Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

learn more… | top users | synonyms (2)

1
vote
0answers
18 views

What is a dominating measure?

When I read papers in statistics, I meet the notion of "dominating measure", can anyone explain this notion to me a little bit ? Thanks
0
votes
1answer
46 views

Are fixed points and equilibria the same thing?

Are fixed points and equilibria the same thing, in terms of a logistic map?
2
votes
0answers
28 views

Unique Union Problem

Given a the set $a = \{1,...,n\}$ and let $b$ denote a set of subsets of $a$. Find a subset of $c$ of $b$ so that the union of all subsets in $c$ is equal to $a$ and the intersection of any of the ...
2
votes
2answers
40 views

How is the start of repeating decimals defined?

Today I tried to find the period length of the repeating decimals of 8/86 by asking WolframAlpha (yes a somewhat stupid question because it's the same as ...
2
votes
5answers
222 views

What does $\prod_{k=-2}^{11}(15-3k)$ mean--and how might I compute it?

$$\prod_{k=-2}^{11}(15-3k)=\;?$$ I'm new to this and have not seen this notation before. Can anyone explain to me what this is called and how to solve or compute it?
0
votes
0answers
24 views

Universal property of tensor product of $R$-algebras

Let $R$ be a commutative ring and $A_1,...,A_{n+1}$ be $R$-algebras. Let $A_1\otimes_R\cdots\otimes_R A_{n+1}$ be equipped with the natural $R$-algebra structure. Let $N$ be an $R$-algebra. Let ...
1
vote
0answers
38 views

Name of this PDE: $\frac{\partial^2u}{\partial t^2}=\frac{\partial^3u}{\partial x^3}$

So I got an exercise to try some numerical methods on the following PDE: $$\frac{\partial^2u}{\partial t^2}=\frac{\partial^3u}{\partial x^3}$$ I tried to find some information about it, but I do not ...
1
vote
1answer
23 views

Why there is a less care of symmetricity of bimodules over a commutative ring?

Let $R$ be a commutative ring. Then, we say $M$ is an $R$-module instead of left $R$-module or right $R$-module or $(R,R)$-bimodule. I'm curious why this convention is acceptable in general. Let's ...
0
votes
0answers
27 views

Understanding what paths,trails and circuits and cycles and walk length mean

My Research I've looked at two questions which seemed similar on MSE. The first one was inadequate for me because most of the answers where just stating book definitions, which I already have. The ...
2
votes
1answer
48 views

How to call “equivalent-looking” vertices in graph..?

In the above figure, the vertices expressed as blue dots are "equivalent-looking." Although my expression is somewhat ambiguous, I believe one can simply answer it. How can we call such vertices? ...
0
votes
0answers
15 views

The terminology of the operation in the linear function

What do we call the term $(m_0 + m_1 \times x_1 + m_2 \times x_2)$ in the linear equation $f_\vec{m}(\vec{x}) = m_0 + m_1 \times x_1 + m_2 \times x_2$? is it correct to call it the linear combination? ...
0
votes
1answer
43 views

How do geometers define “locally looks like” in differential geometry?

From reading some introductory texts on differential geometry, the author would usually invoke the phrase "locally looks like" when it comes to defining a manifold. For example, the real line is a ...
1
vote
0answers
33 views

What to call a non-edge in a network?

Suppose I have a network with nodes and some edges between the nodes. If node $x$ and node $y$ have an edge, then we say that $(x,y)$ corresponds to the edge between $x$ and $y$. Now suppose that $x$ ...
1
vote
1answer
26 views

Does a number matrix have its invariant factors??

I'm just confused by the following statement in my advanced algebra textbook: Frobenius Form: Let $A$ be an $n$th order square matrix over a number field $K$, whose invariant factors are: ...
2
votes
3answers
75 views

What does it mean if a function is onto? [duplicate]

I've heard the term "onto" several times but still not sure what it means or implies. It's often said along with the function is "one-to-one".
1
vote
0answers
28 views

Union of two graphs with exactly one common vertex

Does this operation (in the title) have a name? According to the Graph Union operation definition vertex sets of two graphs must be disjoint, however I'd like to define an iterative process of graph ...
3
votes
1answer
82 views

Name of the matrix transform $AA^*$ given A?

There are a number of places this matrix transform making its appearance: Every positive semi-definite matrix $B$ can have a decomposition $B=AA^*$ If the matrix $A$ is a lower triangular matrix ...
0
votes
0answers
29 views

Is there a name for the subDAG of all the descendants (or ancestors) of a node in a DAG?

