Calorimetric studies of refractory corundum

Calorimetry has been used in the investigations of calcium aluminate materials produced as a binder for aluminate-corundum composites of high refractoriness. The kinetics and of hydration process was thus characterized and the optimum compositions of initial binders and cement-corundum refractory filler blends could be selected for further tests. The acceleration of heat evolution - the shortening of so-called induction period and relatively high heat output in the presence of corundum was observed. It means the acceleration of hydration process, that is early crystallisation of hydration products and subsequent further dissolution of initial anhydrous aluminate phases. In the presence of fine grained corundum particles these phenomena should be attributed to the nucleating effect of fine corundum particles. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fluorescence lifetimes and spectral properties of protochlorophyllide in organic solvents in relation to the respective parameters in vivo

In this work, absorption and fluorescence spectra of protochlorophyllide (Pchlide), as well as its fluorescence lifetime, were investigated in organic solvents having different physical properties. The obtained Pchlide spectral features are discussed in relation to the parameters describing solvent properties (refractive index and dielectric constant) and taking into account the specific solvent-Pchlide interaction. The correlation of Pchlide Qy and Soret absorption bands with solvent polarizability function ((n2 - 1)/(n2 + 2)) has been found; however, the dispersion of the observed points was rather high. A small Stokes shift of a magnitude between 50 and 300 cm(-1) was found, which indicates low sensitivity of Pchlide to nonspecific solvation. The fluorescence decay of Pchlide was single exponential in all the investigated solvents, with the lifetime value ranging from 5.2 ns for dioxane to 3.5 ns for methanol. Dependence of the obtained fluorescence lifetimes on the solvent orientation polarizability, a parameter being the function of both refractive index and dielectric constant, was discussed. In water-methanol mixtures, a further decrease of the fluorescence lifetime was observed, giving values of 2.9 ns for 25% methanol. Double-exponential decay of Pchlide fluorescence was found for Pchlide in a solution of 15% methanol with the lifetimes of 4.5 +/- 0.5 ns and 1.2 +/- 0.3 ns and in pure water with the lifetimes of 2.5 +/- 0.5 ns and 0.4 +/- 0.1 ns. The obtained results are discussed in relation to spectroscopic properties of Pchlide in vivo.     

Finitely convergent deterministic and stochastic iterative methods for solving convex feasibility problems

We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that certain overrelaxation parameters form a divergent series. We combine our methods with a very general class of deterministic control sequences where, roughly speaking, we require that sooner or later we encounter a violated constraint if one exists. This requirement is satisfied, in particular, by the cyclic, repetitive and remotest set controls. Moreover, it is almost surely satisfied for random controls.

     

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     

Influence of substituents on positron annihilation in styrene copolymers

Results of angular correlation of annihilation radiation (ACAR) and positron annihilation lifetime (PAL) measurements are presented for five styrene copolymers: poly(co-styrene-phenylmaleimide) and its three derivatives with chlorine as well as for one with the OH group substituted at the benzene ring. It occurs that the chlorine substituted at three different positions at the benzene ring poly(co-styrene-o (or-m,-p)-chlorophenylmaleimide) inhibits the formation of the positronium to different extent. The greatest effect is observed in case of the chlorine atom substituted at the benzene ring at the ortho-position towards the nitrogen atom. The two long lifetimes (₃ and ₄) observed in the lifetime spectra are connected with the bimodal distributions of the free volume radius in the samples.     

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.