Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems

In this paper, we consider parametric primal and dual equilibrium problems in locally convex Hausdorff topological vector spaces. Sufficient conditions for the approximate solution maps to be Hausdorff continuous are established. We provide many examples to illustrate the essentialness of the imposed assumptions. As applications of these results, the Hausdorff continuity of the approximate solution maps for optimization problems, variational inequalities and fixed-point problems are derived.     

Continuity properties of solution maps of parametric lexicographic equilibrium problems

Inspired by the great importance of equilibrium problems and the lexicographic order, we consider a parametric lexicographic equilibrium problem. Sufficient conditions for the upper semicontinuity, closedness, and continuity of solution maps are established. Many examples are provided to ensure the essentialness of the imposed assumptions. Applications to lexicographic variational inequalities and lexicographic optimization problems are discussed.     

Mixed Type Duality for Set-valued Optimization Problems via Higher-order Radial Epiderivatives

In this article, we introduce a notion of higher-order radial epiderivative for set-valued maps and study its properties. A generalized concept of higher-order strict minimizers in set-valued optimization is proposed as well. By virtue of the radial epiderivative, we establish a mixed dual problem, and then weak, strong, and converse duality theorems are obtained in dealing with generalized strict minimizers.     

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation

     

Community responses to road traffic noise in Hanoi and Ho Chi Minh City

Vietnam is a developing country in southeast Asia, and its environment has been seriously affected by industrialization and urbanization. In large cities like Hanoi (northern Vietnam) and Ho Chi Minh City (southern Vietnam), noise emission from road traffic has been found to be a serious concern among general public. In 2005 and 2007, two large-scale socio-acoustic surveys of community response to road traffic noise were conducted to investigate human reactions to road traffic noise in these cities; the sample sizes were 1503 people in Hanoi and 1471 in Ho Chi Minh City. The noise exposure levels (L_den) were 70–83 dB in Hanoi and 75–83 dB in Ho Chi Minh City. Noise annoyance was estimated using standardized annoyance scales. For both cities, dose–response relationships were established between L_den and the percentage of highly annoyed respondents. Compared to annoyance responses of European people, Vietnamese were less annoyed by road traffic noise by about 5 dB. Hanoi respondents seemed to be more annoyed by noise than Ho Chi Minh City respondents. Conversation and sleep disturbances were not as serious as expected in either city. Furthermore, window orientation in the home was found to affect activity disturbances.     

Stability radius of linear parameter-varying systems and applications

In this paper, we present a unifying approach to the problems of computing of stability radii of positive linear systems. First, we study stability radii of linear time-invariant parameter-varying differential systems. A formula for the complex stability radius under multi perturbations is given. Then, under hypotheses of positivity of the system matrices, we prove that the complex, real and positive stability radii of the system under multi perturbations (or affine perturbations) coincide and they are computed via simple formulae. As applications, we consider problems of computing of (strong) stability radii of linear time-invariant time-delay differential systems and computing of stability radii of positive linear functional differential equations under multi perturbations and affine perturbations. We show that for a class of positive linear time-delay differential systems, the stability radii of the system under multi perturbations (or affine perturbations) are equal to the strong stability radii. Next, we prove that the stability radii of a positive linear functional differential equation under multi perturbations (or affine perturbations) are equal to those of the associated linear time-invariant parameter-varying differential system. In particular, we get back some explicit formulas for these stability radii which are given recently in [P.H.A. Ngoc, Strong stability radii of positive linear time-delay systems, Internat. J. Robust Nonlinear Control 15 (2005) 459-472; P.H.A. Ngoc, N.K. Son, Stability radii of positive linear functional differential equations under multi perturbations, SIAM J. Control Optim. 43 (2005) 2278-2295]. Finally, we give two examples to illustrate the obtained results.     

A direct method to evaluate hole-alignment error in residual-stress measurement

In this paper, a direct method based on the Sandifer and Bowie theory was derived to take hole-alignment error into account in residual-stress measurement. The principal stresses and their orientation are calculated directly from this method when the relaxed strains, hole diameter, eccentricity and orientation are known. It is more convenient to use than other iterative methods.