Highest scored questions
159,029 questions
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strict convexity and Lipschitz continuity [closed]
Consider a continuously differentiable function $f: \mathbb{R}^n \mapsto \mathbb{R}$. If $f$ is strictly convex, does it imply that it is not Lipschitz on $\mathbb{R}^n$?
Because if $f$ is strictly ...
- 125
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votes
2
answers
224
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What happens if I replace a *unique natural number* that form a commutative Monoid with *the set of integers* Z that form a commutative Ring? [closed]
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was ...
-4
votes
1
answer
1k
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Is there an algorithm to generate graph edges given amount of vertices and edges per node? [closed]
Is there currently an algorithm that given the number of vertices / nodes n, and the number of edges per node l, output all ...
- 111
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1
answer
258
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Does the number 1,23571113... has been studied before? [closed]
I just can't get this number out of my head. It's a number that has the decimal digits composed by all the prime numbers.
The first digit is not important, it can be 0,2357... or 1,2357...
Does ...
-4
votes
1
answer
224
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Does one need an external, peer-reviewed grant to become tenured faculty in this field? [closed]
As a secondary question, how important is it to be awarded grants to remain employed as a PhD mathematician at an academic research institution? Is it common or uncommon for PhD mathematicians to have ...
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2
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425
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If mathematics is logic and intuition, then [closed]
I am just wondering why Mathematics is often defined as The study of Structures, Logic and Numbers which I can concur with but still retain various questions in mind.
I am a postgraduate student of ...
-4
votes
2
answers
286
views
Does the Laplacian commutes with the indicator function [closed]
We define the laplacian operator $\Delta$ with the Neumann boundary conditions on the space $H^2(\Omega)$, where $\Omega$ is an open set of $\mathbb{R}^n$ with a smooth boundary $\partial\Omega$, and ...
-4
votes
1
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571
views
Derivatives of infinite order [closed]
Is there any sense of taking an infinite number of derivatives? Is it discussed in the literature?
For example, can one make sense of
$$\frac{\partial^{\infty}f(x_1,x_2,\cdots)}{\partial x_1 \...
- 1,594
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votes
1
answer
514
views
Meaning of the Mobius transformations video [closed]
What is this video trying to tell us?
http://www.youtube.com/watch?v=JX3VmDgiFnY
The statement that fractional linear transformations correspond to rotations of the sphere under the stereographic ...
- 1,783
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1
answer
139
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The solution of Green’s function in Dirac Delta ODE
I’m asking about the solution of the 2nd order Green’s function ODE:
$$\left( \dfrac{d^2}{d\eta^2}+ q^2 - 1 \right) g(\eta) = \delta(\eta-\tilde{\eta}) $$
Which is given by:
$$ g(\eta) = c_1~ e^{t\...
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1
answer
151
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7-sphere x 4-sphere manifold and its physical significance [closed]
I am looking for sources about this manifold 7-sphere*4-sphere and its relations to theoretical physics.
Where to go to read about 7-sphereX4-sphere manifold and its physical significance?
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1
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63
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if $\max_i \frac{x_i}{c_i}>\max_i \frac{y_i}{c_i}$,whether $max_i\frac{x_i}{d_i}>\max_i \frac{y_i}{d_i}$ is right [closed]
if $x_i,y_i,c_i,d_i>0$ all are monotonically decreasing sequences,
$$\max_i \frac{x_i}{c_i}>\max_i \frac{y_i}{c_i}$$
then $$max_i\frac{x_i}{d_i} \geq \max_i \frac{y_i}{d_i}$$
can be derived？
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1
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267
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Is Nested Selection equivalent to AC?
Nested Selection: For every infinite set $G$ of pairwise disjoint infinite sets such that any two distinct elements $x,y$ of $G$ either "$y$ is a set of proper supersets of elements of $x$ and ...
- 11.3k
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1
answer
227
views
What are the applications of spin geometry? [closed]
What are applications of spin geometry to physics? Does it have something to do with gravity?
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2
answers
405
views
Do these irrationals exist?
An irrational $a$ verifies : $\{a\times n+k;(n,k)\in\mathbb Z^2 \}$ is dense in $\mathbb R$.
If you take $a$ universe then : $\forall b\in \mathbb N^*, \{a\times n^{b}+k;(n,k)\in\mathbb Z^2\}=A(a,b)$ ...
- 4,074
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votes
1
answer
186
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Graphics software [closed]
Do you have any suggestions about free mathematical graphics software? I need to do some drawings of polyhedrons and a drawing of intersection between polyhedron and a circle.
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1
answer
178
views
Covering system of congruences with specific properties?
A family of residue classes $a_i (\bmod n_i)$ with $2\leq n_1\leq\cdots\leq n_r$, ($r\geq2$) is called a covering system of congruences if every integer belongs to at least one of the residue classes, ...
