Proper relaxation of optimal control problems

In a recent paper, we proposed different relaxation procedures for optimal control problems involving time delays in the control functions. We introduced a notion of proper relaxation, applicable to problems without side constraints, where we required the minimum cost of the relaxed problem to coincide with the infimum cost of the original one. In this paper, a new and appropriate notion of relaxation for problems with side constraints is introduced. As examples of proper extensions, in the new sense, we describe in detail the standard procedure for delay-free problems and the procedure for one-delay systems which we recently proposed.     

Simulation of dispersive Fourier interferograms of gases in the visible wave number range

Dispersive two-beam Fourier interferograms of N₂-gas in the visible wave number range are calculated numerically for nonabsorbing as well as absorbing gas and compared with experiment. Some problems of inverse Fourier transformation of dispersive interferograms are also discussed.     

Iterative methods for a fourth order boundary value problem

We consider a fourth order nonlinear ordinary differential equation together with two-point boundary conditions and provide a-priori error estimates on the length of the interval (b?a) so that the Picard's iterative method, the approximate Picard's iterative method and the quasilinear iterative method convergence to the solution of the problem.     

Scanning tunneling microscopy of N2H4 on silicon surfaces

The chemistry of N₂H₄ on Si(100)2 × 1 and Si(111)7 × 7 has been studied using scanning tunneling microscopy. At low coverages on Si(100)2 × 1 at room temperature the adsorption sites are distributed randomly on the surface and are imaged as dark spots in the dimer row by the STM. Upon annealing the substrate at 600 K, both isolated reaction products, as well as clusters of reaction products are formed on the surface. The STM images show that the majority of the isolated reaction products are adsorbed symmetrically across the dimers. Based on previous HREELS data, these are most likely NH_x groups. However, the clusters are not well resolved. Because of this we speculate that they are not simply symmetrically adsorbed NH_x groups, but likely have a more complicated internal structure. At higher coverages, the STM images show that the predominant pathway for adsorption is with the N---N bond parallel to the surface, in agreement with HREELS studies of this system. On Si(111)7 × 7, the molecule behaves in a manner which is similar to NH₃. That is, at low coverages the molecule adsorbs preferentially at center adatoms due to the greater reactivity of these sites, while at higher coverages it also reacts with the corner adatoms.     

APPROXIMATING ANALYSIS OF A KIND OF REPAIRABLE STANDBY SYSTEMS

ＬＩＷＥＩ（李伟）；ＣＡＯＪＩＮＨＵＡ（曹晋华）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８０，ＣｈｉｎａａｎｄＡｓｉａ－ＰａｃｉｆｉｃＯｐｅｒａｔｉｏ...     

碳涂覆光纤表面碳膜形成机理研究

通过分析碳涂覆光纤的测试结果，研究碳涂覆光纤碳膜的形成机理，并应用该机理解释涂覆光纤的高可靠性问题和影响光纤初始强度大小的因素。     

渐变折射率光波导的精确分析

本文利用转移矩阵理论和等效衰减系数的概念，导出了渐变折射率光波导的色散方程，数值计算的结果，赢余方程的精度优于目前存在的所有近似方法。