Size of support of initial heat distribution in the 1D heat equation

The size of support of initial heat distribution is determined by the heat flow observed either at any fixed time or at any fixed position     

Two regularization methods for backward heat problems with new error estimates

We introduce two new methods for solving a backward heat conduction problem. For these two methods, we give a stability analysis with new error estimates. Meanwhile, we investigate the roles of the regularization parameters in these two methods. Numerical results show that our algorithm is effective.     

On implicit function theorems for set-valued maps and their application to mathematical programming under inclusion constraints

In this paper we establish some implicit function theorems for a class of locally Lipschitz set-valued maps and then apply them to investigate some questions concerning the stability of optimization problems with inclusion constraints. In consequence we have an extension of some of the corresponding results of Robinson, Aubin, and others.     

Contractibility of the Solution Sets in Strictly Quasiconcave Vector Maximization on Noncompact Domains

We study the contractibility of the efficient solution set of strictly quasiconcave vector maximization problems on (possibly) noncompact feasible domains. It is proved that the efficient solution set is contractible if at least one of the objective functions is strongly quasiconcave and any intersection of level sets of the objective functions is a compact (possibly empty) set. This theorem generalizes the main result of Benoist (Ref.1), which was established for problems on compact feasible domains.The authors thank Dr. T. D. Phuong, Dr. T. X. D. Ha, and the referees for helpful comments and suggestions.     

Existence and robustness of exponential dichotomy of linear skew-product semiflows over semiflows

In this paper we investigate the exponential dichotomy of linear skew-product semiflows over semiflows by considering the operators generated by the integral equation related to strongly continuous cocycles over metric spaces acting on Banach bundles. We characterize the existence of exponential dichotomy by properties of these operators and use this characterization to prove the robustness of exponential dichotomy.     

Molecular analysis of the crystallization behavior of poly(aryl-ether-ether-ketone)

The crystallization behavior, via annealing, of PEEK was investigated using FTIR spectroscopy. It was found that predominantly amorphous PEEK (e.g., quenched polymer) follows two distinct mechanisms when it is annealed. One is a lower energy relaxation process that involves the partial rotation of the ether linkages, allowing the molecular chains in the disordered phase to become better packed, and occurs from 50 to 140°C (slightly below T_g). This relaxation process is also observed by dynamic mechanical analyses. The other process is a crystallization that takes place above the glass transition, with its onset characterized by the rotation of the benzophenone linkages near T_g. Isothermal crystallization kinetics data on PEEK can be described by an Avrami equation with an Avrami constant n of about 1.     

Unbounded Components in the Solution Sets of Strictly Quasiconcave Vector Maximization Problems

Let (P) denote the vector maximization problem