A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear syste...A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.展开更多
Iterative linear programming methods are proposed for optimum balanced animal diet in this paper. According to ＂wooden bucket theory＂ of the nutritional balance, each nutrient in the feeding standard has equal impor...Iterative linear programming methods are proposed for optimum balanced animal diet in this paper. According to ＂wooden bucket theory＂ of the nutritional balance, each nutrient in the feeding standard has equal importance. It＇s unreasonable to use common goal programming to attach different weighted value to different nutritional parameters. This paper introduces an effective algorithm to deal with this kind of problem. When the permitting cost of livestock ration is given, we can design a ration formula with linear program-this is the first round. Then, according to the differences between the permitting cost and the formula cost gained in the first round, adjust the feeding standard and the feeding raw materials, and conduct the second round of linear programming for ration formula. If there is still a very big difference between the formula cost and the permitting cost, the third round will be taken, and so on. In this iteration course the formula cost gradually approaches the permitting cost. It is the key that the feeding standard and feeding raw materials are modified in each round. This method ensured the nutritive equilibrium with the formulation of least-cost ration. This is an especially important method when the primary goal of the optimization tool is to improve economic and nutritive efficiency.展开更多
In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense...In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or oppositely.展开更多
In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients....In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.展开更多
LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that ...LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that the answer to this question is positive (Theorem 6.1) if the dimension of V is sufficiently large and V is indecomposable. We explicitly characterize two-step extensions 0 → S → V → Q → 0, with completely reducible S and Q, whose rationality cannot be obtained by the methods presented here (Theorem 5.3).展开更多
基金supported by the National Natural Science Foundation of China （Grant No.10271074）
文摘A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.
文摘Iterative linear programming methods are proposed for optimum balanced animal diet in this paper. According to ＂wooden bucket theory＂ of the nutritional balance, each nutrient in the feeding standard has equal importance. It＇s unreasonable to use common goal programming to attach different weighted value to different nutritional parameters. This paper introduces an effective algorithm to deal with this kind of problem. When the permitting cost of livestock ration is given, we can design a ration formula with linear program-this is the first round. Then, according to the differences between the permitting cost and the formula cost gained in the first round, adjust the feeding standard and the feeding raw materials, and conduct the second round of linear programming for ration formula. If there is still a very big difference between the formula cost and the permitting cost, the third round will be taken, and so on. In this iteration course the formula cost gradually approaches the permitting cost. It is the key that the feeding standard and feeding raw materials are modified in each round. This method ensured the nutritive equilibrium with the formulation of least-cost ration. This is an especially important method when the primary goal of the optimization tool is to improve economic and nutritive efficiency.
文摘In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or oppositely.
基金supported by the National Natural Science Foundation of China(11371225)National Natural Science Foundation of Guangdong Province(2016A030313686)
文摘In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.
基金supported by the Natural Science Foundation of USA (Grant No. DMS 0701578)supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Gttingen
文摘LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that the answer to this question is positive (Theorem 6.1) if the dimension of V is sufficiently large and V is indecomposable. We explicitly characterize two-step extensions 0 → S → V → Q → 0, with completely reducible S and Q, whose rationality cannot be obtained by the methods presented here (Theorem 5.3).
