All Questions
542 questions
0
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60
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Name for matrix associated to smooth continuation
Is there an established name for the matrices that establish the conditions for a linear combination of $n$ functions $\lbrace f_1(x),\dots,f_n(x)\rbrace$ being the $n$-times smoothly differentiable ...
- 13.2k
0
votes
1
answer
2k
views
Dual of Zorn's Lemma? [closed]
It seems to me that the dual of Zorn's Lemma should be true: if $S$ is a non-empty partially ordered set and every chain of $S$ has a lower bound in $S$, then $S$ has at least one minimal element.
...
- 1
0
votes
1
answer
158
views
Unknown notation in "Boolean function complexity" by Stasys Jukna [closed]
I am currently reading Boolean Function Complexity - Advances and Frontiers by Stasys Jukna and on page 7 of the latest edition there is a paragraph titled Boolean functions as set systems with the ...
- 11
0
votes
1
answer
148
views
Comparing vectors with numbers? [closed]
My question pertains to the paper "A Simplified Proof of the Divergence Theorem" by Djairo Guedes de Figueiredo.
It's not a big question, actually, but it's confusing me a lot: In the statement of ...
- 183
0
votes
1
answer
269
views
What does the *-operation signify in the binary context of two automata?
Hi I have a notation question.
I've recently come across the '*-operation' (star-operation) in the context of a binary operation on two automata e.g., A*B and I'm not sure exactly what it means (and ...
- 141
0
votes
1
answer
74
views
What is the standard notation for bilinear, biquadratic, etc... spaces?
A typical notation for the polynomials of degree $k$ is $P_k$. The space $P_k$ is considered well-suited for interpolation on simplices, although that is hard to put into practice in full generality.
...
- 981
0
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1
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62
views
Is there a common notation to indicate the final form of a simplified definition? [closed]
I'm trying to become better with using proper terminologies and standard notation when taking notes, which lead me to think:
Similar to the indication of a completed proof by use of the Q.E.D. mark, ...
- 23
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votes
1
answer
54
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Writing a set of all possible (symmetric) products condensely? [closed]
I have a set of elements $\{a_1, a_2, a_3...\}$ and $\{b_1, b_2, b_3...\}$ and I want to condensely formally write the set of all possible products of these elements, where the ordering does not ...
- 1,465
0
votes
1
answer
82
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Computability Theory Notation For Entering A Set At A Stage
Is there a standard (or at least common) symbol in computability theory used to indicate that $x$ enters the c.e. set $W_e$ at stage $s$, i.e., $x \in W_{e,s} - W_{e,s-1}$ (at least for $s \neq 0$)?
...
- 3,029
0
votes
1
answer
114
views
Name of a matrix with one column and row removed [closed]
I am looking for the exact name of a matrix where the i-th column and rows have been removed.
I cannot remember how it is called in linear algebra, does anyone got an idea?
Thanks!
- 111
0
votes
1
answer
179
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Theory of integration of Kernel in çinlar probability and stochastic
I'm reading the probabilistic book write by çinlar, but I don't understand the Kernel theory, in details:
$ (E,\mathcal{E}),(F,\mathcal{F})$ are two measurable space
$$K:E \times \mathcal{F} \...
user96954
0
votes
1
answer
328
views
Meaning of $[A,B]$ when $A$, $B$ are self-adjoint
This is just a question about notation, but it got no useful answers on math.stackexchange.
Let $L$ be the Lie algebra of $n\times n$ Hermitian matrices, with Lie bracket $(A,B)\mapsto i(AB-BA)$.
...
- 23k
0
votes
1
answer
155
views
Help with notation for the state of a dynamical system defined by a PDE
Before my question let me briefly describe a simplified version of the dynamical system I'm working with. Suppose that I have a density function $m(\boldsymbol{x},t)$, that describes the abundance of ...
0
votes
1
answer
860
views
Sierpinski Triangle and the Chaos Game
The chaos game is a way to construct (an approximation) of Sierpinski triangle. It's clear (using Thales' theorem!) that if we begin with a point on the sierpinski triangle, then we will never leave ...
