Abstract:Optimal Stopping for Markov chains with infinite time has been discussed in this paper. The sufficient condition for the existence of the optimal stopping variable and the value function of the optimal stopping for Markov chains with infinite states has been obtained. The results show that the condition and calculation of the optimal stopping problem for Markov chains with finite states are equivalent to solving some linear programs.

Abstract:A common method for studying problems about the length of service and grade seniority by Markov manpower model is to divide the states of the model according to grades，lengths of service or grade seniority. In a class of graded manpower systems using homogeneous Markov models in which there are no demotions and in which promotions take place only step by step，the present paper discussed the problems of lengths of service and grade seniority，some computation formulae describing the lengths of service and grade seniority intuitively have been obtained，and finally，a practical example demonstrating the applications of this method is given.

Abstract:In this paper, a new kind of hybrid spectral-difference schemes for three-dimensional vorticity equation with one periodic direction in space is given, the stability and the convergence for each schemes are also discussed.

Abstract:In this paper，a method for solving unconstrained optimization problems，which is called “proper conjugate direction method”，is developed. Compared with general conjugate direction method，such as the conjugate gradient method，this method will save a great deal of one-dimensional search work and raise the rate of convergence.

Abstract:In the paper [l], H.T.Banks and M.Q.Jacobs have discussed the one order differential of the multifuntions ?:R^m→A(Rⁿ)，Their result has been improved in this paper and the sufficient and necessary conditions for the differentiability are given respectively. The limitation of (3.2) in [l] is proved to be unnecessary and the sufficient and necessary conditions for the differentialbility of ? are found. Furthermore，the sufficient and necessary conditions for the higher order differentialbility of ? are gained and a calculus formula is given.

Abstract:In this paper，we have given the definition of full-rank-primes. A prime P supposing that (p,10)=1 is defined as a full-rank-prime，if the length of the decimal repetend of 1/P is exactly P-l，roughly speaking. In the paper several interesting theorems about the decimal repetend of l/P when P is prime，especially a full-rank-prime，have been proved. For example，if P is a full-rank-prime，then the digit permutation of all K/P，1≤k≤p?1，has certain properties.

Abstract:The authors put forward two unsolved problems in the paper [1]，then have studied them in great details in this paper，and have solved them completely by theorem 3-4. Meanwhile，we got a series of important conclusions.

Abstract:In order to further understand the relations between refractive index and porosity in mixed films，We did the experiments of mixed film system TiO₂:Ta₂O₅, using coevaporation. On the basis of our experimental results，we put forward an empirical porosity expression to fit the data of TiO₂:Ta₂O₅ system，and we also improved the calculating procedure of the refractive index of mixed films. The results of theoretical calculations using our empirical porosity expression agree with those of experiments. The results of experiments and theoretical analysis show that it is possible that the mixed films have less porosity than pure thin films，and those films cause a peak in the curve of refractive index of mixed films versus the ratio of the mixed weight.

Abstract:The effective treatment of the‘il1-state' is a key to the design of the program of adaptive optical automatic design. The paper proposes a new idea and method about it. The so-called‘three link-closed chain-circulating treating method' has been put forward here. The treating method consists of reducing iteration step，regulating the rate between the increments of variables，and releasing control1ed aberration. This is much better than the tradtional treatment setup.

Abstract:This paper discusses a small-sized H.V. nanosecond pulse generator which can produce a H.V. pulse with 120kV amplitude，more than 5kV/ns front gradient and 100 ns width. The generator has been used as a trigger to REB accelerator，the pulse resource of H.V. EMP simulator and the energy resource for studying discharge properties of different mediums，as well.

Abstract:This research is a continuation of our experimental research on the breakdown properties of water dielectric switching under submicrosecond negative pulse voltage^[1]. The conclusions show that it is necessary to consider the leakage of the wave impedance of the water capacitance between electrods to pulse energy of the trigger when the nanosecond pulse breakdown experiment is carried out.

