Let R be an associative ring not necessarily possessing an identity and （S,≤） a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having pr...Let R be an associative ring not necessarily possessing an identity and （S,≤） a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having property （F）.It is shown that M is a co-Hopfian left R-module if and only if [M<sup>S,≤</sup>]is a co-Hopfan left [[R<sup>S,≤</sup>]]-module.展开更多
This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows th...This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows that if η : P ?→ M is an ?- cover of M, then [ηS, ] : [PS, ] ?→ [MS, ] is an [?S, ]-cover of left [[RS, ]]-module ≤ ≤ ≤ ≤ ≤ [MS, ], where ? is a class of left R-modules and [MS, ] is the left [[RS, ]]-module of ≤ ≤ ≤ generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[RS, ]]-module [MS, ] are discussed. ≤展开更多
Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P&...Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +展开更多
A simulated annealing particle swarm optimization(PSO)algorithm is utilized in this paper to plan the motion of space manipulators with minimized base disturbance,not only its attitude but also its position.Since spac...A simulated annealing particle swarm optimization(PSO)algorithm is utilized in this paper to plan the motion of space manipulators with minimized base disturbance,not only its attitude but also its position.Since space manipulators must meet the Law of Momentum Conservation,any motion of manipulators will disturb the spacecraft which is free-float in the space environment.This paper tries to limit this effect to the minimum.First,this paper establishes the mathematical model for space manipulators by generalized Jacobian matrix(GJM) and analyzes its inverse kinematics by Theory of Screws.Second,a polynomial function of seventh degree is used to parameterize the joint motion and quaternion representation is also used to represent attitude of spacecraft.Moreover,this paper designs a proper objective function and depicts this algorithm detailedly and clearly.Finally,the results of numerical simulation are verified by the proposed algorithm.展开更多
基金Research supported by National Natural Science Foundation of China,19671063
文摘Let R be an associative ring not necessarily possessing an identity and （S,≤） a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having property （F）.It is shown that M is a co-Hopfian left R-module if and only if [M<sup>S,≤</sup>]is a co-Hopfan left [[R<sup>S,≤</sup>]]-module.
基金the National Natural Science Foundation of China (No.10171082) the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China and NWNU-KJCXGC212.
文摘This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows that if η : P ?→ M is an ?- cover of M, then [ηS, ] : [PS, ] ?→ [MS, ] is an [?S, ]-cover of left [[RS, ]]-module ≤ ≤ ≤ ≤ ≤ [MS, ], where ? is a class of left R-modules and [MS, ] is the left [[RS, ]]-module of ≤ ≤ ≤ generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[RS, ]]-module [MS, ] are discussed. ≤
文摘Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +
文摘A simulated annealing particle swarm optimization(PSO)algorithm is utilized in this paper to plan the motion of space manipulators with minimized base disturbance,not only its attitude but also its position.Since space manipulators must meet the Law of Momentum Conservation,any motion of manipulators will disturb the spacecraft which is free-float in the space environment.This paper tries to limit this effect to the minimum.First,this paper establishes the mathematical model for space manipulators by generalized Jacobian matrix(GJM) and analyzes its inverse kinematics by Theory of Screws.Second,a polynomial function of seventh degree is used to parameterize the joint motion and quaternion representation is also used to represent attitude of spacecraft.Moreover,this paper designs a proper objective function and depicts this algorithm detailedly and clearly.Finally,the results of numerical simulation are verified by the proposed algorithm.