Is there a name for the subDAG of all the descendants (or ancestors) of a node in a DAG? DAG stands for Directed acyclic graph. A bibliographic pointer would be extremely helpful.
0
votes
0answers
39 views

Is there a name for an object with both position and velocity?

I know of "position vectors" and "velocity vectors". I'm looking for the name of an object which contains both a position vector and velocity vector, if such a name exists?
4
votes
4answers
592 views

How to formulate that an equation be shown to have no solutions?

Is there any general way to formulate the statement that an equation has no solution? For example: Prove that this equation has no solution: $$x^{1/\log x}=5$$ N.B. Do not answer with a ...
1
vote
1answer
29 views

Slice, projection, contour: A terminology question.

Consider a multivariate function, say $y=f(x_1,x_2,\dots,x_n)$, and suppose that $z=f(x_1,x_2,\dots,x_{n-1},g(x_1,x_2,\dots,x_{n-1}))$. What do we call $z$ with respect to $y$? Projection, level set, ...
1
vote
0answers
46 views

“Finite” includes Zero?

It is accepted that the empty set, of cardinality 0, is a finite set. So for phrases like "all but finitely many", or there is "a finite number of", is it accepted that they include the 0 ...
1
vote
0answers
21 views

Usage: Holomorphic Functions

This isn't a math question, but rather a question is word usage in mathematics. Why do people say " $f$ is an isomorphism," or "$f$ is a diffeomorphism," but in complex analysis, we say that "$f$ is ...
1
vote
1answer
21 views

Is there a name for the coordinate on a function which has maximum curvature?

I found out how to find the maximum curvature, by differentiating the curve function. I am wondering if there is a mathematical term, or if there isn't one what is the most elegant way to represent ...
19
votes
9answers
4k views

Is there a word similar to “iff” meaning “one and only one”?

I find the word "iff" for "if and only if" quite helpful for brief statements, but is there a similar one meaning "one and only one"? edit In light of the ambiguities some of the answers so far hint ...
0
votes
0answers
13 views

What is the classification for this dynamic model?

I have the following dynamical system \begin{align*} \dot x(t) &= f(x(t),y(t),t) + w(t)\\ 0 &= g(x(t),y(t),t) \end{align*} where $w(t)$ is zero-mean, white Gaussian noise process. I was ...
2
votes
1answer
55 views

What kind of cohomology is meant?

What kind of cohomology is meant in Deligne's work about mixed hodge structure on cohomology groups of an complex algebraic variety? I think it refers to the singular cohomology with coefficients in ...
0
votes
1answer
30 views

what does it mean to extrapolate?

Doing an assignment and got up to this question "Is is sensible to extrapolate the graph back to the moment when the population was zero? Explain" Don't know how to answer it because I do not know ...
0
votes
2answers
49 views

Names for complement of the union and intersection of two sets.

What is a good name for $ (A \cup B)^c $ or the complement of the union of two sets? Not union? NOR? Union complement? And what is a good name for $ (A \cap B)^c $ or the complement of the ...
0
votes
0answers
26 views

Translation of GENUS to Portuguese

Does somebody know a translation (to portuguese) for "genus" in topology? Theorem: A nonsigular projective curve in $\mathbb{P}_2$ is topologically a sphere with $g$ handles. Definition: This number ...
8
votes
6answers
980 views

what is this sort of function called?

I am doing an assignment but I do not know how to do this problem. I have the following: $$ f(x)= \begin{cases} 0 & \text{for $x<0$},\\ x & \text{for $x\geq 0$}. \end{cases} $$ We are ...
0
votes
0answers
21 views

Spelling: nonabelian or non-abelian?

This is not really a maths question, rather an English language question. Apologies if it's already been asked, it's hard to search. If I wanted to be scrupulous about correct spelling, is there any ...
3
votes
4answers
211 views

How should the term “stronger” be used? Example: groups stronger than semigroups or semigroups stronger than groups?

