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.     

Infrared spectroscopic analyses of transformations of chemical species on the silica highly-reacted with gaseous BF3.

Transformations of chemical species formed by the reaction of gaseous BF3 with high pressure and silica preheated at 473 and 1093 K were studied with the use of infrared absorption spectrometry. The species containing -BF2 and the species containing >BF were transformed to each other on the highly-reacted silica depending on the pressure of BF3 in cell, and some of the species containing -BF2 were also desorbed without their transformations to the species containing >BF. H2O played important roles in these transformations.     

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.     

Study on effects of substrate temperature on growth and structure of alignment carbon nanotubes in plasma-enhanced hot filament chemical vapor deposition system

Alignment carbon nanotubes (ACNTs) were synthesized on silicon substrate coated with Ni catalyst film and Ta buffer layer by plasma-enhanced hot filament chemical vapor deposition using CH₄, NH₃, and H₂ as the reaction gas, and they were investigated by scanning electron microscopy and transmission electron microscopy. It is found that the diameter of the bamboo-structured ACNTs is increased from 62 to 177 nm when the substrate temperature was changed from 626 to 756 °C. Their growth rate is enhanced by the substrate temperature in a range of 626-683 °C and it is reversely reduced with the substrate temperature after the substrate temperature is over 683 °C. Beginning with wetting phenomenon, the effects of the substrate temperature on the structure and growth rate of the ACNTs are analyzed.     

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.     

偶氮侧基聚合物光致异构动力学研究

本文对偶氮侧基聚合物相位共轭光时间特性进行了研究,得到了相位共扼光产生机制─光致异构过程的时间常数.在相位共轭光上升阶段,其时间常数在0.4～0.5s之间,在相让共轭光的衰减过程,衰减满足双指数关系,分段拟合得到较好的结果,且得到快过程的时间常数为0.27s,慢过程的时间常数为0.78s.