A bounded,mono-peak,and symmetrically distributed probability density function, called λ-PDF,together with the Gegenbauer polynomial approximation,is used in dynamic response problems of random structures.The λ-PDF ...A bounded,mono-peak,and symmetrically distributed probability density function, called λ-PDF,together with the Gegenbauer polynomial approximation,is used in dynamic response problems of random structures.The λ-PDF can reasonably model a variety of random parameters in engineering random structures.The Gegenbauer polynomial approximation can be viewed as a new extension of the weighted residual method into the random space.Both of them can be easily used by scientists and engineers,and applied to a variety of response problems of random structures.The numerical example shows the effectiveness of the proposed method to study dynamic phenomena in random structures.展开更多
The branch-and-bound method with the revised dual simplex for bounded variables is very effective in solving relatively large-size integer linear programming problems. This paper, based on the general forms of the pen...The branch-and-bound method with the revised dual simplex for bounded variables is very effective in solving relatively large-size integer linear programming problems. This paper, based on the general forms of the penalties by Beale and Small and the stronger penalties by Tomlin, describes the modifications of these penalties used for the method of bounded variables. The same examples from Petersen are taken and the satisfactory results are shown in comparison with those obtained by Tomlin.展开更多
We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniquen...We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.展开更多
基金The project supported by the National Natural Science Foundation of China (10332030)
文摘A bounded,mono-peak,and symmetrically distributed probability density function, called λ-PDF,together with the Gegenbauer polynomial approximation,is used in dynamic response problems of random structures.The λ-PDF can reasonably model a variety of random parameters in engineering random structures.The Gegenbauer polynomial approximation can be viewed as a new extension of the weighted residual method into the random space.Both of them can be easily used by scientists and engineers,and applied to a variety of response problems of random structures.The numerical example shows the effectiveness of the proposed method to study dynamic phenomena in random structures.
文摘The branch-and-bound method with the revised dual simplex for bounded variables is very effective in solving relatively large-size integer linear programming problems. This paper, based on the general forms of the penalties by Beale and Small and the stronger penalties by Tomlin, describes the modifications of these penalties used for the method of bounded variables. The same examples from Petersen are taken and the satisfactory results are shown in comparison with those obtained by Tomlin.
基金supported by the National Research Foundation of Korea Grant Funded by the Korea Government (Grant No. NRF-2015R1D1A3A01019789)
文摘We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.
