On the vector field problem for O(n)/O(1)xO(1)xO(n-2)

We prove new results about the vector field problem on the real flag manifolds O(n)/O(1) x O(1) x O(n - 2). For some infinite families of these manifolds, we completely solve the vector field problem.     

Crystal and molecular structures of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine.

The crystal structure of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine (C15H19NO3) (I) has been determined by X-ray analysis. It crystallizes orthorhombic space group Pbca with a = 24.295(3), b = 15.086(3), c = 7.552(3)A, V = 2768(1)A3, Z = 8, Dcalc = 1.254 g/cm3, mu = (Mo K(alpha)) = 0.87 cm(-1). The title compound has analgesic activity of cycloaliphatic amine part. The molecule is deviated from planar configuration.     

GDDP: Generalized Dual Dynamic Programming Theory

This document presents theoretical considerations about the solution of dynamic optimization problems integrating the Benders Theory, the Dynamic Programming approach and the concepts of Control Theory. The so called Generalized Dual Dynamic Programming Theory (GDDP) can be considered as an extension of two previous approaches known as Dual Dynamic Programming (DDP): The first is the work developed by Pereira and Pinto [3–5], which was revised by Velásquez and others [8,9]. The second is the work developed by Read and others [2,6,7].     

Banach-Saks operators on spaces of continuous functions

Summary Let K be a compact Hausdorff space and let E be a Banach space. We denote by C(K, E) the Banach space of all E-valued continuous functions defined on K, endowed with the supremum norm. We study in this paper Banach-Saks operators defined on C(K, E) spaces. We characterize these operators for a large class of compacts K (the scattered ones), or for a large class of Banach spaces E (the superreflexive ones). We also show by some examples that our theorems can not be extended directly.Partially supported by C.A.I.C.Y.T. grant 0338-84. The author wishes to thank Professor F.Bombal for his encouragement.     

Mössbauer study of spin-glass Fe x Zn1−x F2 system

⁵⁷Fe Mössbauer effect measurements in the diluted Ising antiferromagnet Fe _x Zn_1?x F₂ withx=0.25 andx=0.57 at temperatures between 4.2 and 55 K, are reported. DC suceptibility measurements show a spin-glass (SG) phase at low temperatures forx≤0.31. Our Mössbauer spectra show a phase transition to a SG state with antiferromagnetic order (AFSG) forx=0.25 and only antiferromagnetic order forx=0.57.     

Synthesis and polymerization of o-hexylaniline: Characterization of the corresponding polyaniline

In the field of research on soluble conducting polymers, the poly(o-alkylanilines) are very interesting because we can expect them to give more soluble polymers and new properties. Like poly(o-propylaniline) (POP), which is more soluble than polyaniline (PANi), poly(o-hexylaniline) (POH) appears to be more soluble in organic solvents than POP because of the longer alkyl groups in the 2-position. The higher solubility confers better processability on this new polymer, and because of this solubility, an NMR study in solution became possible.The nitration of hexylbenzene and the reduction of the resulting product to o-hexylaniline were performed according to the literature. The chemical polymerization was easy and it is possible to produce this polymer in large quantities.The polymerization carried out in anhydrous NH₄F, 2.35 HF medium and in 5 M perchloric acid gave a polymer with almost quantitative yield. The electrochemical behaviour of POH displayed faster electron transfers than PANi in organic solvents, depending on the acido-basicity level of the aqueous solutions. Unlike PANi, fractal growth was not observed.     

Generators of some Ramanujan formulas

In this paper we prove some Ramanujan type formulas for 1/π but without using the theory of modular forms. Instead we use the WZ—method created by H. Wilf and D. Zeilberger and find some hypergeometric functions in two variables which are second components of WZ—pairs than can be certified using Zeilberger's EKHAD package. These certificates have an additional property which allows us to get generalized Ramanujan's type series which are routinely proven by computer. We call these second hypergeometric components of the WZ—pairs generators. Finding generators seems a hard task but using a kind of experimental research (explained below), we have succeeded in finding some of them. Unfortunately we have not found yet generators for the most impressive Ramanujan's formulas. We also prove some interesting binomial sums for the constant 1/π². Finally we rewrite many of the obtained series using pochhammer symbols and study the rate of convergence. 2000 Mathematics Subject Classification Primary—33C20