By combining geographic information system (GIS), a new conception of “group” in which covers the complex connected region is introduced in the paper. Based on the conception of group, a generalized Euler formula an...By combining geographic information system (GIS), a new conception of “group” in which covers the complex connected region is introduced in the paper. Based on the conception of group, a generalized Euler formula and its properties are deduced and proved. The paper also describes the mathematical principles of generating topological information of polygon in GIS maps and the methods for checking up the veracity of topological relations of the map with Euler formula and general Euler formula. We have also obtained the quantitative relations among real nodes, chains, islands and groups with the formulas. At the same time, the paper introduces Whole Sphere Stereographic (WSS) projection into the GIS, and defines a new conception of “sea”. The deduction of general Euler formula and the introduction of WSS projection to GIS have developed new ways of delineating GIS topological models from plane to sphere and even constructing three dimensional (3-D) topological models.展开更多
This paper develops Euler ’loadlng formula of large deflection to be easy to measure in-situ and puts forward the differeuce quick iterative solution ror large deflection of beam and column, whick can solve the uon-l...This paper develops Euler ’loadlng formula of large deflection to be easy to measure in-situ and puts forward the differeuce quick iterative solution ror large deflection of beam and column, whick can solve the uon-linear equation like a kind of θ"+K(s)f(θ) =0.展开更多
As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the fi...As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.展开更多
文摘By combining geographic information system (GIS), a new conception of “group” in which covers the complex connected region is introduced in the paper. Based on the conception of group, a generalized Euler formula and its properties are deduced and proved. The paper also describes the mathematical principles of generating topological information of polygon in GIS maps and the methods for checking up the veracity of topological relations of the map with Euler formula and general Euler formula. We have also obtained the quantitative relations among real nodes, chains, islands and groups with the formulas. At the same time, the paper introduces Whole Sphere Stereographic (WSS) projection into the GIS, and defines a new conception of “sea”. The deduction of general Euler formula and the introduction of WSS projection to GIS have developed new ways of delineating GIS topological models from plane to sphere and even constructing three dimensional (3-D) topological models.
文摘This paper develops Euler ’loadlng formula of large deflection to be easy to measure in-situ and puts forward the differeuce quick iterative solution ror large deflection of beam and column, whick can solve the uon-linear equation like a kind of θ"+K(s)f(θ) =0.
基金Supported by the National Natural Science Foundation Fujian province of China(2016J01032).
文摘As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.
