Light-Cone Operator-Product Expansions Revisited: I

We again consider the problem of the light-cone expansion for products of currents and explain the motivations making a rethinking of old results relevant today.     

An effect of application of chiral aluminium alkoxides and amides as adducts to zirconium catalyzed carbo- and cycloalumination of olefins

This paper is dedicated to a study of properties of the following novel optically active organoaluminium compounds (OACs): (1S,2S)-l,7,7-trimethyl-2-[(dialkylalumina)oxy]-bicyclo[2.2.1]heptanes and (1S)-N-(dialkylalumina)-6,7-dimethoxy-1-methyl-1,2,3,4- tetrahydroisoquinolines. The synthesis of the chiral OACs was carried out in the reaction of either natural camphor or salsolidine with both AlEt₃ and i-Bu₂AlH. The main goal of the research was to investigate the stereodifferentiating activity of the chiral OACs in the olefin carbo- and cycloalumination reactions, catalyzed by Cp₂ZrCl₂.     

Gamow Vectors in Exactly Solvable Models

Through two examples: the Friedrichs model and a particular case of central potential scattering, we illustrate the way of constructing Gamow vectors.     

Van der waals waves in free-surface liquids

It is shown that, along with gravity waves, surface and internal waves caused by van der Waals forces may exist in a liquid with a horizontal free surface. A dispersion relation is found by using the stepwise approximation for the coefficients of a wave equation derived for these waves. The surface waves are similar to surface gravity waves in dispersion and amplitude distribution but differ in frequency by several orders of magnitude. Another sequence of roots in the spectrum corresponds to internal van der Waals waves that have an upper frequency bound and the dispersion law typical of a multimode waveguide.     

1,1,3-Trimethyl-3-phenylindan as a Luminescent Additive to a Plastic Scintillator Based on Poly(methyl Methacrylate)

The luminescence and scintillation properties of poly(methyl methacrylate) containing 1,1,3-trimethyl-3-phenylindan were studied.     

Synthesis of New Plant Growth Regulators,Isomeric 1-(Dimethyloctyl)- and 1-Alkylpiperidinium and -morpholinium Halides by Telomerization of Isoprene with Secondary Amines

The known plant growth regulator, Al'den [1-(3,7-dimethyloctyl)-1-allylpiperidinium bromide], and also 1-(3,7-dimethyloctyl)-1-methylpiperidinium iodide were synthesized by treatment with allyl bromide and methyl iodide, respectively, of exhaustively hydrogenated 1-nerylpiperidine which was obtained by anionic telomerization of isoprene with piperidine. Various quaternary ammonium salts having a terpene sub- stituent with unnatural dimethyloctane skeleton, which effectively stimulate florification of Aster Chinensis L., were prepared by the action of alkyl halides on telomerization products derived from isoprene and piperidine or morpholine in the presence of palladium complexes.     

Multilayer optics for XUV spectral region: technology fabrication and applications

We present research investigations in the field of multilayer optics in X-ray and extreme ultra-violet ranges (XUV), aimed at the development of optical elements for applications in experiments in physics and in scientific instrumentation. We discuss normal incidence multilayer optics in the spectral region of “water window”, multilayer optics for collimation and focusing of hard X-ray, multilayer dispersing elements for X-ray spectroscopy of high-temperature plasma, multilayer dispersing elements for analysis of low Z-elements. Our research pays special attention to optimization of multilayer optics for projection EUV-lithography (ψ-13nm) and short period multilayer optics.     

Lattice parameter and luminescence properties of europium activated yttrium oxide

Samples of yttrium oxide doped with trivalent europium have been prepared by ceramic techniques, under different synthesis conditions; barium chloride (BaCl₂) and sodium tetraborate (Na₂B₄O₇) were tested as flux. The improvement of luminescence properties in dependence on substitution of Eu³⁺ for Y³⁺ in the host lattice, under electron and UV excitations is demonstrated. The lattice parameter as a quantitative assessment of activator incorporation degree is proposed. The obtained results are discussed with respect to the employed processing method.     

On separation of gradient Young measures

Let be a linear subspace of real matrices without rank-one matrices and let be a finite set. Suppose is a bounded arcwise connected Lipschitz domain and is a sequence of bounded vector-valued mappings in such that in as , where is the closed -neighbourhood and the distance function to . We give estimates for such that up to a subsequence, in for some fixed . In other words, we give estimates on such that separates gradient Young measure. The two point set with is a special case of such sets up to a translation. Received: 20 July 2001 / Accepted: 23 January 2002 / Published online: 5 September 2002