The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert spa...The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.展开更多
A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of varia...A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.展开更多
We will focus on some results that we hope to give an algorithm for constructing the best approximations in some types of normed linear spaces. Also some results on best approximation will be obtained.
In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Th...In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces.展开更多
This paper deals with regularity properties for minimizing sequences of some integral functionals related to the nonlinear elasticity theory.Under some structural conditions,we derive that the minimizing sequence and ...This paper deals with regularity properties for minimizing sequences of some integral functionals related to the nonlinear elasticity theory.Under some structural conditions,we derive that the minimizing sequence and the derivatives of the sequences have some regularity properties by using the Ekeland variational principle.展开更多
Using only chassical theorems of calculus of variations, we study semi coercive monotone variational problems on reflexive Banach spaces. We obtain the existence of solutions for semilinear equations on reflexive Ban...Using only chassical theorems of calculus of variations, we study semi coercive monotone variational problems on reflexive Banach spaces. We obtain the existence of solutions for semilinear equations on reflexive Banach spaces.展开更多
In the traditional method for the reliability analysis of fault-tolerant system,the system structure is described by means of binary decision diagram (BDD) and Markov process,and then the reliability indexes are calcu...In the traditional method for the reliability analysis of fault-tolerant system,the system structure is described by means of binary decision diagram (BDD) and Markov process,and then the reliability indexes are calculated.However,as the size of system augments,the size of state space will increase exponentially.Additionally,Markov approach requires that the failure and repair time of the components obey an exponential distribution.In this study,by combining dynamic fault tree (DFT) and numerical simulation based on the minimal sequence cut set (MSCS),a new method to evaluate reliability of fault-tolerant system with repairable components is proposed.The method presented does not depend on Markov model,so that it can effectively solve the problem of the state-space combination explosion.Moreover,it is suitable for systems whose failure and repair time obey an arbitrary distribution.Therefore,our method is more flexible than the traditional method.At last,an example is given to verify the method.展开更多
文摘The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.
基金supported by the National Natural Science Foundation of China (No. 10671070)the Fund for E-Institute of Shanghai Universities (No. E03004)the Open Research Fund Program of LGISEM(No. 05PJ14040)
文摘A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.
文摘We will focus on some results that we hope to give an algorithm for constructing the best approximations in some types of normed linear spaces. Also some results on best approximation will be obtained.
基金The NNSF (10471025) of China the Foundation (JA04170) of the Education Department of Fujian Province, China.
文摘In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces.
基金supported by National Natural Science Foundation of China(Grant No.12071021)Natural Science Foundation of Hebei Province(Grant No.A2019201120)+4 种基金the Key Science and Technology Project of Higher School of Hebei Province(Grant No.ZD2021307)supported by the Postgraduate Innovation Project of Hebei Province(Grant No.CXZZSS2020005)supported by Natural Science Foundation of Hebei Province(Grant No.A2018201285)Science and Technology Project of Hebei Education Department(Grant No.QN2020145)Research Funds of Hebei University(Grant No.8012605)。
文摘This paper deals with regularity properties for minimizing sequences of some integral functionals related to the nonlinear elasticity theory.Under some structural conditions,we derive that the minimizing sequence and the derivatives of the sequences have some regularity properties by using the Ekeland variational principle.
文摘Using only chassical theorems of calculus of variations, we study semi coercive monotone variational problems on reflexive Banach spaces. We obtain the existence of solutions for semilinear equations on reflexive Banach spaces.
文摘In the traditional method for the reliability analysis of fault-tolerant system,the system structure is described by means of binary decision diagram (BDD) and Markov process,and then the reliability indexes are calculated.However,as the size of system augments,the size of state space will increase exponentially.Additionally,Markov approach requires that the failure and repair time of the components obey an exponential distribution.In this study,by combining dynamic fault tree (DFT) and numerical simulation based on the minimal sequence cut set (MSCS),a new method to evaluate reliability of fault-tolerant system with repairable components is proposed.The method presented does not depend on Markov model,so that it can effectively solve the problem of the state-space combination explosion.Moreover,it is suitable for systems whose failure and repair time obey an arbitrary distribution.Therefore,our method is more flexible than the traditional method.At last,an example is given to verify the method.
