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
After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. ...After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:展开更多
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
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.
文摘After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:
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.
