数学物理方程某些相关理论和复变函数的发展

doi:10.3969/j.issn.1007-2985.2015.02.009

摘要/Abstract

摘要：首先，讨论了一般方程及其某些解的简化形式；其次，介绍了数学物理方程及其对称性；第三，研究了方程的不动点、定性分析理论和相应的各种应用；第四，由矩阵联系于线性代数；第五，讨论与数学物理相关的各种量；最后，探讨数域的推广和复变函数发展（各种超复变函数）.

关键词： 数理方法, 方程, 定性分析, 线性代数, 数域, 复变函数

Abstract: First,the general equations and some of the simplified forms of their solutions are discussed.Next,the mathematical-physical equations and their symmetries are introduced.Thirdly,the fixed points,the qualitative analysis theory and corresponding applications on these equations are investigated.Fourthly,linear algebra is assorted from matrix.Fifthly,various quantities related with mathematics and physics are discussed.Finally,the extension of the number field and various super complex variables functions developed from the complex variables functions,etc.,are researched.

Key words: mathematical-physical method, equation, qualitative analysis, linear algebra, number field, complex variables functions

张一方. 数学物理方程某些相关理论和复变函数的发展[J]. journal6, 2015, 36(2): 38-45.

ZHANG Yi-Fang. Some Theories About Mathematical-Physical Equations and Development of Complex Variables Functions[J]. journal6, 2015, 36(2): 38-45.

参考文献

[1] 张一方,刘正荣.粒子的相互作用、极限环和相变[J].数学物理学报，1999,19(4):424-431.

[2] 张一方.复数域的新推广及其物理意义[J].吉首大学学报：自然科学版，2008，29(5):31-34.

[3] CHANG Y F.New Extensions of Number System and Complex Field,and Their Physical Meaning [J].International Journal of Modern Mathematical Sciences,2013,7(3):312-320.

[4] 张一方.数学分析的某些发展和新探索[J].吉首大学学报：自然科学版，2009，30(3):35-39.

[5] 张一方.数学中场论的某些新探索及其在物理学中的应用[J].吉首大学学报：自然科学版，2010，31(1):47-53;72.

[6] 勒内·托姆.突变论:思想和应用[M].周仲良，译.上海：上海译文出版社，1989.

[7] YANG C N.Some Exact Results for the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction[J].Phys. Rev. Lett.，1967,19(23):1 312-1 315.

[8] YANG C N.S Matrix for the One-Dimensional N-Body Problem with Repulsive or Attractive Delta-Function Interaction[J].Phys.Rev.，1968,168(5):1 920-1 923.

[9] CHANG Y F.Some Possible Tests of the Inapplicability of Pauli’s Exclusion Principle[J].Hadronic J.,1984,7(6):1 469-1 473.

[10] 张一方.在激光导致的高激发态原子中检验泡利不相容原理的适用性[J].自然杂志，1988,11(8):635-636.

[11] 张一方.粒子物理和相对论的新探索[M].昆明:云南科技出版社，1989.

[12] CHANG Y F.The Nonlinear Quantum Theory and Possible Violation of the Pauli Exclusion Principle[C]//AHN S H.Proc. of the 4th Asia-Pacific Phys. Conf.,V2.World Scientific，1991：1 483-1 486.

[13] CHANG Y F.Test of Pauli’s Exclusion Principle in Particle Physics,Astrophysics and Other Fields[J].Hadronic J.,1999,22(3):257-268.

[14] 张一方.各种可能的Pauli不相容原理的破缺和相应的统一(Ⅰ)[J].信阳师范学院学报，2010,23(3):360-365.

[15] 张一方.各种可能的Pauli不相容原理的破缺和相应的统一(Ⅱ)[J].信阳师范学院学报，2011,24(1):43-48.

[16] 张一方.地震的非线性动力学系统的探索[J].大自然探索，1997,16(3):51-55.

[17] 张一方.地震预报和某些新的理论探索[J].吉首大学学报：自然科学版，2010,31(2):48-54.

[18] CHANG Y F.Nonlinear Dynamics,Magnitude-Period Formula and New Research on Earthquake[J].International Journal of Sciences，2012,11:1-9.

[19] 雷克L E.统计物理现代教程[M].黄畇，译.北京：北京大学出版社，1983.

[20] LIU Zhengrong,HU B,LI J.Global and Local Bifurcation in Perturbations of Non-Symmetry and Symmetry of Hamiltonian System[J].Int. J. Bifurcation & Chaos，1995,5(3):809-820.

[21] 栗弗席兹 E M,皮塔耶夫斯基 JT Л.统计物理学II(凝聚态理论)[M].王锡绂，译.北京：高等教育出版社，2008.

[22] CHANG Y F.A Nonlinear Dynamical Model of Formation of Binary Stars from a Nebula[J].Chinese Astron. Astrophys.(UK)，2000,24(3):269-274.

[23] STEINITZ R,FARBIASH N.Spectroscopically and Spatially Resolving the Components of Close Binary Stars[C].Dubrovnik,Croatia:ASP Conference Series,2003:20-24.

[24] CHANG Y F.Hydrodynamics and a Nonlinear Dynamical Formation Model on Binary Stars[J].Phys.Scr.，2007,76(4):385-387.

[25] CHANG Y F.Lorenz Model and Plane General Relativity Model on Formulation of Binary Stars[J].International Journal of Modern Theoretical Physics，2013,2(1):1-12.

[26] 张一方.数学,物理中分维的发展和分维时空理论[J].大自然探索，1991,10(2):49-54.

[27] CHANG Y F.Fractal Relativity,Generalized Noether’s Theorem and New Research on Space-Time[J].Galilean Electrodynamics,2010,21(6):112-116.

[28] 罗曼 P.基本粒子理论[M].蔡建华，译.上海：上海科学技术出版社，1966.

[29] 张一方.粒子的分形模型,复数维及其意义[J].大自然探索，1988,7(2):21-23.

[30] CHANG Y F.Imperfection of the Lorentz Transformation[J].Galilean Electrodynamics，2007,18(2):38-39.

[31] CHANG Y F.Extension and Complete Structure of the Special Relativity Included Superluminal and Nutrino-Photon with Mass[J].International Journal of Modern Theoretical Physics，2013,2(2):53-73.

[32] CHANG Y F.New Tree-Field Representations in Graph Theory,Extension of Dirac Extraction,Differential Test for Series of Positive Terms,Complex Dimension and Their Applications[J].Journal of Modern Mathematical Sciences,2014,9(1):1-12.