Large Sample Properties of Mixture Models with Covariates for Competing Risks

We study the large-sample properties of a class of parametric mixture models with covariates for competing risks. The models allow general distributions for the survival times and incorporate the idea of long-term survivors. Asymptotic results are obtained under a commonly assumed independent censoring mechanism and some modest regularity conditions on the survival distributions. The existence, consistency, and asymptotic normality of maximum likelihood estimators for the parameters of the model are rigorously derived under general sufficient conditions. Specific conditions for particular models can be derived from the general conditions for ready check. In addition, a likelihood-ratio statistic is proposed to test various hypotheses of practical interest, and its asymptotic distribution is provided.     

SECOND BEST TAXES AND QUOTAS IN NITROGEN REGULATION

This paper investigates second best policies to regulate nitrogen leaching. When the policy maker controls the total nitrogen use, an overall tax is superior to an action equivalent overall quota. When the goal is to regulate the expected level of nitrogen leaching, expected profit of a risk neutral farmer is greater under an overall tax than under an overall quota under a reasonable condition. The welfare ranking of action equivalent taxes and quotas for a risk averse farmer is generally ambiguous. In the numerical analyses, overall taxes turned out to be superior to overall quotas with both targets, despite a very high value of absolute risk aversion, 0.01. These results suggest that an overall tax is probably a superior policy to an overall quota to regulate expected total nitrogen use or expected nitrogen leaching for risk neutral and most of risk averse farmers.     

Principles and recent developments in ultrasound contrast agents

The behaviour of gas bubbles and gas encapsulated spheres as echographic contrast agents is reviewed. Compared with rigid spheres, gas bubbles are superior scattering agents and they offer a number of useful properties which can be exploited in a variety of ways. The analysis of their velocity of sound, back-scatter intensity, second harmonic emission and resonant frequency opens up new perspectives in the development of contrast agents for echocardiographic research with potential clinical applications.     

Fixed Point Theorems on Product Topological Spaces and Applications

A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.     

On a stochastic hyperbolic integro-differential equation

In this paper we study an initial-boundary-value problem for a hyperbolic integro-differential equation with random memory and a random noise. We establish the existence, uniqueness and exponential stability of solutions. Our method consists of finite-dimensional approximation and energy estimates.     

Globally anisotropic high porosity silica aerogels

We discuss two methods by which high porosity silica aerogels can be engineered to exhibit global anisotropy. First, anisotropy can be introduced with axial strain (i.e. axial compression). In addition, intrinsic anisotropy can result during growth and drying stages and, suitably controlled, it can be correlated with preferential radial shrinkage in cylindrical samples. We have performed small angle X-ray scattering (SAXS) to characterize these two types of anisotropy. We show that global anisotropy originating from either strain or shrinkage leads to optical birefringence and that optical cross-polarization studies are a useful characterization of the uniformity of the imposed global anisotropy.     

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.