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26 December 1982, Volume 2 Issue 4 Previous Issue    Next Issue

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A DIRECT METHOD OF OPERATIONAL CALCULUS(Ⅰ)——Research for the solution of second-order linear ordinary differential equations with variable coefficients Qiu Lianrong Acta mathematica scientia,Series A. 1982, 2 (4):  435-448.  Abstract ( 51 )   RICH HTML PDF (696KB) ( 17 )   Save According to Mikusinski's fundamental view, we reconstruct a direct method of operation a calbulus which may be adapted to search for the solution of differential equations with variable coefficients. The present paper is devoted to solutions of two types——indirect (undetermined) method and direct (series of integral) method-for solving second-order linear differential equations:The latter displays forthright feature while the former can solve second-order linear differential equation and interrelate first-order Riccati's non-linear differential equation at the same time. Related Articles | Metrics

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SOME NONLINEAR OPERATOR EQUATIONS AND THEIR APPROXIMATE SOLUTIONS Lu Tao Acta mathematica scientia,Series A. 1982, 2 (4):  449-463.  Abstract ( 55 )   RICH HTML PDF (749KB) ( 15 )   Save Consider nonlinear operator equation:Ax+Fx=α, where A is a dense closed linear operator, F is a nonlinear operator. In this paper, we shall give the criterion about solution existence of this equation and the convergence criterion of Galerkln approximate solutions. Related Articles | Metrics

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L2 SCATTERING THEORY AND STATIONARY STATE SCATTERING WAVE FUNCTION Qian Min Acta mathematica scientia,Series A. 1982, 2 (4):  465-478.  Abstract ( 50 )   RICH HTML PDF (672KB) ( 15 )   Save There exist two approaches to the theory of quantum scattering, the stationary and the time dependent approaches. In the stationary formalism, for the calculation of the scattering cross section, the standard method is to solve the Schrödinger equation. Related Articles | Metrics

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ON THE ALGORITHM TO REALIZE THEOREM PROVING AND SOLVING PROBLEM Zeng Xianchang Acta mathematica scientia,Series A. 1982, 2 (4):  479-484.  Abstract ( 48 )   RICH HTML PDF (325KB) ( 37 )   Save This paper describes the algorithm and concrete process with BASIC program to realize theorem proving and solving some artificial intelligence problem. For theorem proving we introduce "subsumption test", "omiting method" and "programing technics" to speed up for finding proofs of theorem as the previous paper[1]. Related Articles | Metrics