We establish the concept of shapes of functions by using partial differential inequalites. Our definition about shapes includes some usual shapes such as convex,subharmonic,etc.,and gives many new shapes of functions....We establish the concept of shapes of functions by using partial differential inequalites. Our definition about shapes includes some usual shapes such as convex,subharmonic,etc.,and gives many new shapes of functions.The main results show that the shape preserving approxi- mation has close relation to the shape preserving extension.One of our main results shows that if f∈C(Ω)has some shape defined by our definition,then f can be uniformly approximated by polynomials P_n ∈p_n(n∈N)which have the same shape in Ω,and the degree of the ap- proximation is Cω(f,n^(-β))with constants C,β>0.展开更多
Deformation is a powerful tool for geometric modeling and design. Such a toolcan be used to create a new shape from existing shape without restarting whole design process. Anew mathematical model for producing control...Deformation is a powerful tool for geometric modeling and design. Such a toolcan be used to create a new shape from existing shape without restarting whole design process. Anew mathematical model for producing controllable periodic deformations is proposed. By introducingcosine extension functions construct a shape operator matrix and then use the matrix to transformthe position vector of some points on the object surface so as to create the deformation effects.Because the cosine extension functions have a number of variable parameters with differentproperties, the method has corresponding interactive control means. The user can manipulate thoseparameters to get desirable periodic deformation effects. Experimental results show that the methodis feasible and applicable to engineering and research fields such as sheet metal forming bystamping and CAD.展开更多
An interval optimization method for the dynamic response of structures with inter- val parameters is presented.The matrices of structures with interval parameters are given.Com- bining the interval extension with the ...An interval optimization method for the dynamic response of structures with inter- val parameters is presented.The matrices of structures with interval parameters are given.Com- bining the interval extension with the perturbation,the method for interval dynamic response analysis is derived.The interval optimization problem is transformed into a corresponding de- terministic one.Because the mean values and the uncertainties of the interval parameters can be elected design variables,more information of the optimization results can be obtained by the present method than that obtained by the deterministic one.The present method is implemented for a truss structure.The numerical results show that the method is effective.展开更多
A new method for shape modification or deformation of all kinds of parametric surfaces is presented. Instead of using any control mesh and designing any auxiliary tools for modification or deformation, this method onl...A new method for shape modification or deformation of all kinds of parametric surfaces is presented. Instead of using any control mesh and designing any auxiliary tools for modification or deformation, this method only needs to multiply the equation of the original surface by several shape operator matrixes so that deformation effects are achieved. Due to introducing interactive control parameters with different properties those parameters can be changed to get more ideal effects of deformation or shape modification. The core of the method is that so-called cosine extension function is proposed by which the shape operator matrix can be created. Experiment shows that the method is simple, intuitive and easy to control, and diversified local deformations or shape modifications can easily be made via small and random variations of interactive control parameters.展开更多
Tje global dynamical correlation energies for 575 even even nuclei with proton numbers ranging from Z = 8 to Z = 108 calculated with the covariant density functional theory using the PC-PK1 parametrization are present...Tje global dynamical correlation energies for 575 even even nuclei with proton numbers ranging from Z = 8 to Z = 108 calculated with the covariant density functional theory using the PC-PK1 parametrization are presented. The dynamical correlation energies include the rotational correction energies obtained with the cranking approximation and the quadrupole vibrational correction energies. The systematic behavior of the present correlation energies is in good agreement with that obtained from the projected generator coordinate method using the SLy4 Skyrme force although our values are systematically smaller. After including the dynamical correlation energies, the root- mean-square deviation predicted by the PC-PK1 for the 575 even-even nuclei masses is reduced from 2.58 MeV to 1.24 MeV.展开更多
文摘We establish the concept of shapes of functions by using partial differential inequalites. Our definition about shapes includes some usual shapes such as convex,subharmonic,etc.,and gives many new shapes of functions.The main results show that the shape preserving approxi- mation has close relation to the shape preserving extension.One of our main results shows that if f∈C(Ω)has some shape defined by our definition,then f can be uniformly approximated by polynomials P_n ∈p_n(n∈N)which have the same shape in Ω,and the degree of the ap- proximation is Cω(f,n^(-β))with constants C,β>0.
