Mahler's polynomial approximation for odd and even p-adic functions

Basic Properties of Even and Odd Functions

In this paper x, r are real numbers. Let A be a set. We say that A is symmetrical if and only if: (Def. 1) For every complex number x such that x ∈ A holds −x ∈ A. Let us note that there exists a subset of C which is symmetrical. Let us observe that there exists a subset of R which is symmetrical. In the sequel A denotes a symmetrical subset of C. Let R be a binary relation. We say that R has s...

p-ADIC LOGARITHMS FOR POLYNOMIAL DYNAMICS

We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of the affine space A over a p-adic field, endowed with polynomial actions on each coordinate of A. We use analytic methods similar to the ones employed by Skolem, Chabauty, and Coleman for studying diophantine equations.

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

Polynomial Approximation of Functions

Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hubert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer o...

Synchrotron Radiation Studies on Even-Odd and Odd-Even Nylons

Aliphatic polyamides derived from odd diamine or odd dicarboxylic acid units cannot adopt a conventional sheet structure when molecular chains have an all trans conformation. However, typical fiber diffraction patterns of this sheet structure were observed in several polyamides derived from odd units such as nylons 65 and 56. Consequently, a new structure based on the establishment of intermole...