Abstract:
This paper deals with the existence and uniqueness of solutions for a class of infinite-horizon systems derived from optimal control. An existence and uniqueness theorem is proved for such Hamiltonian systems under some natural assumptions.

Abstract:
This paper considers the approximate controllability for a class of semilinear delay control systems described by a semigroup formulation with boundary control. Sufficient conditions for approximate controllability are established provided the approximate controllability of corresponding linear systems. 1. Introduction In this paper, we consider the boundary control system described by the following delay differential equation: where system state takes values in a Banach space ; control function takes values in another Banach space and for ; is a closed, densely defined linear operator; is a linear operator from to a Banach space ; is a linear bounded operator; is a nonlinear perturbation function, where is the Banach space of all continuous functions from to endowed with the supremum norm. For any and , is defined by for . In most applications, the state space is a space of functions on some domain of the Euclidean space , is a partial differential operator on , and is a partial differential operator acting on the boundary of . Several abstract settings have been developed to describe control systems with boundary control; see Barbu [1], Fattorini [2], Lasiecka [3], and Washburn [4]. In this paper, we use the setting developed in [2] to discuss the approximate controllability of system (1.1). The norms in spaces and are denoted by and , respectively. In other spaces, we use the norm notation with a space name in the subindex such as , , and . Let be the linear operator defined by We impose the following assumptions throughout the paper. (H1) and the restriction of to is continuous relative to the graph norm of .(H2)The operator is the infinitesimal generator of an analytic semigroup for on .(H3)There exists a linear continuous operator and a positive constant such that (H4)For each and , one has . Also, there exists a positive function with such that (H5)There exists a positive number such that for all and . Based on the discussions in [2], system (1.1) can be reformulated as The following system is called the corresponding linear system of (1.6) Approximate controllability for semilinear control systems with distributed controls has been extensively studied in the literature under different conditions; see Fabre et al. [5], Fernandez and Zuazua [6], Li and Yong [7], Mahmudov [8], Naito [9], Seidman [10], Wang [11, 12], and many other papers. However, only a few papers dealt with approximate boundary controllability for semilinear control systems, in particular, semilinear delay control systems; the main difficulty is encountered in the construction of

Abstract:
The solvability for a class of abstract two-point boundary value problems derived from optimal control is discussed. By homotopy technique existence and uniqueness results are established under some monotonic conditions. Several examples are given to illustrate the application of the obtained results.

Abstract:
The solvability for a class of abstract two-point boundary value problems derived from optimal control is discussed. By homotopy technique existence and uniqueness results are established under some monotonic conditions. Several examples are given to illustrate the application of the obtained results.

Abstract:
Generally there are two strategies in fitting the measured structural relaxation time of glass-forming liquids: the single-formula approach e.g. the Vogel-Tammann-Fulcher equation,and the multi-branch approach. In this note, a two-branch method was presented. By analyzing existing single- and multi-branch approaches, I am trying to recall the attention of researchers in this field to the possibilities of the multi-branch approach.

Abstract:
The continuability, boundedness, monotonicity, and asymptotic properties of nonoscillatory solutions for a class of second-order nonlinear differential equations [()？(())(())]=()(()) are discussed without monotonicity assumption for function g. It is proved that all solutions can be extended to infinity, are eventually monotonic, and can be classified into disjoint classes that are fully characterized in terms of several integral conditions. Moreover, necessary and sufficient conditions for the existence of solutions in each class and for the boundedness of all solutions are established.

Abstract:
A fusion prediction method is introduced on the basis of attribute clustering network and radial basis functions. An algorithm of quasi-self organization for developing the model for the fusion prediction is introduced. Some simulation results for chaotic time series are presented to show the performance of the method.

Abstract:
By means of r--ray attenuation method, the density of pure In and its relationship with temperature were measured in both solid and liquid states. The results show that the density data of pure In obtained by this method have a good repeatability within heating run and cooling run each other.