By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it...By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.展开更多
A generic property that there is no differentiable iterative root on the dosed interval I = [0, 1] for a kind of strictly increasing C’-smooth functions with two hyperbolic fixed points 0 and 1 is given. This is an i...A generic property that there is no differentiable iterative root on the dosed interval I = [0, 1] for a kind of strictly increasing C’-smooth functions with two hyperbolic fixed points 0 and 1 is given. This is an interesting result because for the same kind of functions, the existence and uniqueness of continuous root on I, diflerentiable at one of the fixed points, is well known.展开更多
Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years...Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.展开更多
The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important re...The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important results for this research area in locally convex spaces.展开更多
Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating ob...Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiate almost everywhere w. r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.展开更多
In recent years more attention has been paid to the mathematical model for aflying ve-hicle which can be considered as an Euler--Bernoulli beam equation with damping. Its character is that the boundary conditions sati...In recent years more attention has been paid to the mathematical model for aflying ve-hicle which can be considered as an Euler--Bernoulli beam equation with damping. Its character is that the boundary conditions satisfied by the elastic and damping operators are non-local and coupling to each other. It is a difficult problem how to study the mathematicalproperties of this system. This paper provides an approach to study this problem, unifies andcovers all of the previous work. The results obtained are very convenient for applications tothe initial boundary-value problems of linear hyperbolic equations with variable coefficientsand damping.展开更多
In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dim...In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 10471114)
文摘By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.
文摘A generic property that there is no differentiable iterative root on the dosed interval I = [0, 1] for a kind of strictly increasing C’-smooth functions with two hyperbolic fixed points 0 and 1 is given. This is an interesting result because for the same kind of functions, the existence and uniqueness of continuous root on I, diflerentiable at one of the fixed points, is well known.
文摘Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.
文摘The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important results for this research area in locally convex spaces.
基金the National Natural Science Foundation of China (Grant Nos. 59805004, 59990470) the National Distinguished Youth Foundation (Grant No. 59725514).
文摘Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiate almost everywhere w. r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.
基金Project supported by the National Natural Science Foundation of China.
文摘In recent years more attention has been paid to the mathematical model for aflying ve-hicle which can be considered as an Euler--Bernoulli beam equation with damping. Its character is that the boundary conditions satisfied by the elastic and damping operators are non-local and coupling to each other. It is a difficult problem how to study the mathematicalproperties of this system. This paper provides an approach to study this problem, unifies andcovers all of the previous work. The results obtained are very convenient for applications tothe initial boundary-value problems of linear hyperbolic equations with variable coefficientsand damping.
基金Supported by the National Natural Science Foundation of China and the Natural Science Foundtion of Zhejiang Province.
文摘In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension.
