Application of the sequential gradient-restoration algorithm to thermal convective instability problems

The problem of the thermal stability of a horizontal incompressible fluid layer with linear and nonlinear temperature distributions is solved by using the sequential gradient-restoration algorithm developed for optimal control problems. The hydrodynamic boundary conditions for the layer include a rigid or free upper surface and a rigid lower surface. The resulting disturbing equations are solved as a Bolza problem in the calculus of variations. The results of the study are compared with the existing works in the literature.The authors acknowledge valuable discussions with Dr. A. Miele.     

A method for minimizing the sum of a convex function and a continuously differentiable function

This paper presents a method for minimizing the sum of a possibly nonsmooth convex function and a continuously differentiable function. As in the convex case developed by the author, the algorithm is a descent method which generates successive search directions by solving quadratic programming subproblems. An inexact line search ensures global convergence of the method to stationary points.     

On projective group properties of the 6D pseudo-Riemannian space

We study the six-dimensional pseudo-Riemannian spaces with two time-like coordinates that admit non-homothetic infinitesimal projective transformations. The metrics are manifestly obtained and the projective group properties are determined. We also find a generic definition of projective motion in the 6-dimensional rigid h-space. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Geostatistical computing of acoustic maps in the presence of barriers

Acoustic maps are the main diagnostic tools used by authorities for addressing the growing problem of urban acoustic contamination. Geostatistics models phenomena with spatial variation, but restricted to homogeneous prediction regions. The presence of barriers such as buildings introduces discontinuities in prediction areas. In this paper we investigate how to incorporate information of a geographical nature into the process of geostatistical prediction. In addition, we study the use of a Cost-Based distance to quantify the correlation between locations.     

Exact solution of a class of nonlinear knapsack problems

We consider a class of nonlinear knapsack problems with applications in service systems design and facility location problems with congestion. We provide two linearizations and their respective solution approaches. The first is solved directly using a commercial solver. The second is a piecewise linearization that is solved by a cutting plane method.     

Mean-square stability of Milstein method for linear hybrid stochastic delay integro-differential equations

In this paper we study the mean-square (MS) stability of the Milstein method for linear stochastic delay integro-differential equations (SDIDE) with Markovian switching by extending the techniques of [Z. Wang, C. Zhang, An analysis of stability of Milstein method for stochastic differential equations with delay, Computers and Mathematics with Applications 51 (2006) 1445–1452; L. Ronghua, H. Yingmin, Convergence and stability of numerical solutions to SDDEs with Markovian switching, Applied Mathematics and Computation 175 (2006) 1080–1091]. It is established that the Milstein method is MS-stable for linear stochastic delay differential equations (Wang and Zhang (2006); in the above reference). Here we prove that it is MS-stable for linear SDIDE with Markovian switching also under suitable conditions on the integral term. A numerical example is provided to illustrate the theoretical results.     

Risk analysis in investment appraisal based on the Monte Carlo simulation technique

This work has been prepared for the purpose of presenting the methodology and uses of the Monte Carlo simulation technique as applied in the evaluation of investment projects to analyze and assess risk. In the deterministic appraisal the basic decision rule for a project is simply to accept or reject the project depending on whether its net present value (NPV) is positive or negative, respectively. Similarly, when choosing among alternative (mutually exclusive) projects, the decision rule is to select the one with the highest NPV, provided that it is positive. Recognizing the fact that the key project variables (as: volume of sales, sales price, costs) are not certain, an appraisal report is usually supplemented to include sensitivity and scenario analysis tests. Both tests are static and rather arbitrary in their nature. During the simulation process, random scenarios are built up using input values for the project's key uncertain variables, which are selected from appropriate probability distributions. The results are collected and analyzed statistically so as to arrive at a probability distribution of the potential outcomes of the project and to estimate various measures of project risk. Received 25 September 2000     

Effect of preparation methods on Pt/alumina catalysts for the hydrogen iodide catalytic decomposition

Three kinds of Pt/alumina catalysts were prepared by impregnation-hydrogen reduction,impregnation-hydrazine reduction and electroless plating methods.Their differences in the structures,specific areas and particle sizes were characterized by XRD,BET and TEM,respectively.Furthermore,their catalytic activities for the hydrogen iodide(HI)decomposition were evaluated in a fixed bed reactor.The results show that the catalyst 5%Pt/Al_2O_3 prepared by the electroless plating has the optimum catalytic properties...