Highest scored questions
159,037 questions
-2
votes
2
answers
134
views
On the 2018 paper "On the discretization of Laine equations" by K. Zheltukhin, et al [closed]
I desperately need to read this paper, before meeting a would-be supervisor but with limited undergraduate knowledge that I have like Aluffi's Algebra and Churchill's Complex Analysis, Rudin's ...
user135767
-2
votes
1
answer
108
views
Sum of: k permutations of n $\times e^x$
Simplify the following:
\begin{equation}
\sum\limits_{\ell =1}^n P(n,\ell) (e^x -1)^\ell
\end{equation}
to something like $n!n^n$. I got curious about this expression after going through this ...
- 37
-2
votes
1
answer
91
views
Decomposition of one Matrix into six matrices [closed]
He folks, here's my problem:
Let $\mathbf{A}, \mathbf{B}, \mathbf{X}_1, \mathbf{X}_2, \mathbf{X}_3, \mathbf{Y}_1, \mathbf{Y}_2, \mathbf{Y}_3\in\mathbb{R}^{3\times 3}$ with determinante det()=+1. The ...
- 3
-2
votes
1
answer
47
views
Using common samples to numerically estimate pairwise equality of three random variables
Let $X,Y,Z$ be three discrete random variables which I can numerically sample. I need to numerically estimate the probability that $X=Y$ and the probability that $X=Z$. I would like to know whether ...
-2
votes
1
answer
66
views
I need help with snake's position bounds based on center point(rounded) and the length of the snake problem [closed]
First of all, if it's an existing problem just tell me the name, please. To solve the problem a formula/algorythm which receivs a center point of a snake (snake game type (points on a grid connected ...
- 9
-2
votes
1
answer
209
views
Strong estimates for the zeta function on natural numbers
Let $$\zeta(s) = \sum_{n = 1}^\infty \frac{1}{n^s}$$
be the Riemann zeta function (here we just consider real $s$).
We do have a description given by
$$\zeta(s) = \frac{s}{s-1}-s\int_{1}^\infty \frac{...
- 749
-2
votes
1
answer
140
views
Find a columns of matrix $A$ which form a basis of columns space of matrix $A$ [closed]
We have a matrix $A$ whose rows are data records and whose columns are features. We would like to omit useless features such as zero or constant columns, duplicate columns, columns that are equal to ...
- 1
-2
votes
1
answer
118
views
Six stacked circles, not quite symmetrical [closed]
There are six neatly-stacked circles of radius r.
➊ Circle with centre at {−1,0}.
➌ Circle with centre at {+1,0}.
➋ Circle between ➊ and ➌ with centre at {x,0}, x ∈ ℝ, r−1 ≤ x−r, x+r ≤ 1−r.
➍ A ...
- 199
-2
votes
1
answer
92
views
An inequality between two real-valued concave functions
Can anyone help me prove the following inequality? Thanks!
- 9
-2
votes
1
answer
48
views
Rotating a known vector over two axis-es to result to another known vector [closed]
Lets assume i have a known vector, for example x = [1,0,0]
After 2 rotations, one over the y axis and one over the z axis, i result in a vector which in this example is x' = [0.5774, 0.5774, 0.5774]
...
-2
votes
1
answer
125
views
When are/ if recursive identities used? [closed]
Due to the fact that $$\Gamma(x)\Gamma(1-x)\sin \pi x=\pi$$
is this necessarily true:
$$\Gamma(x)\Gamma(1-x)\sin(\Gamma(1+x)\Gamma(1-x)\sin(\cdots))=\pi$$
Is this at all used as a tactic to create ...
- 107
-2
votes
1
answer
187
views
behavior of multiplicity in exact sequences
Bruns-Herzog define multiplicity When the ring and module are not necessarily graded as $e(M)=e(gr_m(M))$, see B-H 4.6. I have two questions:
Question1. Many concepts in commutative algebra have ...
