A note on a problem arising from risk theory

In this note we give an answer to a problem of Gheorghiţă Zbăganu that arose from the study of the properties of the moments of the iterates of the integrated tail operator.     

Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface Embedded in a Porous Medium with Anisotropy Effect

The steady boundary-layer flow near the stagnation point on a vertical flat plate embedded in a fluid-saturated porous medium characterized by an anisotropic permeability is investigated. Using appropriate similarity transformation, the governing system of partial differential equations is transformed into a system of ordinary differential equations. This system is then solved numerically. The features of the flow and the heat transfer characteristics for different values of the governing parameters, namely, the modified mixed convection parameter Λ, and the anisotropy parameter A are analyzed and discussed. It is found that dual solutions exist for both assisting and opposing flows. Moreover, the range of Λ for which the solution exists increases with A.     

Boundary layer flow at a three-dimensional stagnation point in power-law non-Newtonian fluids

Similarity solutions for the three-dimensional flow and heat transfer of a power-law fluid near a stagnation point of an isothermal surface are presented. The results of the numerical integrations are given in tables and shown on graphs for some different values of the power-law index n, geometric parameter c, and the Prandtl number Pr. Whenever possible, these results are compared with available analytical solutions and found to be highly accurate.     

Mixed Convection Stagnation-Point Flow Over a Vertical Plate with Prescribed Heat Flux Embedded in a Porous Medium: Brinkman-Extended Darcy Formulation

This article considers the problem of mixed convection stagnation-point flow towards a vertical plate embedded in a porous medium with prescribed surface heat flux. It is assumed that the free stream velocity and the surface heat flux vary linearly from the stagnation point. Using a similarity transformation, the governing system of partial differential equations is transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and the heat transfer characteristics are analyzed and discussed. It is found that dual solutions exist for both buoyancy assisting and opposing flows.     

ChemInform Abstract: Beyond the Icosahedron: A Density Functional Theory Study of 14‐Atom Germanium Clusters.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Structural studies of tetrazoles. Crystal and molecular structure and ab initio calculations of 1-phenyl-1H-tetrazole-5-thiolate,as its [diaqua(18-crown-6)sodium] salt: An anionic tetrazole free of direct metal interactions

The structure of the anionic heterocycle obtained by deprotonation of 1-phenyl-1H-tetrazole-5-thione was determined by X-ray diffractometry. The counterion is [Na(18-crown-6)(H₂O)₂]⁺. There are no direct interactions between the metal and the tetrazole, while hydrogen bonds between sodium ion coordinated water molecules and neighboring azole anions give cohesion to the crystal. The thiotetrazolato ion displays extensive π-delocalization, with all members of the ring and the exocyclic sulfur contributing to it; however, no interannular conjugation between the phenyl and azole rings is found. The structure of the heterocycle is best described as a resonance hybrid. The geometric parameters of the metal-free tetrazole could be used as the input of ab initio MO calculations at the 6-31G*//3-21G* level, which supported the proposal that the negative charge is mainly concentrated on the N₄-C₅-S portion of the tetrazolate. Some small but significant and consistent bond length differences are found in the uncoordinated tetrazole with respect to metal-bonded analogues. The coordination behavior of the crown ether, with five oxygens bonded to sodium in the complex cation, is rare. © 1997 John Wiley & Sons, Inc.     

Multipolymers with Fischer-Tropsch olefins

Multipolymers consisting of ethylene, 1-heptene, 3-methylpentene and 4-methylpentene were prepared with a heterogeneous Ziegler-Natta catalyst. The polymers were prepared in such a way that the molar fraction of the comonomers remained the same. Copolymers of ethylene/1-heptene and ethylene/4-methylpentene were prepared in order to study the changes in polymer characteristics as one moves from an ethylene/linear alpha olefin copolymer through ethylene multipolymers to an ethylene/4-methylpentene copolymer. The mechanical, rheological and application properties showed expected trends.     

Heats of formation of organic molecules by ab initio methods: Thiaalkanes

The bond energy scheme for calculating heats of formation of organic molecules from ab initio data (6–31G*) has been extended to include 24 compounds containing sulfur in the sulfide oxidation state. The rms deviation from the experimental values for these compounds is 0.54 kcal/mol, which is approximately experimental error.