadrature.
In other words, do they implicitly admit that they use the Legendre orthogonal ...

**5**

votes

**1**answer

83 views

### A special function solution of a fourth-order ODE

I want to consider the solutions of the following fourth-order ODE:
$$
f^{(4)}(t)+a tf^{(1)}(t)+b f(t)=0,
\tag{$\ast$}$$
where $a,b$ are complex parameters. It turns out that with a Fourier ...

**6**

votes

**0**answers

151 views

### What's the name of the cohomology class associated to a projective representation?

Suppose $\rho : G \to PGL_n(k)$ is a projective representation of a group $G$ over a field $k$. It's classical that the obstruction to lifting this to a linear representation $G \to GL_n(k)$ is a ...

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votes

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149 views

### Terminology for vanishing of Hochschild homology with symmetric coefficients?

In a title or abstract for a paper, if I say "Hochschild cohomology of this algebra $A$ vanishes in degrees two and above" then
it should hopefully be understood by most readers as saying ...

**13**

votes

**0**answers

197 views

### Is there support for the term “Gelfand algebra”?

In this question Yemon Choi asked whether there is a standard term for Banach algebras for which the submultiplicative law
($\|ab\| \leq \|a\| \|b\|$) is weakened to merely requiring the product to be ...

**2**

votes

**0**answers

112 views

### For f: X -> Y -> X, what is the name of the property whereby for all x in X and y1, y2 in Y, f(f x y1)y2 = f(f x y2)y1?

My PL group has been discussing this (so we are really professional reject mathematicians, but this is more about the math behind what we are doing). Some of us called it a "generalized ...

**4**

votes

**1**answer

112 views

### Is this notion of 'closed subset' of a semigroup action something people have thought of?

Suppose $S$ is a semigroup (or a monoid, or a category), and $X$ is an $S$-set -- that is, a set with an action of $S$. Say that a sub-$S$-set $Y$ is "downward closed" (or maybe "well-generated") if ...

**4**

votes

**0**answers

47 views

### Is there a name for a bifurcation where a stable fixed point bifurcates into three fixed points: stable, unstable and saddle?

Consider the differential equation on $\mathbb{R}^2$ whose polar-coordinate representation is given by
$$ \begin{array}{r c l} \dot{r} & = & r(\alpha - r^2) \\ \dot{\theta} & = & ...

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votes

**4**answers

753 views

### What is the term for combining functions $f_1,f_2,\dots,f_n$ into a tuple $(f_1,\dots,f_n)$?

This is an embarrassingly simple question, but I was not able to find a definitive answer from literature search.
Suppose one has some collection of functions $f_1: X \to Y_1, \dots, f_n: X \to Y_n$ ...

**7**

votes

**0**answers

397 views

### Name for an operation on matrices?

Given two matrices $A$ and $B$ of size $a \times n$ and $b \times m$ consider the following operation $A \dagger B$ whose result is an $a b^n \times n m$ matrix. $A \dagger B$ is a block matrix with ...

**8**

votes

**0**answers

203 views

### What is the name for a Banach space property closed under ultraproducts?

In Banach space theory, a super-property is a property of a Banach space that is preserved under ultrapowers. (Update (2015-09-28): The property must also be closed under isometric embeddings.) ...

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votes

**0**answers

101 views

### Synonyms for “labeling” of a graph

In Preprint 1 we write numerical labels 0 or 1 at each vertex of a Dynkin diagram $D$. We call it a labeling of the graph (Dynkin diagram) $D$.
In Preprint 2 we consider an extended (affine) Dynkin ...

**3**

votes

**2**answers

162 views

### Name for an orthogonal decomposition of $L^2 (\mathbb{R}^2; \mathbb{C})$

The space $L^2 (\mathbb{R}^2; \mathbb{C})$ can be decomposed as
$$
L^2 (\mathbb{R}^2; \mathbb{C}) = \bigoplus_{k \in \mathbb{Z}} L^2_k (\mathbb{R}^2; \mathbb{C}),
$$
where
$$
L^2_k (\mathbb{R}^2; ...

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votes

**2**answers

218 views

### Is the “inverse” (i.e., the “cohomological”) numeration for singular (i.e., $H\mathbb{Z}$-)homology of spectra “acceptable”? [closed]

I have recently realized that in one of my (published) papers I have used the "inverse" numeration for the $H\mathbb{Z}$-homology of the objects of the stable homotopy category (so, if we consider ...

**4**

votes

**1**answer

246 views

### Does the (singular)cohomology of any acyclic spectrum vanish?

I am interested in those objects in the ("topological") stable homotopy category $SH$(I call them spectra) whose homology (with integral coefficients; should I call it singular or stable, or ...

