Lyapunov-type inequalities for nonlinear systems

In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations.     

Romanovski polynomials in selected physics problems

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.     

Anodic stripping coulometry with collection for absolute trace analysis of lead, using flow-through electrochemical cells with porous working electrodes

Summary Flow-through electrochemical cells with porous working electrodes made of crushed reticulated vitreous carbon and plated with mercury were used for absolute analysis of trace amounts of lead by anodic stripping coulometry with collection (ASCWC) in a flow system. The role of mercury coating, flow rate and pH were investigated. The coulombic content of the collection peak corresponded to the theoretical values calculated by Faraday's law in a concentration range from about 10^–9 to 10^–6 mol/l. The relative error and the relative standard deviation was +0.15% and 0.8%, respectively for 2×10^–6 mol/l analyte concentration. The absolute detection limit (3 s) was 0.1 ng of Pb, the linear response range 7×10⁴. One leave from: Department of Analytical Chemistry, Slovak Technical University, CS-812 37 Bratislava, Czechoslovakia     

Some examples of application of the metric entropy method

We show how the metric entropy method can be substituted for the dyadic chaining, to prove in a unified setting several classical results. Among them are Stechkin's theorem, Gál--Koksma theorems and quantitative Borel--Cantelli lemmas. We give simpler proofs and improve some of these results. Two classes of examples are given: firstly stationary Gaussian sequences with applications to upper and lower classes and the law of the iterated logarithm for subsequences, and secondly in Diophantine approximation relatively to Gál and Schmidt's theorems.     

Crystal and molecular structures of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine.

The crystal structure of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine (C15H19NO3) (I) has been determined by X-ray analysis. It crystallizes orthorhombic space group Pbca with a = 24.295(3), b = 15.086(3), c = 7.552(3)A, V = 2768(1)A3, Z = 8, Dcalc = 1.254 g/cm3, mu = (Mo K(alpha)) = 0.87 cm(-1). The title compound has analgesic activity of cycloaliphatic amine part. The molecule is deviated from planar configuration.     

Hochschild cohomology and “smoothness” in monoidal categories

We introduce and investigate the properties of Hochschild cohomology of algebras in an abelian monoidal category M. We show that the second Hochschild cohomology group of an algebra in M classifies extensions of A up to an equivalence. We characterize algebras of Hochschild dimension 0 (separable algebras), and of Hochschild dimension ≤1 (formally smooth algebras). Several particular cases and applications are included in the last section of the paper.     

Investigation of the stability of metal species with respect to liquid chromatographic separations

Summary For accurate speciation analyses it is important to know the stability of the respective species, especially in the case of metal complexes. Factors affecting the chromatographic stability of such metal species are investigated. By using thermodynamic models for complex formation and chromatographic retention equilibria the influence of species concentration, stoichiometry and excess of ligand is calculated and compared with experimental results for iron complexes (lactate, gluconate and citrate species). Iron citrate is the only species, that is chromatographed as 1:2 complex (metal: ligand), while iron lactate and gluconate are transformed to 1:1 species. Problems resulting from the coelution of different species are discussed.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Simulated cosmic strings in a “big bang” in superfluid3He at 100 μK

During studies of the impact of single neutrons on superfluid³He at around 100μK we have measured the thermal energy released in the superfluid following the nuclear reaction, n+³He→p+³H+764keV. However, we find that the measured energy deposited in the quasiparticle system shortly after this reaction is substantially less than what we expect. We believe that this energy deficit represents that energy which has gone into the creation of vortices, in analogy to the creation of cosmic strings in the early universe via the Kibble mechanism. Furthermore, from the magnitude of the deficit, we can infer the vortex density which compares favorably with that predicted in Zurek’s scenairo.