- 87
0
votes
0
answers
123
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Is there a good or commonly accepted short notation for the set of differentiable, but not necessarily continuously differentiable maps?
Every once in a while I find myself in need of some short notation for the set of differentiable, but not continuously differentiable maps, say, $X \to Y$. Always having to specify "...
- 7,127
0
votes
0
answers
35
views
How to talk about the “shape” of the kernel of an integral transform
So I'm learning about integral transforms, and although it isn't a complete specification, the fact that the Fourier transform decomposes functions into sinusoids, the Laplace into damped sinusoids, ...
0
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0
answers
149
views
Notation $\le_{a,b,n,\ldots}$ in Analysis
In modern Analysis, especially Functional Analysis, one proves, or one uses inequalities of the form
$$F(X)\le_{a,\ldots,n}G(X).$$
The meaning of the subscripts in the inequality sign means that there ...
- 52.4k
0
votes
0
answers
105
views
Definition of term functions, in universal algebra
According to the definitions in Sankappanavar's universal algebra :
Assume $p$ is a term, then $p(x_1,x_2,...,x_n)$ indicates that the variables occurring in $p$ are among $x_1,...,x_n$. But there is ...
- 11
0
votes
0
answers
102
views
Merging two composable walks in a graph
Let $G$ be a graph (i.e., an undirected graph in which we allow for loops and parallel edges). Denote by $V$ the vertex set, by $E$ the edge set, and by $\psi$ the incidence function of $G$, and let $\...
- 10.5k
0
votes
0
answers
304
views
Is Baire's theorem stronger than needed for functional analysis?
Many classic theorems in functional analysis involve using Baire's theorem to prove facts about topology that relate to maps between Banach spaces (or, more generally, F-spaces). The application ...
- 109
0
votes
0
answers
148
views
About the theorem of Weierstrass?
Is $E=Vect\{1,x,x^2,...,x^{2^n},...\}$ dense in $C([0,1])$ for the uniform norm?
While looking for a short proof for Weierstrass' theorem, I came across this justification(*) (which shows this result)...
- 4,074
0
votes
1
answer
125
views
Are there search algorithms that are competitive against (gradient based) optimization routines for continuous problems?
Suppose that $f: \mathbb{R}^n \to \mathbb{R}$ is a continuous function for which we want to minimize. We may arbitrarily impose good conditions for $f$, such as Lipschitzness, smoothness, convexity, ...
- 479
0
votes
0
answers
290
views
A question about chaining Vinogradov notation
This is not a research question, but I hope it is still legitimate to ask for this platform. Suppose $A(x)$, $B(x)$, $C(x)$, $D(x)$ are positive-valued functions of $x$, and
$A(x) \ll B(x)$ and $ C(x) ...
- 6,224
0
votes
0
answers
39
views
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 ...
- 188
0
votes
0
answers
45
views
Notation of $P^+$-families - bibliography searching
have you ever met with notation of $P^+$-families in other papers than Iian B. Smythe "A local Ramsey theory for block sequences" and his phd?
Thank you in advance
0
votes
0
answers
645
views
Notation for iterated summation
Is there a more compact way to write
$$
\sum_{i_1=0}^{N}
\sum_{i_2=0}^{N-i_1}
\sum_{i_3=0}^{N-i_1-i_2}
\cdots
\sum_{i_{K}=0}^{N-i_1-i_2-i_3-\ldots-i_{K-1}}
a_{i_1i_2i_3\ldots i_K}
$$
as something like
...
- 113
0
votes
0
answers
82
views
Format of grading Witt Lie Algebra
Let $W(n,m)$ be generalized Jacobson-Witt algebra over a field of characteristic $p>3$. According to the grading of $W(n,m)$, we know that it inherits the grading from $A(n,m)$ as follows: $$W(n,m)...
- 367
0
votes
1
answer
552
views
Teaching profession:Differential Equations and Mean Value Theorems
Usually I teach Algebra,Algebra and Geometyry, Topology, at various University levels. This semester (Spring 2014) I have to teach Differential Equations to University second year students (4th ...
