This paper presents some important properties emanating from the pair of conjugate trees. The properties are obtained by resorting to the fundamental loops and cutsets in the circuit topology. The existence of such a ...This paper presents some important properties emanating from the pair of conjugate trees. The properties are obtained by resorting to the fundamental loops and cutsets in the circuit topology. The existence of such a pair is one of the conditions for a nonlinear resistive circuit to have one and only one DC solution.展开更多
We proposed an improved graphics processing unit(GPU)acceleration approach for three-dimensional structural topology optimization using the element-free Galerkin(EFG)method.This method can effectively eliminate the ra...We proposed an improved graphics processing unit(GPU)acceleration approach for three-dimensional structural topology optimization using the element-free Galerkin(EFG)method.This method can effectively eliminate the race condition under parallelization.We established a structural topology optimization model by combining the EFG method and the solid isotropic microstructures with penalization model.We explored the GPU parallel algorithm of assembling stiffness matrix,solving discrete equation,analyzing sensitivity,and updating design variables in detail.We also proposed a node pair-wise method for assembling the stiffnessmatrix and a node-wise method for sensitivity analysis to eliminate race conditions during the parallelization.Furthermore,we investigated the effects of the thread block size,the number of degrees of freedom,and the convergence error of preconditioned conjugate gradient(PCG)on GPU computing performance.Finally,the results of the three numerical examples demonstrated the validity of the proposed approach and showed the significant acceleration of structural topology optimization.To save the cost of optimization calculation,we proposed the appropriate thread block size and the convergence error of the PCG method.展开更多
Ⅰ. INTRODUCTION In this paper, fróm the molecular orbital graphical theory we have derived the closed formula of π-bond order and frontier charge density distribution of conjugated polyene and demonstrated the ...Ⅰ. INTRODUCTION In this paper, fróm the molecular orbital graphical theory we have derived the closed formula of π-bond order and frontier charge density distribution of conjugated polyene and demonstrated the connection between conjugated polyene bend order, frontier charge density and the molecular topology. The π-electron bond order展开更多
Some chaotic sequences generated from maps conjugated with tent map can be reconstructed precisely by short sequence prediction,since the problem of finite precision degrades the statistical properties of chaotic ma...Some chaotic sequences generated from maps conjugated with tent map can be reconstructed precisely by short sequence prediction,since the problem of finite precision degrades the statistical properties of chaotic maps.This paper discusses the topological conjugation properties of the chaotic maps;analyzes in detail the reconstruction process of the chaotic sequences and the security of the oversampled chaotic map (OSCM) binary sequences.The result demonstrates that OSCM binary sequences can sustain the attack of the short sequence prediction,that is,they cant be reconstructed.Furthermore,all attack strategies aiming at the chaotic systems based on synchronization will fail,meaning that they are secure.展开更多
This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-c...This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.展开更多
文摘This paper presents some important properties emanating from the pair of conjugate trees. The properties are obtained by resorting to the fundamental loops and cutsets in the circuit topology. The existence of such a pair is one of the conditions for a nonlinear resistive circuit to have one and only one DC solution.
基金This work is supported by the National Natural Science Foundation of China(Nos.51875493,51975503,11802261)The financial support to the first author is gratefully acknowledged.
文摘We proposed an improved graphics processing unit(GPU)acceleration approach for three-dimensional structural topology optimization using the element-free Galerkin(EFG)method.This method can effectively eliminate the race condition under parallelization.We established a structural topology optimization model by combining the EFG method and the solid isotropic microstructures with penalization model.We explored the GPU parallel algorithm of assembling stiffness matrix,solving discrete equation,analyzing sensitivity,and updating design variables in detail.We also proposed a node pair-wise method for assembling the stiffnessmatrix and a node-wise method for sensitivity analysis to eliminate race conditions during the parallelization.Furthermore,we investigated the effects of the thread block size,the number of degrees of freedom,and the convergence error of preconditioned conjugate gradient(PCG)on GPU computing performance.Finally,the results of the three numerical examples demonstrated the validity of the proposed approach and showed the significant acceleration of structural topology optimization.To save the cost of optimization calculation,we proposed the appropriate thread block size and the convergence error of the PCG method.
文摘Ⅰ. INTRODUCTION In this paper, fróm the molecular orbital graphical theory we have derived the closed formula of π-bond order and frontier charge density distribution of conjugated polyene and demonstrated the connection between conjugated polyene bend order, frontier charge density and the molecular topology. The π-electron bond order
文摘Some chaotic sequences generated from maps conjugated with tent map can be reconstructed precisely by short sequence prediction,since the problem of finite precision degrades the statistical properties of chaotic maps.This paper discusses the topological conjugation properties of the chaotic maps;analyzes in detail the reconstruction process of the chaotic sequences and the security of the oversampled chaotic map (OSCM) binary sequences.The result demonstrates that OSCM binary sequences can sustain the attack of the short sequence prediction,that is,they cant be reconstructed.Furthermore,all attack strategies aiming at the chaotic systems based on synchronization will fail,meaning that they are secure.
文摘This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.
