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.     

Lower-dimensional linear complementarity problem approaches to the solution of a bi-obstacle problem

A globally convergent Broyden-like method for solving a bi-obstacle problem is proposed based on its equivalent lower-dimensional linear complementarity problem. A suitable line search technique is introduced here. The global and superlinear convergence of the method is verified under appropriate assumptions.     

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     

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.     

High performance 1689-nm quantum well diode lasers

1689-nm diode lasers used in medical apparatus have been fabricated and characterized. The lasers had pnpn InP current confinement structure, and the active region consisted of 5 pairs of InGaAs quantum wells and InGaAsP barriers.     

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.     

A multifractal decomposition according to rate of returns

For one‐dimensional simple symmetric random walk, the Hausdorff and packing dimensions of sets of sample paths with prescribed rate of returns to the origin are determined. This gives a multifractal decomposition of the underlying sample space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.