All Questions

0answers
28 views

Vector application [on hold]

A rope is hung at both ends from a horizontal beam, and a weight m is suspended from it. The left part of the rope exerts a force G at P, while the right part of the rope exerts a force H. Find the ...
1answer
302 views

A nice subcategory of the category of measurable spaces

Is there some notion of "nice" measurable spaces and "nice" maps between them which satisfies the following properties? The real line equipped with the Lebesgue $\sigma$-algebra is nice. Any ...
0answers
58 views

clustering permutations by shared subsequences [on hold]

I have a question, stimulated by some biology, about comparing sets of permutations. The problem Let's think of genes on a bacterial chromosome as beads on a string - atomic, unique objects, with ...
1answer
88 views

Is the module action $M\times M^*\to M^*$ jointly continuous?

Let $M$ be a W*-algebra and consider the following map: $$\gamma: M\times M^*\to M^*: (a,f)\to af$$ where $af(b)=f(ba)$. Let us consider $M$ under the weak topology $\sigma(M,M^*)$ and $M^*$ under ...
0answers
38 views

Maple: In Matrices A x B = C, how do I find matrix A given B and C [on hold]

I have matrix A, B, and C which are all 8x8 matrices in Maple. in the equation A x B = C, when B and C are known, how do I find matrix A? I know how to do it by hand, but I don't know the maple ...
0answers
315 views
+50

Is the Flajolet-Martin constant irrational? Is it transcendental?

Facebook has a new tool to estimate the average path length between you and any other person on Facebook. An interesting aspect of their method is the use of the Flajolet-Martin algorithm. In the ...
0answers
44 views

A set containing more than half elements of a group [on hold]

I wish to prove the exercise which states that for a set $A$ containing more than half elements of a group $G$, every element of $G$ is a product of two elements of $A$. My attempt: By Lagrange ...
0answers
53 views

Weyl-type inequality for non-Hermitian matrices?

What is the weakest known condition under which a Weyl-type eigenvalue perturbation inequality holds? Does some analogue hold for normal matrices, for example?
1answer
131 views

l-adic local system. on hensel schemes

Let $k$ be a field, $\ell$ a prime different from the characteristic. If I take $S$ a closed subscheme of $Y$, which is a $k$-scheme of finite type, is it true that any $\mathbb{Z}_{\ell}$-local ...
0answers
35 views

Arrange numbers? [on hold]

hello the question i would like to ask is very difficult as english is not my native language so here it goes...I need a program or exel chart that arrange numbers in a group in order to get the ...
0answers
31 views

How to calculate how much more wins to get a certain winrate? [on hold]

I have two values, wins and total games played. To calculate the win rate I use the normal «formula»: wins/totalGamesPlayed*100; But let's say I have 21 wins ...
1answer
235 views

Reference request for an introduction to deformation theory in algebraic geometry

I'd like some introductory references for deformation theory in algebraic geometry. I'm interested in survey articles too but I primarily want references which give all the definitions and go through ...
0answers
61 views

Inverses of probability generating functions: positivity of derivatives

Let $\mathcal{G}$ be the set of probability generating functions of random variables taking positive integer values, considered as functions on $[0,1]$. So $G\in\mathcal{G}$ can be written ...
0answers
136 views

$L^\infty$ bound on solutions of linear parabolic equations

We work on a closed Riemannian manifold $M$. Let $u$ and $v$ be the non-negative weak solutions of $$au_t - 2d\,\Delta au = cv - f$$ $$bv_t - d\,\Delta bv = f$$ $$u(0)=u_0, \quad v(0)=v_0$$ where $f$ ...
2answers
83 views

Relationship between group $C^\ast$-algebras $C^\ast(G)$ and graph $C^\ast$-algebras $C^\ast(E)$

Let $E=E(G,S)$ be the graph defined by a group $G$ and a subset $S$ of $G$. What is relationship between group $C^\ast$-algebras $C^\ast(G)$ and graph $C^\ast$-algebras $C^\ast(E)$?
1answer
52 views

Win/Lose ratios and selection [on hold]

Imagine a following scenario: You're on a TCG tournament which allowed you to bring N decks with you. After each game, you might select another deck for your next game. You are allowed to keep ...
1answer
114 views

Can tests for the convergence and divergence of series be used to create undecidable sentences?

