In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regul...In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.展开更多
In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of E...In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of Euclidean N-space （N ≥ 3）, u：Ω → R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition ｜Du｜^p＊ ｜u｜^p＊-a（x） ≤ f（x,u,Du） ≤ L（｜Du｜^p＋｜u｜^p＊ ＋ a（x））, （2） where L≥1, 1pN,p^＊ = Np/N-p , and a（x） is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of （1）. Our method is to compare the ω-minima of （1） with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.展开更多
In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated ...In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated assembly of global stiffness matrix and repeated inverse operations of the matrix caused by constant changes of structure topology. A new criterion of degenerate of the structure into mechanism is introduced. The calculation examples are satisfactory.展开更多
Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by bal...Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The results of experiments show that this new method is superior to the old one.展开更多
In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a resul...In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a result about integrability of products of the form gοf.f'f(k)under suitable mild conditions and, finally, we prove that a Nemytskij operator Sg maps BV''[a,b] a distinguished subspace of the space of all functions of second bounded variation, into itself if, and only if, g BV''loc(R) A similar result is obtained for the space of all functions of bounded (p,2)-variation (1≤p≤1),展开更多
文摘In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.
基金Supported by the Program of Fujian Province-HongKong
文摘In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of Euclidean N-space （N ≥ 3）, u：Ω → R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition ｜Du｜^p＊ ｜u｜^p＊-a（x） ≤ f（x,u,Du） ≤ L（｜Du｜^p＋｜u｜^p＊ ＋ a（x））, （2） where L≥1, 1pN,p^＊ = Np/N-p , and a（x） is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of （1）. Our method is to compare the ω-minima of （1） with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.
文摘In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated assembly of global stiffness matrix and repeated inverse operations of the matrix caused by constant changes of structure topology. A new criterion of degenerate of the structure into mechanism is introduced. The calculation examples are satisfactory.
文摘Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The results of experiments show that this new method is superior to the old one.
文摘In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a result about integrability of products of the form gοf.f'f(k)under suitable mild conditions and, finally, we prove that a Nemytskij operator Sg maps BV''[a,b] a distinguished subspace of the space of all functions of second bounded variation, into itself if, and only if, g BV''loc(R) A similar result is obtained for the space of all functions of bounded (p,2)-variation (1≤p≤1),
