Cis-coordination of the chromate anions in helical Co/Ni block-type polymeric systems. Structural and spectroscopic characteristics of catena(μ-CrO4-O,O′)[Co(HIm)3H2O] and catena(μ-CrO4-O,O′)[Co0.43Ni0.57(HIm)3H2O]

Two polymeric complexes: catena(μ-CrO₄-O,O′)[Co(HIm)₃H₂O] (1) and catena(μ-CrO₄-O,O′)[Co_0.43Ni_0.57(HIm)₃H₂O] (2) (where HIm=imidazole) with a cis-bridging coordination mode of the CrO₄ ²⁻ anion have been synthesized and characterized by X-ray and spectroscopic methods. These crystals were isolated from nine systems of varying reagent molar ratios and three excluding anions: Cl⁻, NO₃ ⁻ and SO₄ ²⁻ exclusively as mer [M(HIm)₃O₃]-type isomers. The unit cell of these isostructural complexes (monoclinic crystal system P2₁ /n) contains two independent helixes, left- and right handed, stabilized by intrahelical and interhelical hydrogen bonding and π–π interaction between pairs of the imidazole rings from neighbouring helixes. The Raman spectra at 77 K of 1 and 2 deconvoluted into lorentzian components revealed the block-type polymeric structure of the complexes. Moreover, the solution studies at millimolar concentrations of 1 and 2 indicated their complete decomposition in water. Four K electronic spectral analysis of the crystals (band deconvolution into gaussian components) enhanced with the data obtained in the polarized light allowed for assignment of the bands to the respective d–d transition (D_4h symmetry). It was found that the metallic centres are independently absorbing species, which supports the suggestion of a block-type structure of the polymers. The respective crystal field parameters for Co and Ni were calculated.     

Investigation of the tensile properties of “epoxy resin‐monomer” systems using cationic UV‐crosslinkable blends

The compatibility of cycloaliphatic and aromatic multifunctional epoxides with several epoxide resins allows the development of a wide range of cationic radiation‐curable formulations. The influence of different “epoxide resin‐monomer” systems UV‐cured in the presence of suitable cationic photoinitiators on the resulting physicochemical film properties was studied, and the results are stated. Copyright © 2004 John Wiley & Sons, Ltd.     

Differentiable circle maps with a flat interval

We study weakly order preserving circle maps with a flat interval, which are differentiable even on the boundary of the flat interval. We obtain estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set. Also, a sharp transition is found from degenerate geometry to bounded geometry, depending on the degree of the singularities at the boundary of the flat interval.Partially supported by KBN grant Iteracje i Fraktale #210909101.     

Some analytical semigroups occurring in probability theory

One-parameter semigroups occurring in operator-limit distributions are investigated. The topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup.     

Heuristic methods for evolutionary computation techniques

Evolutionary computation techniques, which are based on a powerful principle of evolution—survival of the fittest, constitute an interesting category of heuristic search. In other words, evolutionary techniques are stochastic algorithms whose search methods model some natural phenomena: genetic inheritance and Darwinian strife for survival.Any evolutionary algorithm applied to a particular problem must address the issue of genetic representation of solutions to the problem and genetic operators that would alter the genetic composition of offspring during the reproduction process. However, additional heuristics should be incorporated in the algorithm as well; some of these heuristic rules provide guidelines for evaluating (feasible and infeasible) individuals in the population. This paper surveys such heuristics and discusses their merits and drawbacks.An abridged version of this paper appears in the volume entitled META-HEURISTICS: Theory & Application, edited by Ibrahim H. Osman and James P. Kelly, to be published by Kluwer Academic Publishers in March 1996.     

On three-dimensional conformally flat quasi-Sasakian manifolds

LetM be a 3-dimensional quasi-Sasakian manifold. On such a manifold, the so-called structure function is defined. With the help of this function, we find necessary and sufficient conditions forM to be conformally flat. Next it is proved that ifM is additionally conformally flat with = const., then (a)M is locally a product ofR and a 2-dimensional Kählerian space of constant Gauss curvature (the cosymplectic case), or (b)M is of constant positive curvature (the non cosymplectic case; here the quasi-Sasakian structure is homothetic to a Sasakian structure). An example of a 3-dimensional quasi-Sasakian structure being conformally flat with nonconstant structure function is also described. For conformally flat quasi-Sasakian manifolds of higher dimensions see [O₁]     

Jauch-Piron system of imprimitivities for phonons. I. Localizability in discrete space

This paper is devoted to a discussion of the notion of localizability for phonons, i.e., quasiparticles arising from the harmonic vibrations of a system ofn atoms bound to one another by elastic forces. The natural tools for the analysis of localizability are the projection operatorsÊ() acting on the Hilbert space of one-phonon states, where is an arbitrary subset of the set that consists ofn vectors specifying the equilibrium positions ofn atoms. The expectation value ofÊ() is the probability that the phonon belongs to the atoms whose equilibrium positions are characterized by the elements of . For a strongly localizable phonon all of the projection operatorsÊ() commute with one another, whereas in the case of a weakly localizable phonon the operatorsÊ(₁) andÊ(₂) do not commute when ₁ and ₂ overlap. With the aid of the Jauch-Piron quantum theory of localization in space, the present paper describes the method of obtainingÊ() and also shows that if in the system ofn atoms there exist normal modes of zero frequency, then the phonon is only weakly localizable. Given the explicit expression forÊ(), one can define the number-of-phonons operator as well as the quasiparticle analogue (given in a companion paper) of the Wigner distribution function.     

Structure of colloid silica determined by viscosity measurements

The viscosity of nanosized colloid silica suspensions, used as binders in the investment casting, was determined as a function of their weight fraction reaching 52%. A new capillary viscometer was used whose construction eliminated sedimentation effects. The experiments have been carried out at fixed pH 10.0 and controlled ionic strength. It was found that for a low silica concentration range (weight fraction below 5%) the suspension viscosity increased more rapidly than the Einstein theory predicts. This anomalous behavior could not be explained in terms of the primary electroviscous effect predicted to be a few orders of magnitude smaller as observed. This discrepancy was accounted for by postulating a fuzzy, gel-like structure of colloid silicas used in our experiments. Hence, the apparent hydrodynamic radius of silica particles in aqueous suspensions was found to be larger than the primary particle size in accordance with previous observations. Based on this postulate, an apparent density of the silica sols was found to be 1.32-1.37 g/cm(3) instead of 2.2-2.32 g/cm(3) as determined from the suspension dilution method. This behavior was interpreted in terms of the core/shell model with high shell porosity, reaching 85%. Similarly, for higher concentration ranges, silica viscosity increased more rapidly with increased sol concentration than predicted by the Batchelor model derived for hard particles. The deviation was attributed to the secondary electroviscous effect stemming from the electrostatic interactions among silica particles in sheared suspensions. This effect has quantitatively been interpreted in terms of Russel's theory. On the other hand, for the high concentration range the experimental results were well accounted for by the Dougherty-Krieger model. By exploiting our experimental findings a sensitive method of determining the structure and apparent density of silica sols in aqueous media was proposed.     

Quecksilber(II)-Titrationen mit Variaminblau als Redoxindicator

Zusammenfassung Es wird eine volumetrische Methode zur Bestimmung von Cyanid- und Quecksilber(II)-ionen mit titrierter Quecksilber(II)-nitratlösung gegen Variaminblau als Indicator beschrieben. Das Verfahren liefert genaue, wenig streuende Werte.Vorgetragen auf der III. Arbeitstagung für analytische Chemie in Prag am 1. September 1959.