Idealization of a decomposition theorem

In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A _I-sets and A _I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A _I-continuous. This revised version was published online in June 2006 with corrections to the Cover Date.     

On α-I-continuous and α-I-open functions

Montgomery and Vaughan improved a theorem of Erd?s and Fuchs for an arbitrary sequence. Sárközy extended this theorem of Erd?s and Fuchs for two arbitrary sequences which are "near" in a certain sense. Using the idea of Jurkat (differentiation of the generating function), we will extend similarly the result of Montgomery and Vaughan for "sufficiently near" sequences.     

Decompositions of some weaker forms of continuity

The aim of this paper is to give decompositions of some weaker forms of continuity using the concepts of classes B ₁, B ₂, B ₃, αA and αC introduced by ourselves.     

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.     

Charge density fluctuation of low frequency in a dusty plasma

The charge density fluctuation of low frequency in a dusty plasma, which is derived from the longitudinal dielectric permittivity of the dusty plasma, has been studied by kinetic theory. The results show that theP value, which describes the relative charge density on the dust in the plasma, and the charging frequency of a dust particle Ω _c , which describes the ratio of charge changing of the dust particles, determine the character of the charge density fluctuation of low frequency. For a dusty plasma ofP≪1, when the charging frequency Ω _c , is much smaller than the dusty plasma frequency ω_d, there is a strong charge density fluctuation which is of character of dust acoustic eigenwave. For a dusty plasma ofP≫1, when the frequency Ω _c , is much larger than ω _d there are weaker fluctuations with a wide spectrum. The results have been applied to the ionosphere and the range of radius and density of dust particles is found, where a strong charge density fluctuation of low frequency should exist.     

Colour intransparency and the cross sections for colour-singlet and colour-octet hadrons in the Low-Nussinov model

The dependence of cross sections on the colour state of the colliding hadrons is investigated within the Low-Nussinov model of two-gluon exchange. The total cross sections for colour-octet hadrons are practically constant as functions of the hadronic radii, while they tend to zero when the radii of the colour-singlet hadrons approach zero. The slope parameter of the differential clastic cross sections for small momentum transfers is rather insensitive to the colour structure of the colliding hadrons. The integrated colour exchange cross section is calculated.     

Crossing of shears bands in196Pb

High-spin states in¹⁹⁶Pb have been populated using the reaction¹⁷⁰Er(³⁰Si,4n). The previously observed shears bands in this nucleus have been extended and some of their transitions have been reordered. They now form regular bands with band crossings. One of the bands splits into two pathways at high spin.     

On the ordering in [(C2H5)4N]2CuCl4 crystal: an X-ray study and theoretical considerations

The crystal structure [(C₂H₅)₄N]₂CuCl₄ has been determined by X-ray diffraction at 243K. The room temperature phase (phase I) belongs to the space group P4₂/nm [1] whereas the low temperature phase (phase II) is orthorhombic and belongs to the space group Pnna. The phase transition at T_c=258K is of improper ferroelastic type and it is associated with the ordering of the CuCl₄ ^2? and a partial ordering of the [(C₂H₅)₄N]⁺ ions which are disordered in the high temperature tetragonal phase. At lower temperature, there occurs another instability which could correspond to a complete ordering in the crystal.