幂向量、复合向量数及其函数理论
Power Vectors Combinatorial Vector Numbers and Its Theory of Functions
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摘要: 本文提出向量为其幂向量和向量幂级数.向量幂级数由一实数和某一向量联合组成的“复合向量数”及其函数有重要涵义.这数也有运算法则.从复合向量数的函数理论分析知其函数有导数和解析函数的必要和充分条件.这些条件构成了“双曲型”方程的特征以及函数的积分性质等.Abstract: This paper syggests the power vector and the vector power series. The vector power series is a "Combinatorial Vector Number" which is composed of a real number and a certain vector. Combinatorial rector variable and its functions have an important meaning. They have the fundamental operations of arithemetic too. From the theoretical analysis of functions for a combinatorial vector variable we would would know its function has the derivatives. the necessary and sufficient conditions. These conditions make up the charaders of "Hyperbolic equation" and its integralions.
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Key words:
- power vector /
- a combinatorial vector number /
- hyperbolic equation
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[1] 杨文熊,广义非线性、非定常力学理论及在粒子物理学中的应用,应用数学和力学.16(1)(1995),23-32. [2] 杨文熊.全非线性、非定常力学的理论.力学学报(待刊登). [3] 杨文熊,高能物理学中的全非线性效应及对粒子高速运动的应用.物理学报(待刊登). [4] M,R.Spiegel,Schaum's Outline of Theory and Problems of Advanced Mathematics for Engineers and Scientists,McGraw-Hill Book Co,(1971). -
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