Let f(k) be a recursive function which maps the set of positive integers into itself. Let T be a formalized theory which is axiomatizable and contains Peano's Arithmetic as a sub-theory. For example, ...
1answer
92 views

How many uniquely colored degree two vertices in 3-coloring of subcubic graph?

Is there a graph with maximum degree three that has 3 degree two vertices that must get the same (resp. different) color in every 3-coloring of the graph? I'm interested in any similar results as ...
0answers
55 views

Special random variables and monotone class theorem

I am currently reading a proof where the $\pi-\lambda$ Lemma and the monotone class theorem are applied to show a certain property for bounded random variables. The author of the book always shows the ...
0answers
76 views

extending local systems on a neighbourhood

Let $Y$ an affine finite type scheme over an algebraically closed field $k$. Let $S$ be a closed subscheme of $Y$ and $Y'$ the henselization of $Y$ along $S$. If we have a $\mathbb{Z}_{\ell}$ local ...
2answers
103 views

Number of facets of a polyhedron when a vertex is removed

My question, informally: I have a bounded polyhedron in R^n with k facets, and I want to remove a vertex of this problem. How many facets does the remaining polyhedron have at most? More formally: ...
1answer
65 views

writing an integer as particular summation [on hold]

I think my question is an elementary question. Thanks for any help or comment. Is there any formula for the number of writting a natural number $n$ in a summation as follows, $n=a_1+\dots+a_k$, ...
1answer
233 views

If $N = qn^2$ is an odd perfect number, is it possible to have $q + 1 = \sigma(n)$?

The title says it all. Question If $N = qn^2$ is an odd perfect number with Euler prime $q$, is it possible to have $q + 1 = \sigma(n)$? Heuristic From the Descartes spoof, with quasi-Euler ...
3answers
283 views

Description of $\big(\ell^\infty(\mathbb N)\big)^{\!*}$ via ultrafilters

Let $\beta\mathbb N$ is the set of ultrafilters on $\mathbb N$ and $\mathscr F\in\beta\mathbb N$. Assume that $l_{\mathscr F}\in\big(\ell^\infty(\mathbb N)\big)^{\!*}$ is the functional which assigns ...
1answer
49 views

Properties of bipartite graphs

For a connected bipartite graph $G$ are the two following properties equivalent: 1)Every minimal cycle in $G$ has length 4, that is every cycle of length strictly greater than 4 can be divided in ...
1answer
1k views

What did Euler do with multiple zeta values?

When reading about multiple zeta values, I often find the claim that the case of length two $$\zeta(s_1, s_2)=\sum_{n>m \geq 1} \frac{1}{n^{s_1}m^{s_2}}, \qquad s_1 \geq 2, \quad s_2 \geq 1$$ ...
0answers
24 views

Common Point of Intersection of n-dimensional ellipsoids [on hold]

Suppose we have two ellipses in 2-dimensions centered at the origin. It is easy to visualize that (unless one is contained in the other) they will have 4 points of intersection. Can we say that in ...
0answers
70 views

A Künneth-Theorem version for relative singular cohomology

I'm not an expert in algebraic topology, but sometimes I need some results from this area, for example tools to determine singular cohomology groups of product spaces. The Künneth-Theorem which I ...
1answer
120 views

Frankl's union-closed sets conjecture for infinite families

This question is motivated by Frankl's union-closet sets conjecture. Let $X$ be a non-empty set. We say that a family ${\cal A} \subseteq {\cal P}(X)$ is union-closed if $\emptyset\notin{\cal A}$ and ...
0answers
25 views

Trouble with an assignment [on hold]

