Related papers: A local-global theorem on periodic maps

Let $p \in (0, \infty)$ be a constant and let $\{\xi_n\} \subset L^p(\Omega, {\mathcal F}, \P)$ be a sequence of random variables. For any integers $m, n \ge 0$, denote $S_{m, n} = \sum_{k=m}^{m + n} \xi_k$. It is proved that, if there…

We characterize positivity preserving maps $T: B(\mathcal{H})_h \otimes \mathbb{R}[x_1, \dots, x_n] \to B(\mathcal{H})_h \otimes \mathbb{R}[x_1, \dots, x_n]$ on $\mathbb{R}^n$ and on compact sets $K \subseteq \mathbb{R}^n$. This also…

We prove that, for every decreasing sequence {a \sb k} of natural numbers, there exists a map f: X --> X with cat (f\sp k)=a\sb k.

Let $K$ be an algebraically closed field and $\mathrm{M}(2,K)$ be the $2\times 2$ matrix algebra over $K$ and $\mathrm{GL}(2,K)$ be the invertible elements in $\mathrm{M}(2,K)$. We explore the image of polynomials with constants, namely…

We study two global structural properties of a graph $\Gamma$, denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erd\"os--R\'enyi random graph model G(n,p), proving a sharp…

For a finite abelian group $(G,+)$, the constant $C(G)$ is defined to be the smallest natural number $k$ such that any sequence in $G$ having length $k$ will have a subsequence of consecutive terms whose sum is zero. For a subset…

We develop a general theory of local stability up to belonging to an ideal (e.g. having measure zero). From a model-theoretic perspective, we prove a stationarity principle for almost stable formulas in this sense, and build a topological…

We extend the classical result of Lyusternik and Fet on the existence of closed geodesics to singular spaces. We show that if $X$ is a compact geodesic metric space satisfying the CAT($\kappa $) condition for some fixed $\kappa >0$ and…

Ahlswede and Cai proved that if a simple graph has nested solutions (NS) under the edge-isoperimetric problems, and the lexicographic (lex) order produces NS for its second cartesian power,then the lex order produces NS for any finite…

Given a periodic point $\omega$ in a $\psi$-mixing shift with countable alphabet, the sequence $\{S_{n}\}$ of random variables counting the number of multiple returns to shrinking cylindrical neighborhoods of $\omega$ is considered.…

The main result of this article is: THEOREM. Every homogeneous locally conical connected separable metric space that is not a $1$-manifold is strongly $n$-homogeneous for each $n \geq 2$ and countable dense homogeneous. Furthermore,…

In this paper we characterize irreducible generic representations of $\SO_{2n+1}(k)$ where $k$ is a $p$-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic…

Consider the difference equation $x_{k+1}=x_k e^{\alpha-x_{n-d}}$ where $\alpha$ is a positive parameter and d is a non-negative integer. The case d = 0 was introduced by W.E. Ricker in 1954. For the delayed version d >= 1 of the equation…

In this paper, we show that a locally constant cocycle $\mathcal{A}$ is $k$-quasi multiplicative under the irreducibility assumption. More precisely, we show that if $\mathcal{A}^t$ and $\mathcal{A}^{\wedge m}$ are irreducible for every $t…

If $X$ is a topological space and $Y$ is any set then we call a family $\mathcal{F}$ of maps from $X$ to $Y$ nowhere constant if for every non-empty open set $U$ in $X$ there is $f \in \mathcal{F}$ with $|f[U]| > 1$, i.e. $f$ is not…

We prove local and global existence from large, rough initial data for a wave map between 1+1 dimensional Minkowski space and an analytic manifold. Included here is global existence for large data in the scale-invariant norm $\dot L^{1,1}$,…

Let X and Y be compact, simply connected and locally connected subsets of R^2, and let f : X -> Y be a homeomorphism isotopic to the identity on X. Generalizing Brouwer's plane translation theorem for self-maps of the plane, we prove that f…

Completely positive trace-preserving maps $S$, also known as quantum channels, arise in quantum physics as a description of how the density operator $\rho$ of a system changes in a given time interval, allowing not only for unitary…

In this paper, using Kronecker's theorem, we discuss the set of common fixed points of an n-parameter continuous semigroup of mappings. We also discuss convergence theorems to a common fixed point of an n-parameter nonexpansive semigroup.

Let $Z=(Z_t)_{t\geq0}$ be an additive process with a bounded triplet $(0,0,\Lambda_t)_{t\geq0}$. Suppose that for any Schwartz function $\varphi$ on $\mathbb{R}^d$ whose Fourier transform is in $C_c^{\infty}(B_{c_s} \setminus B_{c_s^{-1}}…