- 1,355
-2
votes
1
answer
298
views
If $(X_n+Y_n)$ has bounded variance, is the same true for $(X_n)$ and $(Y_n)$? [closed]
Let $(X_n)$ and $(Y_n)$ be two sequences of random variables defined on the same probability space such that the variance of all components $X_n$, $Y_n$ is finite and the sequence of variances of $X_n+...
- 235
-2
votes
1
answer
870
views
Calculate GPS coordinates at x meters [closed]
I want to calculate a pair of GPS coordinates(lat,long) that is at x meters N/S/E/W from a known point (lat_old,long_old).
I have found the Haversine formula
http://upload.wikimedia.org/math/0/5/5/...
- 101
-2
votes
1
answer
198
views
Inequality with four variables [closed]
Prove or find a counterexample.
Let $a_1, a_2, b_1, b_2 \in \mathbb{R}$ satisfy $a_1+a_2=1$ and $b_1+b_2=1$. Then,
$$
\frac{1}{a_1^2+a_2^2} + \frac{1}{b_1^2 + b_2^2} \geq (\frac{1}{(a_1 b_2)^2 + (a_1 ...
- 57
-2
votes
1
answer
871
views
Rank of a random matrix
Let $x$ a random Gaussian vector of size $n$ with i.i.d coefficients $N(0,1)$. Let $J$ a random matrix with i.i.d coefficients $N(0,\sigma^2/n)$ where $\sigma \in [0,1]$. For any integer T>n, define:
$...
- 840
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votes
1
answer
690
views
A Poincare inequality for the Laplace-Beltrami operator [closed]
Suppose $w \in C^2 (S^{n-1}), \Lambda$ is Laplace-Beltrami operator on the sphere $S^{n-1}$, How can I prove follow Poincare inequality :
$\int_{S^{n-1}} w\Lambda w d\sigma \leq (1-n) \int_{S^{n-1}} |...
- 21
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votes
1
answer
523
views
Inverse Laplace transform in a signal that is a sum of exponentials - MATLAB [closed]
I want to analyze a discrete signal in time, that is sum of exponentials distributed around two distinct values (T1, T2). My goal is to calculate these two different distributions, T1, T2, weights and ...
- 3
-2
votes
1
answer
318
views
Holder class of analytic functions
Assume that $\lim_{(nt) |z|\to 1}|f(z)|(1-|z|)^p=0$, where $f$ is analytic in the unit disk and $p>0$,where $(nt)|z|\to 1$ nontangentially. Does this implies that $\lim_{|z|\to 1}|f(z)|(1-|z|)^p=0$...
- 259
-2
votes
1
answer
332
views
A kind of economic objective function in assignment
I recently thought about a concept that seems like it should come up in economics, but I don't know if there's a name for it and where people would have encountered it elsewhere: Suppose we have a ...
-2
votes
1
answer
1k
views
weak star convergence [closed]
if $F$ is a Banach space and $f_n \subset F^* $ weak star convergent to $f\in F^*$. If further $x\in F$ is the weak limit of $(x_n)_n \subset F$ does then $f_n(x_n) \longrightarrow f(x)$ hold?
We ...
- 1
-2
votes
1
answer
891
views
derivative of a function of time using its inverse fourier transform
What would be the bounds on the derivative of a function using its inverse fourier transform representation. Furthermore what would be the bounds on the absolute value of the function itself?
- 101
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votes
1
answer
444
views
Mul + div using only add/sub ? [closed]
In an algorithm book once the first example was how to compute a multiplication in a loop (only that, so I just remembered, and wanted to do it programmatically but with all operations)
...
- 1
-2
votes
3
answers
2k
views
Convergence of a markov matrix
Consider a markov chain matrix P of size n x n (n states).
P is known to be:
1- Not irreducible (i.e. there exist at least a pair of states i, j such that we cannot go from i to j)
2- Not all ...
- 27
-2
votes
1
answer
211
views
Would this alteration safeguard the resulting theory from inconsistency?
If we replace "Emergence" axiom in the theory $T$ presented at posting "What is the set theory synonymous with this order-set theory?" with the following axiom, call the resulting ...