**1**

vote

**1**answer

72 views

### “Interval” terminology for (partially) ordered sets

Let $(X,\preceq)$ be a poset.
Is there a standard, generally recognised term for a set $A \subset X$ satisfying
$$ \forall x,y,z \in X, \ (x \in A \ \textrm{ and } \ z \in A \ \textrm{ ...

**1**

vote

**0**answers

56 views

### Standard name / symbol for intersection in Brouwerian lattices

A Brouwerian lattice has a lower adjoint $\cdot - B$ to $B\lor\cdot$. It is called pseudodifference. The main reference is http://www.jstor.org/stable/1969038
Once you have pseudodifference, you can ...

**1**

vote

**0**answers

56 views

### Is there an official name for the intersection of the join-irreducible representations of two lattice elements?

Given a lattice provided with a join-irreducible representation of its elements, there is a natural "intersection" operator $A \mathbin{\dot\cap} B$ that returns the join of the setwise intersection ...

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votes

**1**answer

160 views

### Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function) [closed]

Original question:
The symbol looks like a numeral 1 written like an R in $\mathbb{R}$. It has a double vertical line and a serif at the bottom. It represents a function of a parameter: ...

**1**

vote

**2**answers

112 views

### Is there a name for a partial order in which there is a countable chain which “dominates” the whole space?

Is there a name for a partial order $\preceq$ on a set $X$ with the following property: "there exists a countable set $S \subset X$ such that for all $x \in X$ there exists $y \in S$ with $x \preceq ...

**4**

votes

**1**answer

125 views

### Does this axiom (a weak form of class valued choice) has a name?

At some point in my work (which has nothing to do with set theoretics foundation) I need to consider the following axiom:
For any set $X$, any class $V$ with a surjective map $f : V ...

**2**

votes

**1**answer

195 views

### A question on the name of a property

What is the name of the following property of a system $T$?
If $\vdash_{T}\exists x F(x)$ then
there is a term $a$ such that $\vdash_{T} F(a)$
If I recall correctly Heyting Arithmetics has ...

**5**

votes

**1**answer

310 views

### Terminology in combinatorics

I met the following two combinatorial concepts during a study outside of combinatorics. I am wondering if there are common terminologies in combinatorics.
A finite graph $G$ has the following ...

**5**

votes

**2**answers

238 views

### Does the ring generated by the odd power sum symmetric functions have a name?

Let $\Lambda$ be the ring of symmetric functions and recall the power sum symmetric function $p_i = \sum x_1^i + x_2^i + \dots$ generate this ring. Let $\tilde\Lambda$ be the ring generated by the odd ...

**3**

votes

**4**answers

312 views

### Terminology for polygons

As you may know term "polygon" might mean few different things
and its meaning has to guessed from context.
By some reason I have to use few of these meaning in one place.
So I converge to the ...

**5**

votes

**0**answers

156 views

### Is there a name for this quantity between two distributions?

Let $f$ be a probability density on a compact domain $D$, and say that $x_1,\dots,x_n$ are samples from $f$. If we wanted to compute the Wasserstein distance between $f$ and the empirical ...

**2**

votes

**0**answers

51 views

### Terminology for torsion semigroups where the order of elements is uniformly finite

A (multiplicatively written) semigroup $\mathbb A = (A, \cdot)$ with the property that ${\rm ord}_\mathbb{A}(a) := |\{a^n: n \in \mathbf N^+\}| < \infty$ for every $a \in A$ is called a periodic ...

**7**

votes

**1**answer

227 views

### Another name for coin-flipping polynomials

In his paper Functions arising by coin flipping (section 4), Johan Wästlund coined the term "coin-flipping polynomial" for polynomials that arise in connection with observing a finite number of coin ...

**1**

vote

**0**answers

65 views

### Reduced products of (abelian and triangulated) categories: references?

For a filter $U$ on a set $X$ and for a family of categories $C_x$ indexed by $X$ I would like to consider the (corresponding categorical version of) reduced product of $C_x$ (for $x\in X$) with ...

**0**

votes

**0**answers

122 views

### Higher algebra and terminology about 2-objects

It is well known that one way to build higher category theory is to use some induction process, where an $n$-category has as $0$-cells some $n-1$ categories, such that for two $0$-cells $\mathcal{A}$ ...

**0**

votes

**0**answers

126 views

### 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.
...

**1**

vote

**1**answer

72 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 ...

**5**

votes

**1**answer

158 views

### 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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votes

**0**answers

85 views

### 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 ...

**4**

votes

**1**answer

190 views

### 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 ...

**16**

votes

**1**answer

2k views

### 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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votes

**1**answer

215 views

### 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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votes

**2**answers

800 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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votes

**0**answers

170 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 ...

**4**

votes

**1**answer

265 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 ...

**1**

vote

**0**answers

188 views

### 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:
$(M_1\times M_2, f^p(g_1 \times g_2))$
...

**4**

votes

**2**answers

346 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 ...

**2**

votes

**0**answers

64 views

### 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 ...