Solution of the problem of combinatorial characterization of the dimension of the kernel of a starshaped set

It is proved for a nonempty proper subset S of a real topological linear space L that kerS ={convA_z: z bdryS} and for a close connected nonconvex subset S of L that kerS ={convA_z: z slncS}, where bdryS and slncS denote the sets of boundary points and strong local nonconvexity points of S, respectively, and A_z = {s S: z is clearly visible from s via S}.This extends previous results and, combined with standard techniques, yields among others two Krasnosel'skii-type characterizations for the dimension of kerS in R^d in case of a nonempty proper set S with bdryS bounded and a closed connected nonconvex set S with lncS bounded.The assumption of boundedness of S turns out to be irrelevant in these criteria.Herrn Professor Dr. Wilhelm Stoll gewidmetResearch partially supported by the grant PB 2 1140 91 01     

Two-point Padé approximants for formal Stieltjes series

We prove that certain two-point Padé approximants occupying the diagonal of the Padé table form monotone sequences of lower and upper bounds uniformly converging to a Stieltjes function. The results can be applied to the theory of inhomogeneous media for the calculation of the bounds on the effective transport coefficients of heterogeneous materials.     

Fuzzy quantum logics and infinite-valued Łukasiewicz logic

A new, physically more plausible definition of a fuzzy quantum logic is proposed. It is shown that this definition coincides with the previously studied definition of a fuzzy quantum logic; therefore it defines objects which are traditional quantum logics with ordering sets of states. The new definition is expressed exclusively in terms of fuzzy set operations which are generated by connectives of multiple-valued logic studied by ukasiewicz at the beginning of the 20th century. Therefore, the logic of quantum mechanics is recognized as a version of infinite-valued ukasiewicz logic.     

Separately harmonic and subharmonic functions

Let u(x, y) be defined in B ₁×B ₂ where B ₁ ^m and B ₂ ⁿ , and assume that u(x, ·) harmonic for every fixed x and u(·, y) is subharmonic for every fixed y. We show that if u(·, y) is, in addition, C ² for each y then u is subharmonic in B ₁×B ₂ in both variables jointly.     

A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

Development of a capillary electrophoretic method for the analysis of amino acids containing tablets

Ketosteril is an enteral medicinal product indicated for prevention and therapy in chronic renal insufficiency in connection with a low protein diet. Tablets of Ketosteril contain five essential amino acids like: Lys, His, Thr, Trp, Tyr and another five amino acids in the form of their hydroxy and keto analogues as calcium salts, that are: alpha-ketoleucine, alpha-ketoisoleucine, alpha-ketovaline, alpha-ketophenylalanine and alpha-hydroxymethionine. The composition of Ketosteril tablets is routinely tested with three LC methods. Capillary electrophoretic method seems to be a good alternative for amino acids and their analogues determination in multicomponent pharmaceuticals because of short analysis time and the possibility to assay all components during a single run without any pretreatment. Electrophoresis was performed in 50 microm I.D. fused-silica capillaries with 65 cm distance to the detector. Capillaries were installed in Waters Quanta 4000 electrophoretic equipment with a positive power supply and on-line UV detection at 214 nm. Separations were done in a buffer containing 40 mM Tris and 160 mM boric acid titrated with NaOH to pH 10. The method developed allows the separation of all investigated analytes with an efficiency of n = 230,000 and 20 min analysis time. The method was applied for determination of all components of Ketosteril in commercial tablets.     

Electronic structure of octacyanides of molybdenum IV and V according to the SCCC MO method

The SCCC MO method has been used to calculate the electronic structure and spectrum of Mo(CN) ₈ ^4– and Mo(CN) ₈ ^3– ions of a D _4d symmetry. All metal-ligand and ligand-ligand interactions and all overlap integrals (over products of HF atomic orbitals) have been included within the SCCC MO scheme. Basing on these calculations a new assignment of some absorption bands is proposed. The overall agreement between the calculated and observed electronic spectrum is satisfactory.

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Zusammenfassung Elektronenstruktur und Spektrum der [Mo(CN)₈]^–4- und [Mo(CN)₈]^–3-Ionen in D _4d -Symmetrie wurden mit der SCCC-MO-Methode berechnet. Alle Metall-Ligand- und Ligand-Ligand-Wechsel-wirkungen und Überlappungsintegrale wurden berücksichtigt. Die Bandenzuordnung wurde neu vorgenommen. Die Übereinstimmung der berechneten und gemessenen Spektren ist befriedigend.

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Résumé Application à Mo(CN) ₈ ^4– et Mo(CN) ₈ ^3– de la méthode SCCC MO basée sur des orbitales atomiques HF approchées, en tenant compte du recouvrement et de toutes les interactions ligand-ligand. Dans la partie I on discute le cas de la symétrie D _4d . L'accord global avec l'expérience est satisfaisant en ce qui concerne les spectres. On montre aussi que toutes les attributions antérieures basées sur la théorie du champ cristallin semblent inadéquates.

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The authors are grateful to Prof. W. Jakób, Dr. Z. Stasicka and Dr. A. Samotus for many interesting discussions, to Prof. J. Chojnacki for providing us with new X-ray results before publication and to Dr. A. J. Sadlej for a help in dealing with the computer.     

Propagating transverse electric and transverse magnetic modes in liquid crystal-clad planar waveguides

ABSTRACT

In a planar dielectric waveguide, weak confinement of a propagating mode in a high index core leads to a measurable evanescent interaction with the cladding. In this work, we study the effect of a reorientable anisotropic cladding on the behaviour of Transverse Electric (TE) and Transverse Magnetic (TM) mode polarisations using a liquid crystal (LC)-clad waveguide architecture. The polarised evanescent field of a guided mode interacts with a voltage-tunable birefringent LC cladding to deflect an out-coupled beam. Experimental measurements are coupled with a theoretical framework and show good consistency with simulation results. We isolate the effect of mode confinement by changing the thickness of the high index core. Interactions between the LC index ellipsoid and the mode polarisation are probed by changing the initial alignment of the LC. Finally, we examine the difference in deflection between TE and TM modes, which incorporates both a change in mode confinement and a difference in LC index components.     

Proton and lithium cation affinities calculated with floating orbital geometry optimization (FOGO)

The FOGO method is used to calculate proton affinities and lithium cation affinities. The molecules of primary interest in this study are the methyl-substituted amines. In addition, the lithium cation affinity of HF, H₂O, CH₃OH, H₂CO, and HCN are calculated for comparison. Geometries of all species are fully optimized with a double-zeta (DZ) basis set, including polarization on hydrogen and the first-row elements by floating orbitals. Comparison with experimental values demonstrates that structural data and proton affinities resulting from this type of ab initio calculation are of chemical accuracy. The lithium cation affinities are also reasonably well reproduced, but the small experimental differences are not within the accuracy, which can be expected from this type of calculation.