- 11.3k
-2
votes
1
answer
309
views
Follow-up question re: logarithms of matrix-valued functions known not to have any zero eigenvalues [closed]
Given two parametrised "well-behaved" real skew-symmetric matrix-valued functions (of real variable(s)) $K(x)$ and $L(x)$, is it true that there exists another matrix-valued function $M(x)$ ...
- 286
-2
votes
1
answer
205
views
Are there infinitely many karmic numbers, i.e numbers whose primality radii equal one or a prime power?
For $n$ a large enough positive composite integer, say $r$ is a primality radius of $n$ if both $n-r$ and $n+r$ are prime. Say $n$ is a karmic number if the following holds: $r$ is a primality radius ...
- 6,982
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votes
1
answer
185
views
What do you call continous transformations that preserve the finite group structure?
A number of years ago I studied a preon model (Journal of Mathematical Physics 38:3414-3426, 1997) in which the preons interacted like group elements. I thought it curious that you could sometimes ...
-2
votes
1
answer
210
views
class structure constants relation
Let $C_{j,k}^l$ ,usually called class structure constants, eg Jansen and Boon and/or JQ Chen, be the number of times the class $l$ is generated from the product of classes $j,k$ and $c_j=c_{-j}$ (a ...
-2
votes
1
answer
326
views
Expressing a value related to an infinitary relation through ultrafilters
Let $U$ be a set. I denote $\mathfrak{A}$ the lattice of filters on $U$ ordered reverse to set theoretic inclusion of filters. I denote $\bigvee$ and $\bigwedge$ correspondingly the supremum and ...
- 765
-2
votes
1
answer
6k
views
calculate percentiles from a histogram [closed]
Hi,
Could someone explain to me or point out some documentation on how to compute a given percentile from a histogram ?
-2
votes
1
answer
151
views
Quadratic extension and prime ideals
Let $B/A$ be a quadratic Galois extension between local domains. Define ${\mathrm{Gal}}(B/A) = \{e,\sigma\}$.
Choose two prime ideals ${\frak P}_1, {\frak P}_2$ of $B$ such that ${\frak P}_2 = {\...
- 781
-3
votes
4
answers
5k
views
What is the situation with Hilbert's Fifth Problem?
The common knowledge in this regard seems to be that Hilbert's Fifth Problem was completely solved by Gleason, Montgomery, and Zippin. However, such wisdom was contested by Peter Olver:
Olver, Peter ...
-3
votes
2
answers
820
views
Is there a "weak" fundamental theorem of algebra for matrices?
Let $R$ be the ring of complex $n\times n$ matrices, where $n>1$.
Does every nonconstant polynomial in $R[X]$ have a root in $R$?
Note: The "strong" fundamental theorem of algebra for ...
- 360
-3
votes
1
answer
2k
views
Quantum dynamics on varieties and Salmon Prizes
Concluding Progressive Remarks
A new finding is Bates and Oeding's preprint "Toward a salmon conjecture" (arXiv:1009.6181), with its reference to the Salmon Prize.
The Salmon Prize (photo of the ...
-3
votes
3
answers
2k
views
Closed form solution to x^(x+1)=(x+1)^x [closed]
From an elementary question in differential entropy for decision sequences...
Numerical solutions is: x = 2.293166287408052...
The equality is only well defined (with respect to its origination) in ...
- 33
-3
votes
2
answers
241
views
Continuum hypothesis and cardinality of infinite tree paths [closed]
Suppose a tree with nodes located at levels $1,2,3...$. At each level the nodes branch into several nodes or do not branch.
Does the cardinality of the set of all infinite paths in this tree depend on ...
- 10.1k
-3
votes
3
answers
810
views
Is true arithmetic + $\lnot Con (TA)$ consistent?
Is the theory $TA+\lnot Con(TA)$ consistent?
In particular, for every $TA \vdash \phi$, we take as an axiom $\phi$, and $TA \vdash \phi$. We also assert $TA \vdash 0 = 1$. We call this theory $TA + \...
