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.     

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.     

Synthesis of single crystalline layered lithium manganese oxide nanorods

Single-crystalline layered lithium manganese oxide nanorods were prepared via a low-temperature molten salt synthesis method. The material was investigated by a variety of techniques, including X-ray powder diffraction (XRD), transmission electron microscopy (TEM), and X-ray photoelectron spectrum (XPS).     

Structural effects of multiple-bonds on aggregating tendencies of long-chain esters

The kinetics of the hydrolysis of p-nitrophenyl esters of three types of single-chain carboxylic acids, namely, saturated, olefinic and acetylenic, was investigated in two aquiorgano binary solvent systems, DMSO-H₂O and dioxane (DX)-H₂O. The ester probes used are: octanoic (C8), dodecanoic (C12) , stearic (C18) , oleic (C18-ol) , elaidic (C18-el ) and stearolic (C18-st). The order of measured CAgC values is: C18-ol>C18-el>C18>C18-st, whereas the order of decreasing magnitude of the observed hydrolytic rate constants of the monomeric species (k_m) is: C18>C18-el>C18-ol> C18-st. These rather unanticipated results are discussed.     

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.     

Sharp condition of global existence for second-order derivative nonlinear Schrödinger equations in two space dimensions

This paper discusses a class of second-order derivative nonlinear Schrödinger equations which are used to describe the upper-hybrid oscillation propagation. By establishing a variational problem, applying the potential well argument and the concavity method, we prove that there exists a sharp condition for global existence and blow-up of the solutions to the nonlinear Schrödinger equation. In addition, we also answer the question: how small are the initial data, the global solutions exist?     

超软X射线流气式正比计数管

介绍了一种用于测量183～933eV超软X射线的圆柱形、侧窗式、流气式正比计数管,工作气体是0.11MPa的P-10气体或氦气-丙烷混合气体。计数管内径为φ25mm,直径为φ0.3mm的入射窗是由厚度80～90μgcm~2聚乙烯甲醛制成的。该计数管的特点:(1)薄窗,对软X射线透过率高。(2)流气式,工作寿命长。(3)能量分辨率好。(4)计数率高(1×10~(14)个/s)。(5)可测能区宽(0.183～10keV)。(6)可以方便更换窗膜材料、厚度及窗口直径。近几年来该计数管已经为高强度低能X光源提供较好监测。     

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.