p-Adic Dynamics and Sullivan's No Wandering Domains Theorem

In this paper we study dynamics on the Fatou set of a rational function . Using a notion of components of the Fatou set defined by Benedetto, we state and prove an analogue of Sullivan's No Wandering Domains Theorem for p-adic rational functions which have no wild recurrent Julia critical points.     

Tensor Products of Non-Archimedean Weighted Spaces of Continuous Functions

It is shown that the completion of the tensor product of two non-Archimedean weighted spaces of continuous functions is topologically isomorphic to another weighted space. Several applications of this result are given.     

On Convergence Approach Spaces

The extension of two axioms due to Cook and Fischer to the category CAP of convergence approach spaces leads to the study of non-Archimedean approach spaces as well as two versions of regularity appropriate to CAP and related categories.     

An effective non-Archimedean anti-degeneracy/cycling linear programming method especially for data envelopment analysis and like models

A non-Archimedean effective anti-degeneracy/cycling method for linear programming models, especially Data Envelopment Analysis (DEA), processing networks and advertising media mix models is herein developed. It has given a tenfold speed increase plus elimination of cycling difficulties over conventional Marsden or Kennington/Ali LP software modules in a 1000 LP DEA application.     

Stability of the generalized quadratic and quartic type functional equation in non-Archimedean fuzzy normed spaces

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of non-Archimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-Archimedean absolute value of $2$ is less than $1$ cannot be omitted in our corollaries. The results improve and extend some recent results.     

Algebraic Numbers Close to 1 in Non-Archimedean Metrics

Let 1 be an algebraic number with relatively small height. Recently, many authors, including Amoroso, Dubickas, Mignotte and Waldschmidt, stated sharp lower bounds for the quantity | – 1|. Here, we provide a p-adic analogue of their results. For instance, we give an upper bound for the absolute value of the norm of – 1, and we show that our estimate is rather sharp in terms of the degree of . Further, we discuss a generalization in several variables of our result.     

Zero-dimensional spaces from linear structures

It is well known that spaces defined from a separated uniform structure with a linearly ordered base of uncountable cofinality (ω_μ-metrizable spaces) are ultraparacompact and have an ortho-base, hence are non-Archimedean spaces in the sense of A. Monna. Our results concern whether certain wider classes of spaces defined from linear structures retain these properties. We construct for every regular cardinal ω_μ, examples of ω_μ-additive, ω_μ-stratifiable spaces (i.e., ω_μ-Nagata spaces) that do not have an ortho-base. We give a number of examples of linearly stratifiable spaces, one of which is related to an example of Eric K. van Douwen concerning countable box products of stratifiable spaces.     

A Generalized abc-Conjecture over Function Fields

In this paper, we derive a generalized version of abc-conjecture and prove its analogue for non-Archimedean entire functions as well as a generalized Mason's theorem on polynomials.     

A MODEL FOR WHITE NOISE ANALYSIS IN P-ADIC NUMBER FIELDS

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非Archimedean随机空间中混合型泛函方程的解及稳定性

在非-Archimedean 随机赋范空间的框架下,证明了Euler-Lagrange二次映象的广义稳定性．另外,文中还介绍了 随机空间理论、非-Archimedean 空间理论、以及泛函方程理论之间的联系．