We study transcendency properties for graded field extension and give an application to valued field extensions. 1. Introduction. An important tool to study rings with valuation is the so-called associated graded ring construction: to a valuation ring R, we can associate a ring gr(R) graded by the valuation group. This ring is often easier to study, and one tries to lift properties back from gr...

Dibromination of [2.2]paracyclophane (I) led to predominantly pseudo-ortho2 (11) and pseudo-para2 (111) disubstituted compounds, and to lesser amounts of pseudo-meta (IV) and para (V) isomers. Oxidation of these dibromides gave terephthalic acids whose esters were identified by vpc, and whose structures allowed homoannular and transannular bromination to be differentiated. Tetrabromination of I...

The title compound, C(3)H(6)N(4)O(2), exhibits partial disorder with the refined occupancy ratios of the two components being 0.582 (5):0.418 (5). In the major component, the nitroso groups have a relative syn spatial arrangement [O=N⋯N=O pseudo-torsion angle = 1.1 (4)°], whereas the other component has an anti disposition [177.6 (1)°]. The N-N=O moieties are almost coplanar with a dihedral ang...

In recent years, the theory of almost automorphic functions has been developed extensively see, e.g., Bugajewski and N’guérékata 1 , Cuevas and Lizama 2 , and N’guérékata 3 and the references therein . However, literature concerning pseudo-almost automorphic functions is very new cf. 4 . It is well known that the study of composition of two functions with special properties is important and bas...

a cartan manifold is a smooth manifold m whose slit cotangent bundle 0t *m is endowed with a regularhamiltonian k which is positively homogeneous of degree 2 in momenta. the hamiltonian k defines a (pseudo)-riemannian metric ij g in the vertical bundle over 0 t *m and using it, a sasaki type metric on 0 t *m is constructed. a natural almost complex structure is also defined by k on 0 t *m in su...

We characterize the polynomial closure of a pseudo-convergent sequence in valuation domain V arbitrary rank, and then we use this result to show that is never topological when has rank at least 2.

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (P : P) if and only if P is not invertible. Furthermore, if P is invertib...

1.1. The p-adic measure. Let p be a prime number. We consider a field K with a valuation ord : K× → Z, extended to K by ord(0) = ∞. We denote by OK the valuation ring OK = {x ∈ K|ord(x) ≥ 0} and we fix an uniformizing parameter $, that is, an element of valuation 1 in OK . The ring OK is a local ring with maximal ideal MK of OK generated by $. We shall assume the residue field k := OK/MK is fin...

The research is financed by by the National Natural Science Foundation of China (11071001) and the Research Fund for the Doctoral Program of Higher Education of China(20093401110001) Abstract In this paper, we study weighted pseudo-almost periodic solutions to general neutral integral equations. By applying the properties of weighted pseudo-almost periodic functions and the fixed point theorem,...

In this paper, we shall deal with μ-pseudo almost automorphic solutions to a semi-linear fractional differential equation by a new concept of μ-pseudo almost automorphic functions presented recently. First we establish some new properties of μ-pseudo almost automorphic functions, and then apply the obtained results to prove some existence theorems combined with the Leray-Schauder alternative th...