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.     

Synthesis and characterization of hollandite-type material intended for the specific containment of radioactive cesium

The hollandite Ba₁Cs_0.28Fe_0.82Al_1.46Ti_5.72O₁₆, which has been proposed for the cesium-specific conditioning, can be synthesized either by an alcoxyde or a dry route. In both cases, a two-step protocol is applied, i.e., a calcination at 1000 °C followed by a sintering at 1200 °C. After sintering, both synthetic processes lead to a tetragonal form. According to the X-ray diffraction (XRD) patterns collected at the barium and the cesium K absorption edges, the different positions of these two elements have been evidenced with a more centered position in the oxygen cubic site of the tunnel for Ba than for Cs. On the contrary, after calcination, the two synthetic routes yield different products. The alcoxyde route gives rise to a mixture of the aforementioned Cs- and Ba-containing tetragonal I4/m hollandite, a Cs-only-containing monoclinic I2/m hollandite and an unidentified phase with a weak coherence length containing only Ba. The dry route yields a single tetragonal hollandite material containing Ba and Cs slightly different in composition from the targeted compound.     

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.     

Solvent-generated HPLC systems with β-cyclodextrin derivatives as chiral additives

It is shown that enantioselective solvent-generated liquid-liquid and liquid-solid Chromatographic systems with -cyclodextrin derivatives can be realized. The liquid-liquid systems are based on ternary solvent systems of limited miscibility, containing chiral additives; the chiral stationary phase is spontaneously generated on the porous microparticulate silica used as a solid support. In the solvent-generated adsorption systems a very small proportion of -cyclodextrin derivatives is added to the mobile phase. These components act as column activators, since they are strongly adsorbed on the RP solid support where they form new stereoselective adsorption sites. It is demonstrated that dynamically generated systems with -cyclodextrin derivatives as chiral agents are powerful and versatile tools for enantioseparation of different types of compounds. This technique creates not only a new type of selectivity but also leads to very stable and reproducible Chromatographic columns.Dedicated to Professor J. F. K. Huber on the occasion of his 65th birthday     

Thermal decomposition of Cr(III) dithiocarbamates

The thermal stability of chromium(III) complexes with dithiocarbamate acid derivatives was studied. The general formula of these complexes is (RCS₂)₃Cr where: The thermal stability of these complexes was found to depend on the kind ofR and the decomposition occur in several stages.The final product of the decomposition of the complexes in the 20–600 temperature range investigated is chromium sulphide, Cr₂S₃ or with incomplete combusted sulfur atoms.

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Zusammenfassung Die Thermostabilität von Chrom(III)-Komplexen mit sauren Derivaten von Dithiocarbamat wurde untersucht. Die allgemeine Formel dieser Komplexe ist (RCS₂)₃Cr. Es wurde festgestellt, da\ die Thermostabilität dieser Komplexe von der Art von R abhängt und die Zersetzung in mehreren Stufen verläuft.Das Endprodukt der Zersetzung der Komplexe im untersuchten Temperaturbereich von 20 bis 600 ist Chromsulfid, Cr₂S₃, oder solches mit überschüssigem Schwefel.

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Résumé On a étudié la stabilité thermique des complexes du chrome(III) avec les dérivés de l'acide dithiocarbamique. La formule générale de ces complexes est (RCS₂)₃Cr où: On a trouvé que la stabilité thermique de ces complexes dépendait de la nature du radical et que la décomposition se déroulait en plusieurs étapes.Dans l'intervalle de température étudié, de 20 à 600, le produit final de la décomposition des complexes est le sulfure de chrome, Cr₂S₃, éventuellement accompagné de soufre résultant d'une combustion incomplÊte.

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(III) - . — (RCS₂)₃ Cr, , R . 20–600 Cr₂S₃ .

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The autors would like to thank Doc. dr h. J. F. Biernat for valuable discussions.     

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.     

Investigation of eutectic transformation of Zn−Al alloy by DTA

The paper discusses the investigation of crystallization of metals and alloys by differential thermal analysis (DTA). It was assumed that this method allows determination of the mechanism and kinetics of volumetric crystallization underiso conditions (e.g. anisothermal) on the basis of the parameters of the equation expressing an integral form of the DTA curve. From DTA, a course of eutectic transformation was determined for a technical Zn?Al alloy containing 4wt% Al. Investigations were carried out under continuous cooling at various rates and the kinetics parameters were determined with the KEKAM equation:-ln(1-x)=kl _n     

Average local electrostatic potential and the core-valency separation in atoms

The average local electrostatic potential function, V(r)/ ρ(r), is calculated for 87 atoms, Li-Ac, in the ground state using the nonrelativistic average-over-configuration numerical Hartree-Fock density. It is found empirically that in a given atom the shell boundaries are expressed as the successively increasing maxima in V(r)/ ρ(r) and the outermost maximum presents good approximate estimates of the core-valence separation in atoms. The likeness in behavior of V(r)/ ρ(r) at each shell boundary with the maximum hardness principle is discussed. The single-exponent-fit parameters for the electron density in the valency region are provided for all atoms. © 1995 John Wiley & Sons, Inc.