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31 December 1981, Volume 1 Issue Z1 Previous Issue    Next Issue

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THE INITIAL PROBLEM WITH INTEGRAL NONLINEAR SCHRöDINGER SYSTEM OF EQUATIONS Guo Boling Acta mathematica scientia,Series A. 1981, 1 (Z1):  261-274.  Abstract ( 45 )   RICH HTML PDF (619KB) ( 21 )   Save In[2] from the study of the nonlinear Langmuir wave of plasma,a class of nonlinear Schrödinger equations with integral terms is presented for the perturbation of Zakhrov equation with soliton solution.In this paper, based on[1] we consider the more general initial problem of the fol-lowing two classes of the nonlinear Schrödinger system of equations with the integral pairing method. Related Articles | Metrics

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THE NONDISCRETE PHENOMENA OF MIXED PROBLEM POSSESSING THE 3RD CLASS BOUNDARY CONDITION Wang Chuanfang, Qin Yuchun Acta mathematica scientia,Series A. 1981, 1 (Z1):  275-284.  Abstract ( 57 )   RICH HTML PDF (480KB) ( 52 )   Save F. Treves[1] had studiied an interesting example on the discrete phenomena in the uniqueness of the initial value problem. He showed the Cauchy problem. Related Articles | Metrics

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ERROR ANALYSIS OF POLYNOMIAL SMOOTHING AND POLYNOMIAL SMOOTHING WITH MODEL ERROR Jia Peizhang, Zhu Zhengtao Acta mathematica scientia,Series A. 1981, 1 (Z1):  285-300.  Abstract ( 88 )   RICH HTML PDF (770KB) ( 104 )   Save In this paper the model error introduced by the polynomial smoothing is analyzed and the estimating formula for the tolerable interval of the memory is given.When the memory interval is greater than the tolerable value, then the effect of the model error must be considered and the usual polynomial smoothing is no longer the linear minimum covariance estimate. It is shown that in this care the polynomial smoothing with model error should be applied and that it will give the linear minimum covariance estimate. This smoothing method is demonstrated in the second part of this paper and there the simulation results are also given for comparison with the usual one. Related Articles | Metrics

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A SIMPLIFIED NONLINEAR FILTERING Wang Zu-Rong Acta mathematica scientia,Series A. 1981, 1 (Z1):  313-324.  Abstract ( 49 )   RICH HTML PDF (570KB) ( 161 )   Save This paper presents a simplified nonlinear filtering-direct compensation and dimension raising. Using this method, the original system will be simplified by a higher order polynomial dynamic model and realize transition matrix constancy. So the computation will be very simple. Specially, it is suitable for the problems of the real time treatment. After thorough the simulant compute, its effect achieves good results. We can apply this method to filming theodolite or radar for automatic tracking of the flying target. Related Articles | Metrics

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THE GENERALIZED MARTINGALE AND ITS CONVERGENCY Liu Peide Acta mathematica scientia,Series A. 1981, 1 (Z1):  325-334.  Abstract ( 61 )   RICH HTML PDF (491KB) ( 30 )   Save The Purpose of this paper is to define a generalized martingale and to discuss its Convergency, we have studied the existence of right-closed element and its relation to Some Convergency; an upcrossing inequality to generalize Doob's Convergence theorem Concerning martingale and Semi-martingale; and introduced the generalized Potential, for proving the new decomposition theorem. Related Articles | Metrics

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ON EXISTENCE OF OPTIMAL CONTROL FOR A CLASS DISTRIBUTED PARAMETER SYSTEM-PROBLEMS OF CONTROL IN COEFFICIENTS(1) Yu Wenhuan Acta mathematica scientia,Series A. 1981, 1 (Z1):  335-348.  Abstract ( 52 )   RICH HTML PDF (730KB) ( 99 )   Save It has been studied in this paper that a control of distributed parameter systems is contained in coefficients of linear 2nd order elliptic or parabolic equations, which has been called the problem of control in the coefficients and applied to a numcer of mathemaitcal physics problems. We first give a sufficient condition under which the systein state depends continuously on the control. And then we give conditions respectively for the systems governed by the mentioned equations. Under anyone of them the system has the optimal control minimizing the given cost functional. Related Articles | Metrics

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SEVERAL CLASSES OF HADAMARD MATRICES Xia Mingyuan Acta mathematica scientia,Series A. 1981, 1 (Z1):  349-358.  Abstract ( 56 )   RICH HTML PDF (465KB) ( 93 )   Save All elements are either+1 or -1 and the orthonormal N-order matrix of any two rows is called Hadamard matrix, for short, N-order H-matrix. H-matrix is much applied in practical design, radar range finding[3,5,6,8,10] and communication coding and it is also often used in solving other problems of combinatorics[9,12]. Related Articles | Metrics

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THE OPERATOR △κ2+n2T2 AND PLURIHARMONIC FUNCTIONS ON HEISENBERG GROUP Ouyang Caiheng Acta mathematica scientia,Series A. 1981, 1 (Z1):  359-378.  Abstract ( 70 )   RICH HTML PDF (948KB) ( 30 )   Save The well-known example of an equation with real coefficients without solution was given by F.Trèves in 1962. i.e. the operator of the 4th order ZZZZ is 《without solution》. In this paper we first have discussed some properties of the multidimensional operator of the 4th order △k2+n2T2(=Σi,k=1n ZjZjZkZk). Related Articles | Metrics

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ON A CLASS OF NONLINEAR INTEGRAL EQUATION IN TRANSPORT THEORY Liu Qingrong Acta mathematica scientia,Series A. 1981, 1 (Z1):  379-385.  Abstract ( 70 )   RICH HTML PDF (344KB) ( 96 )   Save In the theory of radiation and neutron transportations, the following equation plays an important role. Related Articles | Metrics

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THE UNIVERSAL LINEAR HYPOTHESIS TESTING IN THE LINEAR MODELS Zhang Yaoting, Bian Guorui Acta mathematica scientia,Series A. 1981, 1 (Z1):  387-394.  Abstract ( 64 )   RICH HTML PDF (365KB) ( 38 )   Save In this paper, we discuss, the following testing problem: Suppose. Related Articles | Metrics

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ON THEORETICAL FOUNDATION CONCERNING DISTRIBUTION OF MOMENT Guo Youzhong Acta mathematica scientia,Series A. 1981, 1 (Z1):  395-401.  Abstract ( 44 )   RICH HTML PDF (364KB) ( 18 )   Save Here we present the theoretical foundation concerning the distribution of moment(or/and displacement):the mathematical description, convergence and error estimation of approximate solution and the generalization to that of net shell theory. Related Articles | Metrics

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AN INHOMOGENEOUS QUASILINEAR HYPERBOLIC SYSTEM Wang Ching-hua Acta mathematica scientia,Series A. 1981, 1 (Z1):  403-421.  Abstract ( 46 )   RICH HTML PDF (898KB) ( 40 )   Save We consider the initial value problem for the inhomogeneous hyperbolic system. Related Articles | Metrics