RELATIVISTIC VARIATION PRINCIPLES AND EQUATION OF MOTION FOR VARIABLE MASS CONTROLLABLE MECHANICAL SYSTEM

With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical system are given the relativistic Chaplygin equation. Nielsen equation and Appell equation .for variable mass controllable mechanical system in quasi-coordinates and generalized- coordinates are obtained, and the equations of motion of relativistic controllable mechanical system for holonomic system and constant mass system are diseussed

Study On Financial Policies To Promote The Development Of Energy-Saving And Environmental Protection Industries In Shanghai： International Experiences And Enlightenments

International experiences show that when make full use of the regulation and service functions of financial mechanism, such as the establishment of greenhouse gas emissions trade market, further strengthening investigation in environmental risk of the financing projects according to equator principles, more fiscal and taxation policies that to encourage financial institutions to innovate green financial products, participation of supporting the international financial organizations in energy-saving and environmental protection （hereafter referred to as ESEP） projects, people can significantly improve the quality of the environment, and effectively control pollution emissions in a low cost. In order to improve the efficiency of Shanghai ESEP work, the local government should learn from the international advanced experiences to accelerate the establishment of green financial service system of ESEP, so that to better use finance leverage to build a resource conserving and environment-fxiendly society.

A variational formula for controlled backward stochastic partial differential equations and some application

An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.

Multibody Dynamics Formulations Based on Variational Principle

The formulation of multibody dynamics was studied based on variational principle. The body coonection matrix was introduced to define the connection configuration. The expression for the system kinematics was obtained by using the body connection matrix. From variational principle the general dynamical equations for multibody system were derived and the dynamical equations were given for multibody system subjected to the constraints.

GLOBAL REGULARITY FOR MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATIONS

We consider the n-dimensional modified quasi-geostrophic（SQG） equations δtθ ＋ u·△↓θ＋kΛ^αθ=0, u = Λ^α-1R^⊥θ with κ 〉 0, α∈（0, 1] and θ0∈ W^1,∞（R^n）. In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu, who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case.The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol.

Common Fixed Point Theorems and Q-property for Quasi-contractive Mappings under c-distance on TVS-valued Cone Metric Spaces without the Normality

In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.

Stochastic maximum principle for mean-field forward-backward stochastic control system with terminal state constraints

In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.

Stochastic Differential Games with Reflection and Related Obstacle Problems for Isaacs Equations

In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations （RBSDEs）. We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bettman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of E1 Karoui, Kapoudjian, Pardoux, Peng and Quenez （1997）, which turns out to be very useful because it allows us to estimate the LP-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle.