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Khanh Le Chau Pham Duc Chinh 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(4):614-622
In this paper inequalities for the effective conductivity of isotropic composite materials are derived. These inequalities depend on several coefficients characterizing the microstructure of composites. The obtained coefficients can be exactly calculated for models of a two-component aggregate of multisized, coated ellipsoidal inclusions, packed to fill all space. As a result, new bounds for effective conductivity, considerably narrower than those of Hashin-Shtrikman, are established for such models of composite materials. 相似文献
3.
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. 相似文献
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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. 相似文献
6.
Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints
Pham 《Applied Mathematics and Optimization》2002,46(1):55-78
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. 相似文献
7.
G. Merle J. P. Pascault Q. T. Pham C. Pillot R. Salle J. Gol I. Rashkov I. Panayotov D. Gurard A. Hrold 《Journal of polymer science. Part A, Polymer chemistry》1977,15(9):2067-2074
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. 相似文献
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The self association of cumyl hydroperoxide and its complexing with polar monomers have been studied by proton magnetic resonance. These complexations are exothermic and strongly temperature dependent. It has been suggested that the complexation of cumyl hydroperoxide by polar monomers could be one of the causes of its efficiency in initiating the radical polymerization of vinyl monomers on an ethyl-zinc terminated polyethylene chain to form radical block copolymers. However, if this phenomenon has an effect on the initiation, it should not affect the propagation mechanisms, because the hydroperoxide is destroyed by ZnEt2 during initiation. Moreover, the tacticity of radical polymethylmethacrylate, obtained at 60° with (ZnEt2—cumyl hydroperoxide) in heptane does not differ from the conventional radical polymer. 相似文献