- 841
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1
answer
250
views
What are the patterns of the sequence of polynomials? [closed]
In my research, I obtained a sequence of polynomials (I am only able to compute the first 4 of them):
\begin{align}
& f(2) = 1+t, \\
& f(3) = 1+4t+3t^2, \\
& f(4) = 1+6t+12t^2+7t^3, \\
&...
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1
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412
views
A topological groupoid structure on a pair $(X,A)$
Assume that $X$ is a compact Hausdorff space and $A\subset X$ is a retract of $X$.
Is there a topological groupoid structure on the topological pair $(X,A)$ where, in the corresponding ...
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2
answers
226
views
Diagonal argument for even perfect numbers
Following this, let's define the notion of perfect sequence as follows:
$(u_{i})_{i}$ is a perfect sequence if and only if it is the sequence of divisors of an even perfect number in increasing order ...
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1
answer
224
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Elliptic Curve Multiplication [closed]
What would happen if I performed Elliptic Curve multiplication on some random point within the FiniteField that wasn't actually on the curve? I assume that I would get a point in return but would that ...
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votes
1
answer
1k
views
Space packing fraction of tetrahedron and octahedron [closed]
If four equal size spheres form close-packed tetrahedron, what is the fraction of space that is occupied/unoccupied by the spheres in the tetrahedron.
Similarly, if six equal size spheres form close-...
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votes
2
answers
357
views
Representing quaternions as matrices [closed]
Assume F is a field of characteristic different than 2. Let a, b be invertible elements in F, and let A(a,b) be the generalised quaternions. Using the Artin–Wedderburn theorem, there is a ...
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1
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200
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How I can choose $(t_1,t_2,...,t_{r}) \in (0,1)^{r}$ such that $f^{(k)}\left(1-2\prod_{j=1}^{k}t_{j}\right)=0$?
Let $f:\mathbb{R} \to \mathbb{R}$ be a real analytic function. Assume that $f$ has simple trivial zeros at each nonpositive integer. Then, all the $k$-th derivatives $f^{(k)}$ of $f$ have necessarily ...
- 1,197
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1
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483
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Why $z \in \overline{A}$? [closed]
In the Picture blew:
The paper can be downloaded here. Why $z \in \overline{A}$?
Thanks.
A point $x$ of a space $X$ is called $G_\omega$-separated from a subset $Y$ of $X$ if there is a closed $G_\...
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8k
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How to transform a plane into a sphere? [SOLVED] [closed]
Given a 2-dimensional array of MxN heights, how to transform it to a sphere? Every element of this array is just a 3D point (x,y,z) where z represents some height. One has to transform this array into ...
- 555
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173
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To which arithmetic\set theory this theory is bi-interpretable?
$\textbf{Logic:}$ Mono-sorted first order logic with equality.
$\textbf{Extralogical Primitives: } <, \in$
$ \textbf{Axioms:}$
$ \textbf{Order:} \ x < y < z \to x < z $
$ \textbf{...
- 11.3k
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1
answer
108
views
An integral similar to the Delta function [closed]
I have an integral on the form
$\int_{-\infty}^{\infty} e^{-k \omega' |\tau|} e^{i \tau(\omega'-\omega)} d\tau$
that I would like to simplify (or basically solve). This indeed comes from a problem ...
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1
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635
views
Can we arrange {1,...,9} in 3×3 grid so the set of products of rows equals the set of products of columns? [closed]
I find a interesting question of Prmo mock and Promys 2020
For which $n\in\mathbb{N}$ is it possible to arrange $\{1,…,n^2\}$ in an $n\times n$ grid so that the set of products of columns equals the ...
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2
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255
views
$a^2+b^2$ is the product of two numbers one the reverse of the other [closed]
As an example:
$429^2+101^2=394\cdot 493$.
394 is the reverse of 493.
Are there infinitely many
$a^2+b^2$ which are the product of a number and his reverse?
a,b positive integers
Second question:
Are ...
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votes
1
answer
525
views
Need list of top journals with shortest review time [closed]
I want to publish a paper in a math journal. I want to know the list of top journals which have the shortest review time.
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1
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409
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Scaled Riemann zeta function with no zero in the critical strip
Update: I added $exp[i\theta_k(s)]$ in the definition of $\eta^*(s)$ to address some critical convergence issues. Thanks for the contributors who pointed to these issues.
Prime numbers are denoted as $...
- 3,098
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1
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371
views
Is delta function symmetric against real axis? [closed]
Is $\delta\left(a+bi\right)=\delta\left(a-bi\right)$?
I wonder whether Dirac Delta (as defined via Fourier transform) is symmetric against the real axis.
We can write Delta function as
$$\delta(z) = \...
- 10.1k
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votes
1
answer
66
views
Can we say that $\{f_n\}\text{ is uniformly integrable over }E\setminus (\cap_p B_p)$? [closed]
Let $(E,\mathcal{A},\mu)$ be probability space and $\{f_n\}$ be sequence of functions such that
$$
\sup_n\int_{E}|f_n|d\mu<+\infty.
$$
Let $\{B_p\}$ be a sequence non-increasing in $\mathcal{A}$...