Abstract:In this paper，a simplized handling scheme with more general significance for the theoretical model of two-dimensional projected plate in air driven by explosive has been proposed.

Abstract:The important factors to affect the limit speed of a projected plate driven by explosive are first analysed in this paper. This analysis is combined with a discussion about the range of application of the empirical formulae. Then two important laws，which are summarized from the results of the numerical computations to two-dimensional projected plate，are formulated: ①When mass ratios of explosive and projected plate are the same，there is a certainly similar relation among limit speeds of two-dimensional projected plate；② The revised Gurney Formula may be used to calculate the limit speed of two-dimensional projected plate.

Abstract:In this paper，the topological entropy of two-dimensional dissipative maps from period doubling bifurcation or the same period bifurcation to chaos is calculated. The arbitrary relation of bifurcational routes in dissipative maps and topological entropy corresponding to these routes are found and the intrinsic relation between chaos and topological entropy is also revealed.

Abstract:From the thermodynamic relationship among the thermal expansion coefficient α，specific heat Cv，and volume elastic modulusk，We proposed a simple practical recursion method to calculate the thermal expansion coefficient. The coefficient of thermal expansion of solid，as the function of temperature，can be determined very accurately by this method. As an example We have calculated the thermal expansion coefficient of three alkali halide crystals below the room temperature，the results are in sound agreement with the experiments.

Abstract:In this paper; the influnces of the diffraction effects，atmospheric turbulence，the absorption and scattering losses from both moleculae and aerosol particles in the atmosphere on the atmospheric transmission of the laser beam are considered together. The methods of reducing these influnces are analysed. The conclusion on the transmission properties of the laser beam affected by the wavelength of the laser beam，the transmitting aperture，climatic condition and emission angle is found.

Abstract:Based on the experiments，the heat treating technology process for the dual phase roping steel wire is suggested as follows： austenization and water quenching for full martensite structure→critical annealing and quenching for dual phase structure followed by tempering→after acid pickling and phosphorisation，continuous cold drawing multisteps until expected end dimension of the wire→artificial aging for stress relief. According to the production process，the tensile strength of the wire may be achieved over 1800 MPa while the anti-torsion and bending fatique properties can exceed the value stipulated in the National Standard.

Abstract:In this paper，the polyphenylacetylene(PPA) is synthesised by the polymerization of phenylacetylene with two kinds of catalysts，anhydsous AlCl₃and (Ph₃P)₂PdCl₂. Using anhydrous AlCl₃ as catalyst，the cis-trans PPA is obtained. And using (Ph₃P)₂PdCl₂,the trans-cis PPA is found. Therefore，the polymerization of phenylacetylene may follow complex catalysis mechanism when anhydrous AlCl₃ is used as a catalyst and it may follow metathesis catalysis mechanism when (Ph₃P)₂PdCl₂ is used.

Abstract:The thermal degradation temperatures and the rate of char yields of homopolymers and coplymers of arylacetylenes were determined by thermogravimetry. The correlations between these properties and the composition and structure of polyarylacetylenes were also revealed. The more diethynylaromatic copolymer contains and the bigger cross link density，the higher the thermal degradation temperature and char yields. Char yields of copolymer of diethynylaromatic and phenylacetylene are much greater than that of the calculated data from their homopolymers.

Abstract:Reversible thermochromism in the aqueous solutions of Ln(III)=MTB chelates (Ln=14 kinds of lanthanide elements except Pm; MTB=Methylthymol blue，i. e. ，3'，3"-Bis-[N，N-(dicarboxymethyl) aminomethyl] thymolsulfonphthalein) have been investigated by spectrophotometry. The resu1ts indicated the effect of acidities and temperatures on the colors and electron spectrum of the cited systems. The results also show that the thermochromic mechanism is similar to that of the Ln(III)-Xo(Xylenol Orange) chelates systems. This is a part of the fundamental studies for developing rare earth temperature-indicating materials.