On special rational curves in Grassmannians

Numerical and geometric characterizations, among all morphisms , of those which are -equivalent to the canonical morphism induced by the Morita equivalence –, are presented. The author was partially supported by KBN grants 1P03A 036 26 and 115/E-343/SPB/6.PR UE/DIE 50/2005-2008. Received: 10 September 2005     

Independent systems of representatives in weighted graphs

The following conjecture may have never been explicitly stated, but seems to have been floating around: if the vertex set of a graph with maximal degree Δ is partitioned into sets V _i of size 2Δ, then there exists a coloring of the graph by 2Δ colors, where each color class meets each V _i at precisely one vertex. We shall name it the strong 2Δ-colorability conjecture. We prove a fractional version of this conjecture. For this purpose, we prove a weighted generalization of a theorem of Haxell, on independent systems of representatives (ISR’s). En route, we give a survey of some recent developments in the theory of ISR’s. The research of the first author was supported by grant no 780/04 from the Israel Science Foundation, and grants from the M. & M. L. Bank Mathematics Research Fund and the fund for the promotion of research at the Technion. The research of the third author was supported by the Sacta-Rashi Foundation.     

Product measures and convergence theorems for product integrals in integration theory for semigroup valued functions

In [11] Sion has investigated measures and integrals having values in uniform semigroups. In this paper a result which gives sufficient conditions for the existence of a unique product of semigroup valued measures is established. Moreover a convergence theorem for product integrals of semigroup valued functions is proved.     

Characterization of BCN films synthesized by radiofrequency plasma enhanced chemical vapor deposition

Boron carbonitride (BCN) films have been synthesized on Si(1 0 0) substrate by radio frequency plasma enhanced chemical vapor deposition using tris-(dimethylamino)borane (TDMAB) as a precursor. The deposition was performed at the different RF powers of 400-800 W, at the working pressure of 2×10⁻¹ Torr. The formation of the sp²-bonded BCN phase was confirmed by Fourier transform infrared spectroscopy. X-ray photoelectron spectroscopy measurements showed that B atoms were bonded to C and N atoms to form the BCN atomic hybrid configurations with the chemical compositions of B₅₂C₁₂N₃₆ (sample 1; prepared at the RF power of 400 W), B₅₂C₁₀N₃₈ (sample 2; at 500 W) and B₄₆C₁₈N₃₆ (sample 3; at 800 W), respectively. Near-edge X-ray absorption fine structure (NEXAFS) measurements indicated that B atoms were bonded not only to N atoms but also to C atoms to form various configurations of sp²-BCN atomic hybrids. The polarization dependence of NEXAFS suggested that the predominant hybrid configuration of sp²-BCN films oriented in the direction perpendicular to the Si substrate.     

Fluorescence characteristics of Dy/CdS nanocrystals doped silica xerogel

Cadmium sulfide semiconductor nanocrystals along with dysprosium ions were incorporated in silica xerogels through sol-gel route. The fluorescence properties were analyzed for samples annealed at different temperatures. The incorporation of the CdS semiconductors as nanocrystallites was confirmed from the HRTEM measurements. The fluorescence intensities were compared for Dy³⁺, CdS and Dy³⁺/CdS-doped silica xerogels. Enhanced blue emission was observed for codoped samples annealed up to 100 °C.     

Elastic behaviour of strontium-doped lanthanum calcium manganites in the vicinity of TC

Colossal magnetoresistance (CMR) manganites with compositional formula, La_0.67Ca_0.33−xSr_xMnO₃ (where x=0, 0.09, 0.11, 0.13, 0.33) were prepared by citrate gel route mainly to understand the elastic behaviour in the vicinity of their magnetic transition temperature T_C. The structural characterizations of all the materials clearly indicate that samples upto x=0.13 doping, are having orthorhombic structure with Pbnm space group and sample with x=0.33 is having rhombohedral structure with space group. The magnetic transition temperatures (T_C) are determined by AC susceptibility measurements and are found to increase continuously with increasing strontium concentration. Finally, a systematic investigation of the ultrasonic longitudinal velocities of all the samples was carried out. Further, all the samples are found to exhibit anomalous behaviour in the vicinity of their magnetic transition temperatures and the observed behaviour is explained using Landau's theory.     

Preparation of organic acid anion-modified magnesium hydroxides by coprecipitation: A novel material for the uptake of heavy metal ions from aqueous solutions

New layered magnesium hydroxides whose brucite layers had been bridged with malate²⁻ and tartrate²⁻ were prepared by dropwise addition of Mg(NO₃)₂ to malate and tartrate solutions at a constant pH of 10.5. Malate²⁻ and tartrate²⁻ may have been also absorbed on the surfaces of hydroxides. In the case of using citrate solution, Mg(OH)₂ absorbed with citrate³⁻ was produced. These materials were found to take up Cu²⁺ rapidly from an aqueous solution at pH 5.0. Copper uptake by precipitates is attributed to the formation of chelate complexes of Cu²⁺ with citrate³⁻, malate²⁻, and tartrate²⁻.     

CLP-compactness for topological spaces and groups

We study CLP-compact spaces (every cover consisting of clopen sets has a finite subcover) and CLP-compact topological groups. In particular, we extend a theorem on CLP-compactness of products from [J. Steprāns, A. Šostak, Restricted compactness properties and their preservation under products, Topology Appl. 101 (3) (2000) 213-229] and we offer various criteria for CLP-compactness for spaces and topological groups, that work particularly well for precompact groups. This allows us to show that arbitrary products of CLP-compact pseudocompact groups are CLP-compact. For every natural n we construct:

(i)

a totally disconnected, n-dimensional, pseudocompact CLP-compact group; and

(ii)

a hereditarily disconnected, n-dimensional, totally minimal, CLP-compact group that can be chosen to be either separable metrizable or pseudocompact (a Hausdorff group G is totally minimal when all continuous surjective homomorphisms G→H, with a Hausdorff group H, are open).