On Subspaces and Quotients of Banach Spaces C(K, X)

 We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces. Received 8 November 2000; in revised form 7 December 2001     

A new class of Ornstein transformations with singular spectrum

It is shown that for any family of probability measures in Ornstein type constructions, the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem [J. Bourgain, On the spectral type of Ornstein class one transformations, Israel J. Math. 84 (1993) 53–63], same result is proved for Rudolph's construction [D. Rudolph, An example of a measure-preserving map with minimal self-joining and applications, J. Anal. Math. 35 (1979) 97–122].     

A class of extreme contractions inL(l p )

Summary In this note we prove that: if T is a contraction in L(l^p) that maps elements of disjoint support to elements of disjoint support, then T is an extreme point of the unit ball of L(l^p), 1

i) form a p-orthonormal sequence or the nonzero elements of (y_i) form a p-orthonormal sequence for which supp (y_i)=N.     

Quadratic spline interpolation on uniform meshes

The interpolation problem at uniform mesh points of a quadratic splines(x _i)=f _i,i=0, 1,...,N ands(x ₀)=f₀ is considered. It is known that s–f=O(h ³) and s–f=O(h ²), whereh is the step size, and that these orders cannot be improved. Contrary to recently published results we prove that superconvergence cannot occur for any particular point independent off other than mesh points wheres=f by assumption. Best error bounds for some compound formulae approximatingf _i andf _i ⁽³⁾ are also derived.     

Properties of RF sputtered ZnxCd1−xS thin films

Zn _x Cd_1–x S thin films (0x0.20) were prepared using rf sputtering in argon atmosphere and characterized using X-ray diffraction, optical transmission, electrical resistivity and photoconductive decay measurements. The films were found to possess hexagonal structure. The crystallite size and degree of preferential orientation were found to decrease with the increase ofx and to improve upon annealing in vacuum at 250 °C. The transmission edge shifted towards shorter wavelengths with the increase ofx in agreement with the expected shift in the energy band gap. The films were found to exhibit room temperature resistivity in the range 100–1000 cm. The obtained values of long wavelength transmission (70–80%) and minority carrier diffusion length (30 m) are high enough for the application of these films in the field of solar cells.     

Pyranoxanthones from Calophyllum Inophyllum

Phytochemical investigation of the stem bark of Calophyllum inophyllum resulted in the isolation of a new dipyrenoxanthone, calophinone ( 1 ), together with four related xanthones ( 2–5 ). Identification of the isolated compounds was achieved through intensive studies of their spectral data, especially 2D NMR.     

Synthesis of condensed systems containing the tetrazole ring by base-catalyzed intramolecular cyclization of quaternary ammonium salts

Quaternary ammonium salts containing propargyl and 3-(2-methyltetrazol-5-yl)propargyl groups undergo base-catalyzed cyclization at room temperature with self heating to form condensed heterocyclic systems containing the tetrazole ring. Heating at 90–92°C for 2 h is necessary to cyclize the allyl analogs of the starting salts.Communication 234 of the series Research on Amines and Ammonium Compounds. For 233, see [1].Institute of Organic Chemistry, National Academy of Sciences of the Republic of Armenia, Erevan 375094. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 390–394, March, 1999.