Levitin–Polyak well-posedness of generalized quasivariational inequalities with functional constraints

In this paper, we study Levitin–Polyak type well-posedness for generalized quasivariational inequality problems with explicit constraints. Four types of Levitin–Polyak well-posedness will be introduced. Various criteria and characterizations will be derived for these types of Levitin–Polyak well-posedness.     

一类二阶奇异微分方程正解的存在唯一性

利用上下解方法,不动点理论研究奇异微分方程u" f(t,u)=0,t∈(0,1)在边界条件au(0)-βu'(0)=0,γu(1) δu'(1)=0下C[0,1]正解和C1[0,1]正解的存在性与唯一性.其中非线性项f(t,u)关于u是减的,仅满足较弱的要求.     

On the sensitivity matrix of the Nash bargaining solution

In this note we provide a characterization of a subclass of bargaining problems for which the Nash solution has the property of disagreement point monotonicity. While the original d-monotonicity axiom and its stronger notion, strong d-monotonicity, were introduced and discussed by Thomson (J Econ Theory, 42: 50–58, 1987), this paper introduces local strong d-monotonicity and derives a necessary and sufficient condition for the Nash solution to be locally strongly d-monotonic. This characterization is given by using the sensitivity matrix of the Nash bargaining solution w.r.t. the disagreement point d. Moverover, we present a sufficient condition for the Nash solution to be strong d-monotonic.     

Homogenization of boundary hemivariational inequalities in linear elasticity

In this paper we consider a mathematical model describing static elastic contact problems with the Hooke constitutive law and subdifferential boundary conditions. We treat boundary hemivariational inequalities which are weak formulations of contact problems. We establish existence and uniqueness of solutions to hemivariational inequalities. Using the notion of H-convergence of elasticity tensors we investigate the limit behavior of the sequence of solutions to hemivariational inequalities.     

The degradation of poly(methyl methacrylate) in the effect of negative thixotropy

An investigation of the degradation of poly(methyl methacrylate) in the case of negative thixotropy of its solutions in tricresyl phosphate showed that the number of polymer bonds broken by flow as expressed through the decrease of molecular weight in the course of the effect is determined by shear energy imposed on the system, irrespective of the velocity gradient and temperature used.     

An analytical solution for the model of drug distribution and absorption in small intestine

According to the physiological and anatomical characteristics of small intestine, neglecting the effect of its motility on the distribution and absorption of drug and nutrient, Y. Miyamoto et al.^[1] proposed a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drug by numerical analysis. In this paper, we give a steady state analytical solution of the above model including deactivation term. The obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence provides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments. The project supported by NSF of Shandong Province     

A class of solutions to the quantum colored Yang-Baxter equation

In this paper, we give a new method to solve the quantum colored Yang-Baxter matrix equation (QCYBE), and a class of solutions to the QCYBE is given.     

Variational Inequalities for Leavable Bounded-Velocity Control

We study the variational inequality associated with a bounded-velocity control problem when discretionary stopping is allowed. We establish the existence of a strong solution by using the viscosity solution techniques. The optimal policy is shown to exist from the optimality conditions in the variational inequality.     

Robust Optimal Stopping-Time Control for Nonlinear Systems

Abstract. We formulate a robust optimal stopping-time problem for a state-space system and give the connection between various notions of lower value function for the associated games (and storage function for the associated dissipative system) with solutions of the appropriate variational inequality (VI) (the analogue of the Hamilton—Jacobi—Bellman—Isaacs equation for this setting). We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense and a positive definite supersolution of the VI can be used for stability analysis.     

不需加人工变量的两阶段法

A method is provided to achieve an initial basic feasible solution of a linear programming in this paper. This method dose not need introducing any artificial variable, but needs only solving an auxiliary linear programming. Compared with the traditional two-phase method, it has advantages of saving the memories and reducing the computational efforts.