- 1,422
0
votes
0
answers
142
views
Notation for substructure, especially for permutations?
Is there a standard notation that expresses substructure?
The specific case that I care about is the following:
Suppose $\sigma,\tau$ are permutations such that $$\sigma(x)\not=x\implies \sigma(x)=\...
- 1,329
0
votes
0
answers
166
views
Is $\{x_{zt}\}_{Z\times~ T}$ a good notation for specifying the indexed family of entities $x_{zt}$ with $z\in Z,\, t\in T$?
I have a model with lots of variables indexed over a few sets.
After having introduced the model, i.e. having already said that $x_{zt}$ has indexes $z\in Z$ and $t\in T$, instead of writing
"we ...
- 151
0
votes
0
answers
379
views
Terminology for the image of the diagonal embedding.
Let $X$ be a topological space equipped with maps into two spaces $\bar X_1$ and $\bar X_2$. Is there a standard notation/terminology for the closure $\bar X$ in $\bar X_1 \times \bar X_2$ of the ...
- 5,359
0
votes
0
answers
678
views
Notation for isometric spaces?
Metric spaces are isometric if there exists a bijective isometry between them.
Is there a standard notation for this, along the same lines as $X\approx Y$ for homeomorphic spaces and $X\simeq Y$ for ...
- 35.9k
0
votes
2
answers
1k
views
What is a maximal set in the context of argumentation in AI [closed]
I am computer scientist, not a mathematician, I've been reading some papers on argumentation in AI that uses the term 'maximal' set without defining it. I think it's left undefined because it's a ...
- 187
0
votes
2
answers
383
views
"X \in \cdot" in Probability Measure [closed]
My question is quite simple, but I was unable to find an answer by googling, since you can't exactly google syntax. What does the $\in \cdot$ mean in:
$$\lim_{n\to\inf}||P(S_n\in\cdot)-P(S_n+k\in\cdot)...
- 3
-1
votes
1
answer
187
views
Typesetting of symbols and "operators" denoting sets [closed]
Question:
what are the conventions for typesetting sets of certain objects, especially the vertices and edges of a graph or those adjacent to an edge or vertex.
For vectors and matrices there is the ...
- 13.2k
-1
votes
1
answer
118
views
Relative degree of a prime over a number field (notation from Algebraic Number Fields from Gerald J. Janusz) [closed]
I´m working with "Algebraic Number Fields" from Gerald J. Janusz (1. edition from 1973) and I have a question about his notation.
In chapter IV proposition 4.5 he states if K is an algebraic number ...
- 13
-1
votes
1
answer
124
views
Typed Values in Formulas
Question:
are there any "standard" ways of indicating the meaning of numerical values in formulas, resp. general mathematical texts (theorems, proofs, etc.)?
I am especially looking for ...
- 13.2k
-2
votes
1
answer
514
views
Correction symbols used for mathematical texts [closed]
When proof reading and correcting a mathematical text, I sometimes see people use special notation symbols in the margin to indicate correction, deletion, replacement and so on. Is there any standard ...
- 177
-2
votes
1
answer
5k
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_{\{0,1\}}(x)...
- 121
-2
votes
1
answer
120
views
Is this single-variable function being called with two variables (and if so, how do I handle that), or am I misreading the notation? [closed]
While working on a project, I came across a paper that includes this sum on page 15 as the definition of a support function $r$ for a surface with tetrahedral symmetry:
$$
r(ξ, \bar{ξ}) = \frac{1}{\#𝒢...
- 105
-3
votes
1
answer
222
views
What is the basis for the quantifier notation? [closed]
The symbols $\forall, \exists$ are the ones officially used to denote universal and existential quantifiers respectively. I understand that the choice of $\exists$ was made by Peano, while of $\forall$...
- 11.3k
-4
votes
2
answers
228
views
An elementary-looking integral inequality
This might seem a bit easy but I still like to ask it for pedagogical reasons.
QUESTION. Is this inequality true for non-negative integers $n$?
$$\frac{\pi}2\int_0^1x^n\sin\left(\frac{\pi}2x\right)dx\...
- 43.2k