- 6,353
-3
votes
1
answer
638
views
Analysis I, simpler proof of Tao's construction of the integers [closed]
In chapter 4 of Analysis I by Terence Tao, we have the following note about the set theoretic construction of the integers:
In the language of set theory, what we are doing here is starting with the ...
- 23
-3
votes
1
answer
575
views
Digit sum of a prime number [closed]
Let 𝑝 be a positive integer and
𝑞 = 𝑆(𝑝) be the digit sum of 𝑝 such that
𝑞 + 1 ≡ 0 (mod 2).
Is it that if 𝑝 is prime then 𝑞 is also prime?
e.g. 𝑝=47(prime)-> 𝑞=4+7=11 (prime)
- 15
-3
votes
3
answers
836
views
Can different extensions of ZF have contradictory consequences for first-order arithmetic?
My question is basically, does there exist a statement X independent of ZF such that ZF + X implies a statement P of first-order arithmetic, but ZF + not X implies not P?
Now X cannot be the axiom ...
- 4,597
-3
votes
1
answer
962
views
Maximum element order in $S_n$ [closed]
Denote by $S_n$ the group of permutations of the set $\{1,\ldots,n\}$ with composition as binary operation. Let $m_n$ denote the maximum order that an element of $S_n$ can have. What is the smallest ...
- 48.9k
-3
votes
1
answer
3k
views
Why sheaves are important and why do we care about them? [closed]
Presheaves are contravariant functors from a category $C$ to the category $Set$, that is functors $P$:
$$P:C^{op}\to Set.$$
For every topology $J$ on $C$ we can generate a reflexive subcategory
$$Sh(...
- 391
-3
votes
1
answer
544
views
Why do we need to represent integers as the sum of three cubes? [closed]
It is conjectured that for any integer $k\not\equiv \pm 4\pmod 9$ there are infinitely many integer solutions to
$$
a^3+b^3+c^3=k.
$$
Some cases for integer $k$ becomes too hard like $42$ which it ...
-3
votes
1
answer
632
views
Can mathematics help in defining free-will? [closed]
In the celebrated Free Will Theorem of Conway and Kochen it is made use of "free will" without giving a "mathematical definition" of it. The definition of the experimenter is the &...
- 3,074
-3
votes
2
answers
261
views
The inequality $\Pi (1-\frac{1}{a_i})^{x_i} \le \Pi (1-\frac{1}{b_j})^{y_j} $ hold? [closed]
Question: Are the properties as follows holds?
Version 1: the answer by Bjørn Kjos-Hanssen
Let $P$ be a positive integers. We written: $P=$ $a_1^{x_1}a_2^{x_2}...a_n^{x_n}$ $=b_1^{y_1}b_2^{y_2}......
- 1,776
-3
votes
1
answer
315
views
Are the injective functions dense in $C([0,1]^n,\mathbb R^n) $?
Let $n\geq 2$. Are injective functions dense in $C([0,1]^n,\mathbb R^n) $ with the uniform norm?
- 4,074
-3
votes
1
answer
251
views
Is the imaginary part of $\displaystyle\ \zeta(s)\zeta(1-s)=0$ for $\operatorname{Re}(s)=\frac{1}{2}$ [closed]
Some of my computations here showed to me that the imaginary part of $\displaystyle\ \zeta(s)\zeta(1-s)=0$ for $\operatorname{Re}(s)=\frac{1}{2}$, really i w'd like to know if there is any paper ...
-3
votes
1
answer
266
views
Does differentiation widen, or narrow, the class of functions?
Let $\cal F^k$ be a set of functions, each of class $C^k$,
i.e., both, for every function in $\cal F^k$:
$k^{\textrm{th}}$ derivatives exist, and
are continuous.
Let $D(\cal F^k)$ be the set of all ...
- 151k
-3
votes
1
answer
3k
views
Are there infinitely many equivalence classes of similar matrices? [closed]
It is easy to show that similarity in matrices is an equivalence relation (two matrices A and B of same size being similar if there exists a matrix P such that B = PAP^(-1) )
Moreover, given a matrix, ...
- 2,855