Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of prob...Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of problems. Multiply constrained problem was relaxed to a singly constrained problem by using the surrogate technique. To compute tighter bounds of the primal problem, the cutting plane method was used to solve the surrogate dual problem, where the surrogate relaxation problem was solved by the 0-1 linearization method. The domain cut technique was employed to eliminate the duality gap and thus to guarantee the convergence of tile algorithm. Numerical results were reported for large-scale multi-dimensional nonlinear knapsack problems.展开更多
A multimode-quartz-crystal oscillator was developed to excite stable dual-mode resonance at different frequencies: The oscillation of the 3rd harmonic resonance of the principle C-mode and an additional resonance B-mo...A multimode-quartz-crystal oscillator was developed to excite stable dual-mode resonance at different frequencies: The oscillation of the 3rd harmonic resonance of the principle C-mode and an additional resonance B-mode of SC-cut crystal. Harmonic combinations of the 3rd and fundamental mode of B-mode with the 3rd harmonics of C-mode are demonstrated. The measurement of the temperature dependence of the oscillation frequency is demonstrated along with the stability determined by root Allan variance. Dependence on the open conductance of the active circuit and the dependence on the coupling capacitors are discussed.展开更多
Free-interface dual-compatibility modal synthesis method(compatibility of both force and displacement on interfaces)is introduced to large-scale civil engineering structure to enhance computation efficiency. The basic...Free-interface dual-compatibility modal synthesis method(compatibility of both force and displacement on interfaces)is introduced to large-scale civil engineering structure to enhance computation efficiency. The basic equations of the method are first set up, and then the mode cut-off principle and the dividing principle are proposed. MATLAB is used for simulation in different frame structures. The simulation results demonstrate the applicability of this substructure method to civil engineering structures and the correctness of the proposed mode cut-off principle. Studies are also conducted on how to divide the whole structure for better computation efficiency while maintaining better precision. It is observed that the geometry and material properties should be considered, and the synthesis results would be more precise when the inflection points of the mode shapes are taken into consideration. Furthermore, the simulation performed on a large-scale high-rise connected structure further proves the feasibility and efficiency of this modal synthesis method compared with the traditional global method. It is also concluded from the simulation results that the fewer number of DOFs in each substructure will result in better computation efficiency, but too many substructures will be time-consuming due to the tedious synthesis procedures. Moreover, the substructures with free interface will introduce errors and reduce the precision dramatically, which should be avoided.展开更多
基金partially supported by the National Natural Science Foundation of China （Grant Nos.10271073, 10571116）
文摘Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of problems. Multiply constrained problem was relaxed to a singly constrained problem by using the surrogate technique. To compute tighter bounds of the primal problem, the cutting plane method was used to solve the surrogate dual problem, where the surrogate relaxation problem was solved by the 0-1 linearization method. The domain cut technique was employed to eliminate the duality gap and thus to guarantee the convergence of tile algorithm. Numerical results were reported for large-scale multi-dimensional nonlinear knapsack problems.
文摘A multimode-quartz-crystal oscillator was developed to excite stable dual-mode resonance at different frequencies: The oscillation of the 3rd harmonic resonance of the principle C-mode and an additional resonance B-mode of SC-cut crystal. Harmonic combinations of the 3rd and fundamental mode of B-mode with the 3rd harmonics of C-mode are demonstrated. The measurement of the temperature dependence of the oscillation frequency is demonstrated along with the stability determined by root Allan variance. Dependence on the open conductance of the active circuit and the dependence on the coupling capacitors are discussed.
基金Supported by the National Natural Science Foundation of China(No.51108089)Doctoral Programs Foundation of Ministry of Education of China(No.20113514120005)the Foundation of the Education Department of Fujian Province(No.JA14057)
文摘Free-interface dual-compatibility modal synthesis method(compatibility of both force and displacement on interfaces)is introduced to large-scale civil engineering structure to enhance computation efficiency. The basic equations of the method are first set up, and then the mode cut-off principle and the dividing principle are proposed. MATLAB is used for simulation in different frame structures. The simulation results demonstrate the applicability of this substructure method to civil engineering structures and the correctness of the proposed mode cut-off principle. Studies are also conducted on how to divide the whole structure for better computation efficiency while maintaining better precision. It is observed that the geometry and material properties should be considered, and the synthesis results would be more precise when the inflection points of the mode shapes are taken into consideration. Furthermore, the simulation performed on a large-scale high-rise connected structure further proves the feasibility and efficiency of this modal synthesis method compared with the traditional global method. It is also concluded from the simulation results that the fewer number of DOFs in each substructure will result in better computation efficiency, but too many substructures will be time-consuming due to the tedious synthesis procedures. Moreover, the substructures with free interface will introduce errors and reduce the precision dramatically, which should be avoided.