Everyone is well-known that every group is a semigroup. Then I should say that "group is stronger than semigroup" or "semigroup is stronger than group". Someone told me that stronger means more ...
3
votes
0answers
28 views

Center of the dual of a Lie algebra

Let $\mathfrak{g}$ be a Lie algebra. Let $C \subset \mathfrak{g}^*$ be the subspace of linear forms that vanish on Lie brackets: $$C = \{\alpha \in \mathfrak{g}^*, ~ [\mathfrak{g}, \mathfrak{g}] ...
0
votes
2answers
31 views

The conditions that partial derivatives commute

State the conditions that partial derivatives commute, namely, $D_1D_2f = D_2D_1f$. I understand how to prove that these partial derivatives are equal but I don't understand what commute means. ...
1
vote
0answers
51 views

What really is inductive reasoning?

I am looking for concrete information on "induction" in the old sense of the word. Now it is used to refer to proof by "mathematical induction"; however, I am aware that it also means inductive ...
1
vote
1answer
37 views

difference between equivalent and equal sign

I am reading a statement in which we have to show that $f(x)$ is equivalent to $0$ on an interval. What is differences $f(x)$ is $0$ and $f(x)$ is equivalently $0$ on an interval. Please help. ...
0
votes
1answer
46 views

Correct name for non-unit length 'hessian normal form' 3D plane.

A plane defined as 4 numbers (x,y,z,distance) is known as the hessian normal form, Where the xyz values are unit-length. However I've found its not necessary to ...
1
vote
2answers
38 views

What do you call the operator that takes in a number and spit out sets?

For example, I want to define an operator $P$ that takes in a value and gives all the partition of that value i.e. $P(3) = \{\{3\},\{2,1\},\{1,1,1\}\}$ What do I call such an "operator" $P$?
2
votes
0answers
43 views

a.s. for all $t$ or for all $t$ a.s.?

Assume that we have some equality, $$ X (t) = Y(t). \quad \quad \quad \quad \quad \quad \quad (1) $$ I imagine that if I say "(1) holds a.s. for all $t>0$" it means that $$ P\{X (t) = Y(t) ...
0
votes
3answers
55 views

What is an nonlinear ordinary differential equation and give an example?

What is an nonlinear ordinary differential equation and give an example? And what is the difference between an linear ordinary differential equation and non-linear ordinary differential equation in ...
5
votes
4answers
132 views

Term for similarity transformation which is not a translation

What's the best (i.e. most concise) term to refer to an orientation-preserving similarity transformation which is not a translation? Here are some descriptions I could think of, but all of them feel ...
1
vote
0answers
43 views

Can $y = x^\sqrt{3}$ be considered a Power function? What about a polynomial?

Can $$y = x^\sqrt{3}$$ be considered a Power function? What about a polynomial? Also, is $$y = \sqrt{3}^x$$ an exponential? I am curious about the boundaries which define each type of function. ...
0
votes
1answer
12 views

What exactly does it mean that the key $e \in \mathcal K$ uniquely determines $E_e$?

What exactly does it mean that the key $e \in \mathcal K$ uniquely determines $E_e$ ? Does it mean that for each $e \in \mathcal K$ there exist only one function $E_e$ corresponding to $e$ ? Does ...
0
votes
1answer
62 views

Number theory used in cryptography [duplicate]

I am entering the realm of cryptography and encountering Number Theory related stuff a lot (As expected). I have a good knowledge and background on mathematics but I have been away for a while. So if ...
2
votes
1answer
72 views

Definition of “descends to”

My textbook keeps saying that maps "descend to" other maps. I have never encountered this terminology before (at least not in English). What does it mean? Here is an example: The function $H$ is ...
1
vote
1answer
40 views

What is isobaric function?

I'm reading My Numbers, My Friends by Paulo Ribenboim and I've encountered this: Thus $U_n = f_n(P,Q)$, where $f_n(X,Y) \in \mathbb{Z}[X, Y]$. The function $f_n$ is isobaric of weight $n-1$, where ...
3
votes
0answers
95 views

Cell theory - What is it? - Reference request

A user with $>10,000$ posts on sci.math called 'plutonium.archimedes' or 'AP' is constantly ranting about some theory he deems superior to calculus(a.k.a 'old math' I believe). I can't find any ...
1
vote
1answer
25 views

Local homeomorphisms: terminology

Let $(E,\pi,X)$ be a local homeomorphism, so for any $x\in E$ there is an open set $U\ni x$ such that $\pi|U$ maps $U$ homeomorphically onto $\pi[U]\subseteq X$, and $\pi[U]$ is open in $X$. Is there ...
0
votes
2answers
21 views

Name for line segment parallel to triangle base

In describing an elegant construction of a regular pentagon, i'm struggling to find a nice way of describing the following: A line segment starting at a point partway up one side of a (in this case, ...