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Functions on discrete sets holomorphic in the sense of Isaacs, or monodiffric functions of the first kind

Science China Mathematics 2005年第Z1期48卷 86-96页

作者： Christer O.Kiselman Department of Mathematics Uppsala University P.O.Box 480SE-751 06 UppsalaSweden

We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of the Cauchy-Riemann operators, domains of holomorphy in one discrete variable, and the Hartogs phenomenon in two discrete variables are investigated.

关键词： monodiffric functions of the first kind, discrete holomorphic functions, functions holomorphic in the sense of Isaacs, discrete Cauchy-Riemann operators, domains of holomorphy, Hartogs' phenomenon.

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A New Inversion Method of Sedimentary Strata For Deriving Double Parameters and Its Applications

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Global Geology 2002年第1期7卷 79-88页

作者： GUO Hua, LIU Cai, LI Yue and YANG Baojun(College of Geo-exploration Science and Technology, Jilin University, Changchun 130026, P. R. China) College of Geo - exploration Science and Technology Jilin University Changchun130026 P. R. China

The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have been trending towards the multiple parameters inversion . We have obtained an inverse method with double -parameter, in which medium density and wave velocity can be derived simultaneously. In this paper, to increase the inverse accuracy, the method is improved as follows. Firstly, the formula in which the Green Function is omitted are derived and used. Secondly, the regularizing method is reasonable used by choosing the stable function. With the new method, we may derive elastic parameter and medium density or medium density and wave velocity. Thus, lithology parameters for seismic prospecting may be *** comparing the derived values from the new method with that from previous method, we obtain the new method through which substantially improve the derived accuracy . The new method has been applied to real depths inversion for sedimentary strata and volcanic rock strata in Chaoyanggou Terrace of Songliao Basin in eastern China. According to the inverse results,the gas - bearing beds are determlned.

关键词： Sedimentary strata, Double - Parameter inversion, Green function, Regularization method, Fredholm integral equation of the first kind, Volcanic rock strata

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