In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.
For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving function...For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.展开更多
Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral...In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between Hαi,βi （f1 , fn, ; g1,..., gn）（z） and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results.展开更多
In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions o...In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions of the class. Moreover, we verify Brannan and Clunie＇s conjecture ｜a_2｜ ≤2^（1/2）for some of our classes. The results in this paper extend many results recently researched by many authors.展开更多
In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stoc...The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.展开更多
Because of the powerful mapping ability, back propagation neural network (BP-NN) has been employed in computer-aided product design (CAPD) to establish the property prediction model. The backward problem in CAPD is to...Because of the powerful mapping ability, back propagation neural network (BP-NN) has been employed in computer-aided product design (CAPD) to establish the property prediction model. The backward problem in CAPD is to search for the appropriate structure or composition of the product with desired property, which is an optimization problem. In this paper, a global optimization method of using the a BB algorithm to solve the backward problem is presented. In particular, a convex lower bounding function is constructed for the objective function formulated with BP-NN model, and the calculation of the key parameter a is implemented by recurring to the interval Hessian matrix of the objective function. Two case studies involving the design of dopamine β-hydroxylase (DβH) inhibitors and linear low density polyethylene (LLDPE) nano composites are investigated using the proposed method.展开更多
In this paper, iterative or successive approximation methods for the Hamilton-Jacobi-Bellman-lsaacs equations （HJBIEs） arising in both deterministic and stochastic optimal control for affine nonlinear systems are de...In this paper, iterative or successive approximation methods for the Hamilton-Jacobi-Bellman-lsaacs equations （HJBIEs） arising in both deterministic and stochastic optimal control for affine nonlinear systems are developed. Convergence of the methods are established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the methods. However, the results presented in the paper are preliminary, and do not yet imply in anyway that the solutions computed will be stabilizing. More improvements and experimentation will be required before a satisfactory algorithm is developed.展开更多
In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estima...In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach.The structure of the new fuzzy approximator benefits a course got by other means展开更多
Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of th...Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.展开更多
In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto...In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).Using these projections,we show that A(ф)~*≌A~1(ф)and A~1(ф)~*≌A(ф).展开更多
A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement i...A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement is realized without any changes to the simple elliptical shape of the bounding surface, and actually reduces the number of parameters associated with the model by one.展开更多
Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk （type fractional differential equation）. The main object of this paper is to investigate inc...Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk （type fractional differential equation）. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.展开更多
The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear...The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear continuous systems confined by a bound function, the nonlinearities of the systems may be of varied forms or uncertain; the designed stabilizer is robust means that a class of nonlinear continuous systems can be stabilized by the same output feedback stabilization schemes; numerical simulation examples are given.展开更多
In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the me...In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.展开更多
In this paper, we research the Miintz rational approximation of two kinds of spe- cial function classes, and give the corresponding estimates of approximation rates of these classes.
In this paper, the exploitation of single population modelled by Richards model is studied. By choosing the maximum annual-sustainable yield as management objective, we investigate the optimal harvesting policies for ...In this paper, the exploitation of single population modelled by Richards model is studied. By choosing the maximum annual-sustainable yield as management objective, we investigate the optimal harvesting policies for autonomous and periodic exploited Richards model. Further, when the functions in the exploited Richards model are stably bounded functions, we study the ultimately optimal harvesting policy and obtain the corresponding average limiting maximum sustainable yield.展开更多
In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bound...In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.展开更多
In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.
文摘In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.
基金supported by Kyungsung University Re-search Grants in 2013.
文摘For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.
基金Research supported by Council of Scientific and Industrial Research, India under award no.9/143(163)/91-EER-
文摘Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(Grant No.14ZB0364)
文摘In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between Hαi,βi （f1 , fn, ; g1,..., gn）（z） and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results.
基金Supported by the National Natural Science Foundation of China(Grant No.11401186)the Research Fund from Engineering and Technology College Yangtze University(Grant No.15J0802)
文摘In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions of the class. Moreover, we verify Brannan and Clunie＇s conjecture ｜a_2｜ ≤2^（1/2）for some of our classes. The results in this paper extend many results recently researched by many authors.
文摘In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
基金Project supported by the Natural Science Foundation of China(10371009) and Research Fund for the Doctoral Program Higher Education.
文摘The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.
文摘Because of the powerful mapping ability, back propagation neural network (BP-NN) has been employed in computer-aided product design (CAPD) to establish the property prediction model. The backward problem in CAPD is to search for the appropriate structure or composition of the product with desired property, which is an optimization problem. In this paper, a global optimization method of using the a BB algorithm to solve the backward problem is presented. In particular, a convex lower bounding function is constructed for the objective function formulated with BP-NN model, and the calculation of the key parameter a is implemented by recurring to the interval Hessian matrix of the objective function. Two case studies involving the design of dopamine β-hydroxylase (DβH) inhibitors and linear low density polyethylene (LLDPE) nano composites are investigated using the proposed method.
文摘In this paper, iterative or successive approximation methods for the Hamilton-Jacobi-Bellman-lsaacs equations （HJBIEs） arising in both deterministic and stochastic optimal control for affine nonlinear systems are developed. Convergence of the methods are established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the methods. However, the results presented in the paper are preliminary, and do not yet imply in anyway that the solutions computed will be stabilizing. More improvements and experimentation will be required before a satisfactory algorithm is developed.
文摘In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach.The structure of the new fuzzy approximator benefits a course got by other means
基金supported by the National Science Foundation of China(No.11161033)Inner Mongolia Normal University Talent Project Foundation(No.RCPY-2-2012-K-036)
文摘Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.
基金Supported in part by the National Natural Science Foundation of China.
文摘In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).Using these projections,we show that A(ф)~*≌A~1(ф)and A~1(ф)~*≌A(ф).
基金supported by the Fulbright Colombia-Colciencias Scholarship and Universidad Militar Nueva Granada
文摘A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement is realized without any changes to the simple elliptical shape of the bounding surface, and actually reduces the number of parameters associated with the model by one.
文摘Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk （type fractional differential equation）. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.
基金This project was supported by the National Natural Science Foundation of China(69974017 60274020 60128303)
文摘The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear continuous systems confined by a bound function, the nonlinearities of the systems may be of varied forms or uncertain; the designed stabilizer is robust means that a class of nonlinear continuous systems can be stabilized by the same output feedback stabilization schemes; numerical simulation examples are given.
文摘In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.
基金Supported by the National Natural Science Foundation of China(11161033)Inner Mongolia Natural Science Foundation (2009MS0105)
文摘In this paper, we research the Miintz rational approximation of two kinds of spe- cial function classes, and give the corresponding estimates of approximation rates of these classes.
文摘In this paper, the exploitation of single population modelled by Richards model is studied. By choosing the maximum annual-sustainable yield as management objective, we investigate the optimal harvesting policies for autonomous and periodic exploited Richards model. Further, when the functions in the exploited Richards model are stably bounded functions, we study the ultimately optimal harvesting policy and obtain the corresponding average limiting maximum sustainable yield.
基金the Doctorial Programme Foundation of EducationMinistry of of China(20030288002)the Science Foundation of Jiangsu Province(BK2006209)+1 种基金NaturalScience Foundation of Jiangsu Higher Education Bureau(07KJD110206)NNSF of China(10771181)
文摘In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.
基金Department of Mathematics and Statistics,Auburn University,AL,USA
文摘In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.
