A remark on accessibility

This note obtains some characteristics of accessibility and Kato’s chaos. Applying these results, an accessible dynamical system whose product system is not accessible is constructed, giving a negative answer to a question in [Li R, Wang H, Zhao Y. Kato’s chaos in duopoly games. Chaos Solit Fract 2016;84:69–72]. Besides, it is proved that every transitive interval self-map is accessible.     

A remark on Mackey-functors

In the following note we characterize the category of Mackey functors from a categoryC, satisfying a few assumptions, to a categoryD as the category of functors from Sp(C), the category of spans inC, toD which preserve finite products. This caracterization permits to apply all results on categories of functors preserving a given class of limits to the case of Mackey-functors.     

A remark on the Stone-Weierstrauss theorem

Siberian Mathematical Journal -     

A remark on the Debs-Saint-Raymond theorem

A theorem of Debs and Saint-Raymond gives sufficient conditions for a -ideal of compact sets to have the covering property. We discuss the necessity of these conditions. Namely, we show that there exists a -ideal that is locally non-Borel, has no Borel basis and has the covering property. This partially answers a question posed by Kechris.

     

A remark on the Danilewski method

Journal of Mathematical Sciences -     

A remark on the Hardy inequalities

This work was supported by a grant from the Minerva foundation.     

A remark on quasi-isometries

We show that if is an quasi-isometry, with , defined on the unit ball of , then there is an affine isometry with where is a universal constant. This result is sharp.

     

关于拟调和映射的一些注记

Several theorems on the finiteness of energy for quasi-harmonic spheres are proved,some counter-examples which state that the energy of quasi-harmonic sphere may be infinite are given. The results support some conditions of a question posed by Lin Fanghua and Wang Changyou.     

A remark on the conrey-ghosh theorem

This paper was written during the author's stay at University Bordeaux I, financially supported by the Commision of the European Communities in the framework of the program “S & T Cooperation with Central and Eastern European Countries.”     

A remark on the non-degeneracy condition

The structure of the set of positive solutions of the semilinear elliptic boundary value problem $\Delta u(x)+\lambda f(u(x))=0\ \ \ {\rm for}\ x\in D,\ \ \ u=0\ \ {\rm on}\ \partial D$ depends on a certain non-degeneracy condition, which was proved by K.J. Brown [1] and T. Ouyang and J. Shi [5]. We provide a short alternative proof of that condition.     

A remark on the Bergman stability

Let , be a sequence of bounded pseudoconvex domains that converges, in the sense of Boas, to a bounded domain . We show that if can be described locally as the graph of a continuous function in suitable coordinates for , then the Bergman kernel of converges to the Bergman kernel of uniformly on compact subsets of .