Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

On the Smoothness of a Generalized Solution of the First Initial Boundary-Value Problem for Strongly Parabolic Systems in a Cylinder with Nonsmooth Base with Respect to Time Variable

We consider the first initial boundary-value problem for strongly parabolic systems in an infinite cylinder with nonsmooth boundary. We establish conditions for the existence of generalized solutions, an estimate for this solutions, and an estimate for the derivative of the solution.     

Infine Functions, Nonsmooth Alternative Theorems and Vector Optimization Problems

In this paper we introduce a new notion of infine nonsmooth functions and give several characterizations of infineness property. We prove alternative theorems with mixed constraints (i.e., inequality and equality constraints) being described by invex-infine nonsmooth functions. We establish a necessary and sufficient condition for a solution of a vector optimization problem involving mixed constraints to be a properly efficient solution.     

Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

Polymérisation anionique amorcée par les composés lamellaires du graphite et du lithium

In the present work, we use the binary insertion compound LiC₁₂ to polymerize styrene, methyl methacrylate, butadiene, isoprene, and to copolymerize isoprene and styrene in various hydrocarbon solvents (aromatics and aliphatic) and etheral solvents. We show that the styrene polymerization in aromatic solvents gives better yields than in the etheral solvents, the polymer being atactic. Methyl methacrylate does not polymerize in toluene but does so completely in DME. More generally, the yields of polymerization are better with KC₃₇ than with LiC₁₂ because of the different capacities of the monomer to get into the carbon layers. The polymerization of dienes with LiC₁₂ shows that the microstructures of the polymer obtained in π-or n-donor solvents are similar to the ones obtained by homogenous polymerization with Li cation in such solvents. However, for isoprene in cyclohexane, the results are different. The isoprene styrene copolymers are statistical ones and the mean length of styrene blocks is less than 5. The monomer interaction with the insertion compound and the growing chain geometry between the carbon layers are the facts which control either the stereospecificity of the polymerization or the selectivity of the copolymerization.     

Validated ion-exclusion chromatographic method for citrate and acetate in medical fluids

In this paper we describe the development and validation of a solid-phase extraction procedure, followed by ion-exclusion chromatographic determination of citrate and acetate in medical fluids. The medical fluids contained trace levels of non-polar compounds, which were not of interest for the purposes of assay requirements, but due to their strong affinity towards the ion-exclusion chromatography column necessitated a 180-min long runtime to elute. The developed SPE procedure, based on trapping the hydrophobic compounds, on a reversed-phase material, while allowing analytes of interest elute off unretained, shortened the runtime to 35 min. The procedure is simple since it has only two steps, conditioning of the SPE cartridge with acetonitrile and treating the sample. The SPE procedure followed by ion-exclusion chromatographic determination was successfully validated per the International Conference on Harmonization (ICH) guidelines in terms of specificity, accuracy as recovery versus untreated sample, precision, range, linearity of response, ruggedness, stability of treated samples, and robustness. The validation data showed that the method is specific, accurate, precise, rugged, and robust. The validated method has been routinely used in the manufacturing environment.     

Substituted γ-lactones. Some observations on the synthesis and reactivity of 4-aroyl-3-hydroxy-2(5H)-furanones

The reaction pathway towards formation of 4-aroyl-3-hydroxy-2(5H)-furanones 1 from the base catalyzed reaction between an acetophenone, diethyl oxalate and formaldehyde was investigated. If methoxide was used as base, a transesterification was found to occur in the first step, while a side reaction, namely the retro Claisen reaction, was in competition with the desired lactone formation in the second step. The nature of the solvent and the acidic character of 1 as well as the basicity of the aminoarylene were found to have a profound influence on the course of the reaction of 1 with aminoarylenes.     

Structural chemistry of azo complexes

Summary Complexes of Co^II, Ni^II, Cu^II, Pd^II, and Pt^IV with 2,4,5-trihydroxybenzoic acid and its substituted phenylazoderivatives have been prepared, together with some mixed-metal (Co, Cu or Ni, Cu) complexes of itsm-nitro,m-carboxy andm-hydroxyarylazo derivatives. The stereochemistries and the modes of bonding of the complexes were elucidated by spectral and magnetic susceptibility measurements.Abstracted from her Ph.D. thesis.     

Mesoporous electrode material from alumina-stabilized anatase TiO2 for lithium ion batteries

A mesoporous electrode material whose structure is composed of anatase nanocrystals stabilized by alumina is reported. Powder X-ray diffraction shows the anatase phase only, but micro-Raman spectroscopy shows that the materials have a core-shell morphology with grains of bulk anatase covered by a thin rutile layer on the surface. This structure is unique when compared to analogous materials stabilized by zirconia (PNNL-1). Nitrogen adsorption isotherms demonstrate a monotonous increase in surface area and mesopore volume with increasing Al content. Thin film electrodes from these materials were characterized by lithium insertion electrochemistry. Cyclic voltammograms exhibit significant differences in Li accommodation in Al-free and Al-stabilized materials.