Necessary conditions for embedding rings into fields

Embedding Henselian fields into power series

Every Henselian field of residue characteristic 0 admits a truncation-closed embedding in a field of generalised power series (possibly, with a factor set). As corollaries we obtain the Ax-Kochen-Ershov theorem and an extension of Mourgues and Ressayre’s theorem: every ordered field which is Henselian in its natural valuation has an integer part. We also give some results for the mixed and the ...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

Embedding normed linear spaces into $C(X)$

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

New Necessary Conditions for

In this paper, we obtain several nonexistence results for abelian Hadamard diier-ence sets. In particular, we prove that there are no Hadamard diierence sets in abelian groups G = Z 2 Z 2 P , where jPj = p 2 , is odd and p is a prime congruent to 1(mod 4). Also we give a detailed proof for a connection between certain reversible Hadamard diierence sets and projective three-weight codes which wa...

Embedding defect sites into hexagonal nondiffracting wave fields.

We present a highly purposive technique to optically induce periodic photonic lattices enriched with a negative defect site by using a properly designed nondiffracting (ND) beam. As the interference of two or more ND beams with adequate mutual spatial frequency relations in turn reproduces an ND beam, we adeptly superpose a hexagonal and a Bessel beam to create the ND defect beam of demand. The...