# All Questions

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### Question on Posets and open sets

i'm sorry if my question is really trivial but this one is really bugging me out.. So let's have a partially ordered set $I$ with the topology in which the open sets are the increasing ones: $i\in U$ ...
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### Intersections in almost complex manifolds

Suppose $(M,J)$ is an almost complex manifold, and $X$ and $Y$ are two almost complex submanifolds (i.e. $J(T(X)) \subset T(X)$ and $J(T(Y)) \subset T(Y)$). Then must $X \cap Y$ also be an almost ...
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### decomposition of polynomials over a field [on hold]

$K|F$ has this property that every polynomial $f(x)∈F[x]$ has a root in $K$.is it true that every polynomial $f(x)∈F[x]$ can be completely decomposed on $K$? i think it is false,because if we write ...
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### How to find secret key and public key for ECC cryptosystem? [on hold]

Develop an ECC cryptosystem based on E31(1;1), point G = (0,1) which has order 32. nA value of 6. What is the secret key? What is the public key?
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### On the existence of compactly supported functions whose its Fourier transform satisfies a given condition

My question is concerned with the existence of compactly supported functions whose its Fourier transform satisfies a given condition: For $\gamma\ge 1$, one can prove that there is no compactly ...
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### How to compute 3P from elliptic curve where P is (28, 8) [on hold]

Consider the elliptic curve E31(1,1): Calculate 3P, where P = (28,8).
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### Is the ISC kaput [on hold]

The very useful Inverse Symbolic Calculator is showing me this What's up? multiple choice (a) No, it's fine at that address: idiot Edgar did something wrong... (b) It is off-line at that ...
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### Disruptive innovations in mathematical notations [on hold]

I am wondering whether there are examples of mathematical notations that, once introduced, have drastically changed or simplified the way to address a problem or a mathematical area, or that have ...
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### Complexity Dick Word in Turing Machine single tape [on hold]

(I precise I don't have a good level in english so I can rewrite if you want) The probleme : I just have two symbols O(open) for "(" and C(close) for ")" The probleme consist to implement an ...
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### Connectedness of the symplectic automorphism of the 2-sphere $S^2$

The 2-sphere, endowed with the round Riemann metric with constant curvature 1, is a symplectic manifolds. My question is: Is the group of symplectic automorphisms of $S^2$ with respect to this ...
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### Conjecture Reference Request

If Second Hardy-Littlewood Conjecture is true then we can claim that $\pi(x)-\pi(y)\leq \pi(x-y)$. Thus the conjecture gives an upper bound for the number of primes between $x$ and $y$. I have found ...
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### a question about minimal non-abelian groups

Let $G$ be a minimal non-abelian group with cyclic Sylow $p$-subgroup $P$ and normal Sylow $q$-subgroup $Q$ , see [ Huppert, Endlich Gruppen I, Aufgaben III, 5.14]. My quesion is, if there is another ...
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### Does $\mathsf{fReR}_0$ prove the existence of the cartesian product of two sets

$\mathsf{fReR}_0$ is the set-theoretical system whose axioms consist of: (1) Axiom of extensionality: $\forall z\in x\ (z\in y)\wedge\forall z\in y\ (z\in x)\rightarrow x=y$ (2) Axiom of empty set: ...
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### Equations over $\mathbb{Z}[[T]]$ vs. equations over $\mathbb{Z}_p$

This question might be deemed totally unanswerable, unless there is an obvious counterexample. Answers to either effect would be welcome. Question. Let $X$ be a finite-type scheme over ...
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### Cohomological dimension of transcendental p-adic extensions

Let $k = \mathbb{Q}_p$ for any prime $p$ and set $L = k(t_1,..,t_n)$. The u-invariant of a field $u(k)$ is defined by $u(k):=\{ max (\mathrm{rank}(q))$ | $q$ is anisotropic over $k\}$. It is ...
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### A metric associated with a continuous surjective map $f:X\to Y$

Assume that $f:(X,d_{1})\to (Y,d_{2})$ is a continuous surjective map between compact metric spaces. We define another metric $d_{f}$ on $Y$ With $$d_{f}(a,b)=Hd(f^{-1}(x), f^{-1}(y))$$ ...
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### Characterizing the real analytic Eisenstein series

Consider the classical real analytic Eisenstein series $$E(z,s)=\left(\pi^{-s}\Gamma(s)\frac{1}{2}\right)\sum_{(m,n)\neq(0,0)}\frac{y^s}{|mz+n|^{2s}},$$ where $z=x+iy$. We think of $E(z,s)$ as a ...
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### Zero-mean assumptions concerning r.d.'s when reading graduate-level probability texts [on hold]

I'm reading through T. Taos book on random matrices (to be found here), and it is frequent to make without-loss-of-generality certain reductions when proving theorems as for example Hoeffdings ...
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### Nagakami behavoir

Is the sum of square Nagakami random variables Erlang distributed? What is the distribution of euclidean norm of complex Nagakami? Cheers!
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### Help in finding distribution of the following function of random variable

Let $X_1$ and $X_2$ be independent complex Gaussian random variables, $$X_1 \sim \mathcal{CN}(0,\sigma)$$ $$X_2 \sim \mathcal{CN}(0,\sigma)$$ If $X= aX_1 + bX_2$ where $a,b$ are constants then the ...
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### What is induction to n^(n-1) >= n! for n=9,10 [on hold]

Can somebody help me? How do I prove n^(n-1) >= n! for n=9,10..... by induction?
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### A homological criterion for collapsibility?

On page 256 of Kirby and Siebenmann one finds the following lemma (its proof an "elementary exercise", so they only give a hint): Taking $A$ to be a point and iterating this collapsing lemma, this ...
Does there exist an $m \times n$ matrix $A$ and a vector $x \in \mathbb{R}^m$ such that: The entries of $A$ are $\in \{0, 1\}$. For all pairs of columns $u, v$ of $A$ the entries of $u - v$ are ...