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1
answer
97
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Two notions of boundedness in metrizable topological vector space [closed]
In a metrizable topological vector space X with the metric d, a subset A is said to be bounded if it can be absorbed by any neighbourhood of 0 and a subset A is said to be d-bounded if its diameter ...
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1
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177
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Topological spaces without retracts [closed]
Is there a way to see whether a topological space $\Omega$ does not allow retractions $r: \Omega \mapsto B$, with $B$ a given subspace of $\Omega$ ?
In other words: when is a space not retractable ...
- 4,555
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359
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Can there be such an elementary embedding?
EDIT: it appears that my original question has some confusion between auto-morphisms and elementary embeddings as it is obvious from the answer below, therefore I'll clarify here what I exactly want.
...
- 11.3k
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1
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158
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Connected infinite graph $G$ with $\delta(G)\geq 2$ and no perfect matching [closed]
Is there a connected infinite graph $G=(V,E)$ such that $\text{deg}(v) \geq 2$ for all $v\in V$, and $G$ possesses no perfect matching?
- 48.9k
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1
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387
views
Eigenvalues of real symmetric matrix [closed]
Suppose $A$ is a $n \times n$ real symmetric matrix with entries $a_{ij}\geq 1 $ and $a_{ii} = 0 $. Is it possible to have sum of the absolute eigenvalues of
$A < 2 (n - 1).$
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votes
1
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218
views
Bipartite graph [closed]
First of all, thank you for your time to reading my post.
I am a researcher but not a mathematician, i have some difficulties in solving a math problem, that why i am here to ask your help. I just ...
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votes
1
answer
2k
views
Open mapping theorem for Riemann surfaces
What restriction must one impose on a Riemann surface M in order for all biholomorphic $f:M\to\mathbb{C}$ to be open mappings, aka mappings of $M$ onto open subsets $f(M)\subset\mathbb{C}$?
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1
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342
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Orthogonality of invariant subspaces for restricted representations [closed]
Let $G$ be a finite group and $H_1$ and $H_2$ are two proper subgroups of $G$. Also, let $\rho:G \rightarrow \mathbb{C}^m \times \mathbb{C}^m$ be an irreducible non-trivial representation of $G$. Let $...
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2
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1k
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In Bayesian statistics, must I use a marginalized prior in conjunction with a marginalized distribution?// [closed]
Suppose I have some sampling distribution g(x,y,z) which has been marginalized over some variables (say y and z) giving us the marginal distribution which we'll call gx(x).
Suppose I now wish to use ...
- 379
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votes
1
answer
197
views
How to express a quadratic polynomial exactly as a power series [closed]
I claim, for $\operatorname{artanh}(\rho) = \frac{1}{2} \ln\left(\frac{1+\rho}{1-\rho}\right)$, i.e., the inverse hyperbolic tangent function, the following holds approximately under assumptions given ...
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1
answer
56
views
What is 30th permutation of elements 1,3,5,7,9? [closed]
The answer is: 31975
But how do I get the answer with a method?
-4
votes
1
answer
112
views
Uncountable Cantor's diagonal argument on $S^2$ [closed]
Let $F: S^2 \rightarrow \mathbb{R}^2$ be a continuous function. Does there exist a unit vector $v \in \mathbb{R}^2$ and a continuous function $f(x):S^2\rightarrow \mathbb{R}$ such that $f(x)>0$ on $...
- 434
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votes
1
answer
159
views
Numbers that can be expressed as the sum of a Power of six and a Power of seven. Are there presumibly infinitely many Wagstaff so expressible? [closed]
Wagstaff Number $2617$ can be expressed as $7^4+6^3$.
Is there an Oeis sequence that lists all the numbers that can be expressed as the sum of a Power of six and a Power of seven?
Are there other ...
- 3
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votes
1
answer
136
views
Exponential order of unipotent elements in an endomorphism ring of abelian groups
$\DeclareMathOperator\End{End}\newcommand{\Id}{\mathrm{Id}}$Let $E=\End(I)$ be the endomorphism ring of the abelian group $I$.
We have the following statement for $B\in E$, $p$ a prime number and $r$ ...
- 93
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votes
1
answer
98
views
Convex combination of $\frac{1}{x}$ inequality [closed]
Let $0 < x_1 \leq ... \leq x_n$ and $\sum \alpha_i = 1, \alpha_i \geq 0$. Show
$\sum \frac{\alpha_i}{x_i} \leq \frac{x_1 + x_n - \sum \alpha_i x_i}{x_1 x_n} $. Since the left side looks like a ...
-4
votes
1
answer
221
views
Defining Legendre polynomials in terms of a sinusoidal function for $|x| \leq 1$
Would it be possible to define Legendre polynomials in terms of a sinusoidal function for $|x|\leq 1$ in a similar manner to Chebyshev polynomials being defined as $T_n(x) = \cos(n \cos^{-1}(x))$?
...
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