Can anyone please be kind enough to help me with this. On one shelf there are 5 hardcover books and 6 paperbacks and on the other shelf there are 7 hardcover and 4 paperback. From the first shelf ...
2answers
259 views

0answers
21 views

AQA A Level Normal Distribution [on hold]

The question goes like: A wholesaler decides to grade such oranges by weight. He decided that the smallest 30% should be graded as small, largest 20% as large and in between as medium. The ...
2answers
320 views

First Galois cohomology of Weil restriction of $\mathbb{G}_m$

Let $L/K$ be a finite Galois extension, write $G:= Gal(L/K)$. Denote by $R = Res(\mathbb{G}_m)$ the Weil restriction of $\mathbb{G}_m$, from $L$ to $K$. I want to show that its first Galois cohomology ...
0answers
84 views

0answers
55 views

Computing abelianizations of some explict finite subgroups of $GL_2(\mathbb{Z}/p^n \mathbb{Z})$

I have been attempting to find some abelianizations of some subgroups of $GL_2(\mathbb{Z}/p^n \mathbb{Z})$. I have been using brute force for the most part but I get very messy results. Here is an ...
1answer
653 views

Hard maths on viXra? [closed]

A few years ago a nice paper surveyed the differences in quality between papers submitted to arXiv and those submitted to arXiv's rough cousin, viXra. However, that paper was about generic ...
0answers
27 views

I have a problem proving that some specific kernels are positive definite. In general, I can find the answer quickly enough but here I have a specific case involving a logartihm : $K : ... 1answer 94 views A question about Borel sets on the unit interval It is known that each non-decreasing continuous function$\phi$induces a$\sigma$-additive measure$d\phi$such that$\int_0^1 f(x) d\phi(x)$exists for every bounded real-valued Baire function$f$. ... 1answer 127 views Some very weak statements on choice This is a follow-up question to Does$|(X\times\{0\}) \cup (X\times\{1\})| \leq |X|$for$X$infinite imply${\sf AC}$? Consider the statements$(\text{S}1)$For any infinite set$X$there ... 0answers 71 views A simple question about ordinary diffential equations of first order [closed] An ODE (Ordinary Differential Equation) of order$n$becomes a relation: $$F(x,y,y',...,y^{(n)})=0$$ Then$F(x,y,y^{(1)})=0$defines a an ODE of order one. In "basic standard texts", for purposes ... 1answer 55 views A question on matrix polynomial [on hold] Suppose${P_\Delta }(\lambda ) = ({A_m} + {\Delta _m}){\lambda ^m} + ....... + ({A_1} + {\Delta _1}){\lambda ^1} + ({A_0} + {\Delta _0})$is a matrix polynomial, and$\lambda $is a complex ... 0answers 34 views If$N = {q^k}{n^2}$is an odd perfect number given in Eulerian form, is$n^2$solitary? (Note: A similar question was asked in MSE two months ago.) Let$\sigma(x)$be the sum of the divisors of the natural number$x$, and denote the abundancy index$\sigma(x)/x$by$I(x)$. Here is my ... 1answer 119 views Does$|(X\times\{0\}) \cup (X\times\{1\})| \leq |X|$for$X$infinite imply${\sf AC}$? Consider the statement For any infinite set$X$there is an injection$\varphi$from$(X\times\{0\}) \cup (X\times\{1\})$into$X$. Does this imply the${\sf AC}$? 1answer 65 views Covariance matrix as optimization problem solution? I have seen the expectation of a random vector expressed as the solution to the optimization problem: \mathbb{E}[X]=argmin_{v \in \mathbb{R}^n}\mathbb{E}[\|X-v\|_{l^2}^2](:= ... 0answers 82 views A quantity measuring weak compactness Let us fix some notations. If$A$and$B$are nonempty subsets of a Banach space$X$, we set$d(A,B)=\inf\{\|a-b\|\mid a\in A,b\in B\},\widehat{d}(A,B)=\sup\{d(a,B)\mid a\in A\}.$Let$A\$ be a ...

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