基金This project is supported by National Natural Science Foundation of China (No.60273097) Provincial Natural Science Foundation of Jiangsu, China (No.BK 2001408).
文摘Deformation is a powerful tool for geometric modeling and design. Such a toolcan be used to create a new shape from existing shape without restarting whole design process. Anew mathematical model for producing controllable periodic deformations is proposed. By introducingcosine extension functions construct a shape operator matrix and then use the matrix to transformthe position vector of some points on the object surface so as to create the deformation effects.Because the cosine extension functions have a number of variable parameters with differentproperties, the method has corresponding interactive control means. The user can manipulate thoseparameters to get desirable periodic deformation effects. Experimental results show that the methodis feasible and applicable to engineering and research fields such as sheet metal forming bystamping and CAD.
基金Project supported by the National Natural Science Foundation of China(No.10202006).
文摘An interval optimization method for the dynamic response of structures with inter- val parameters is presented.The matrices of structures with interval parameters are given.Com- bining the interval extension with the perturbation,the method for interval dynamic response analysis is derived.The interval optimization problem is transformed into a corresponding de- terministic one.Because the mean values and the uncertainties of the interval parameters can be elected design variables,more information of the optimization results can be obtained by the present method than that obtained by the deterministic one.The present method is implemented for a truss structure.The numerical results show that the method is effective.
基金This research is supported by Provincial Natural Science Foundation of Shaan Xi under grant no. 2000SL08
文摘A new method for shape modification or deformation of all kinds of parametric surfaces is presented. Instead of using any control mesh and designing any auxiliary tools for modification or deformation, this method only needs to multiply the equation of the original surface by several shape operator matrixes so that deformation effects are achieved. Due to introducing interactive control parameters with different properties those parameters can be changed to get more ideal effects of deformation or shape modification. The core of the method is that so-called cosine extension function is proposed by which the shape operator matrix can be created. Experiment shows that the method is simple, intuitive and easy to control, and diversified local deformations or shape modifications can easily be made via small and random variations of interactive control parameters.
基金We acknowledge S. Goriely, B. Sun, and P. W. Zhao for stimulating discussions. This work was supported in part by the National Undergraduate Training Programs for Innovation and Entrepreneurship (Project No. 201210635132), the National Basic Research Program of China (973 Program) (Grant No. 2013CB834400), the National Natural Science Foundation of China (Grant Nos. 10975008, 10947013, 11175002, 11105110, 11105111, and 11205004), the Research Fund for the Doctoral Program of Higher Education (Grant No. 20110001110087), the Natural Science Foundation of Chongqing (Grant No. cstc2011jjA0376), and the Fundamental Research Funds for the Central Universities (Grant Nos. XDJK2010B007 and XDJK2011B002).
文摘Tje global dynamical correlation energies for 575 even even nuclei with proton numbers ranging from Z = 8 to Z = 108 calculated with the covariant density functional theory using the PC-PK1 parametrization are presented. The dynamical correlation energies include the rotational correction energies obtained with the cranking approximation and the quadrupole vibrational correction energies. The systematic behavior of the present correlation energies is in good agreement with that obtained from the projected generator coordinate method using the SLy4 Skyrme force although our values are systematically smaller. After including the dynamical correlation energies, the root- mean-square deviation predicted by the PC-PK1 for the 575 even-even nuclei masses is reduced from 2.58 MeV to 1.24 MeV.
基金supported by National Science CenterPoland(Grant No.2018/30/M/ST1/00061)+1 种基金the Wroc law University of Science and Technology(Grant No.049U/0052/19)supported by National Natural Science Foundation of China(Grants Nos.11671094,11722103 and 11731003)。
文摘In this survey we will present the symbolic extension theory in topological dynamics,which was built over the past twenty years.