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.     

Long-range magnetic ordering in iron jarosites prepared by redox-based hydrothermal methods

The iron jarosites, plumbojarosite, Pb0.5Fe3(OH)6(SO4)2, argentojarosite, AgFe3(OH)6(SO4)2, and thallium jarosite, TlFe3(OH)6(SO4)2, along with the selenate-capped jarosite analogues of potassium, KFe3(OH)6(SeO4)2, and rubidium, RbFe3(OH)6(SeO4)2, have been prepared in their analytically pure forms by employing redox-based hydrothermal methods. The crystal structures of these materials have been determined, and all are found to be essentially isostructrual including Pb0.5Fe3(OH)6(SO4)2, which is distinct from the structure reported for naturally mined samples. All iron jarosites show long-range order (LRO), signified by a sharp transition temperature, T(N), which falls in the narrow temperature range of 61.4 +/- 5 K. The mechanism responsible for this ordering has been established by examining magnetostructural correlations for the jarosites possessing various interlayer cation and capping groups. We show that all magnetic properties of jarosites, including LRO, find their origin in the basic magnetic unit, the intralayer Fe3(mu-OH)3 triangle. Field-dependent magnetization experiments are consistent with the antiferromagnetic stacking of an out of plane moment developed from spin canting within Fe3(mu-OH)3 triangles. Together with the previously reported AFe3(OH)6(SO4)2 (A = Na+, K+, Rb+ and NH4+) jarosites, these compounds provide a framework for probing magnetic ordering in a spin frustrated lattice of the largest series of isoelectronic and isostructural kagomé systems yet discovered.     

Organometallic reactions of α-haloimines as a useful tool in organic synthesis

The reaction of organometallic reagents, e.g. alkyllithiums, cuprates and alkylcoppers, with α-haloimines gave selectively a variety of synthetically useful reactions, including coupling to 1,4-diimines, homologation, and production of heterocycles.     

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     

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.