Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the mu...Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.展开更多
In this paper, a linear relationship between the logarithm of capacity factor k and normal boiling point to of the homologues has been derived, based on the basic retention equation of liquid chromatography according ...In this paper, a linear relationship between the logarithm of capacity factor k and normal boiling point to of the homologues has been derived, based on the basic retention equation of liquid chromatography according to statistical thermodyoamics proposed by professor Ln Peizhang and others, This equation has been verified by a large number of experimental data, all the strsight lines of lnk- of bumologues for different mobile phass coaiposltion cross each other at the same point, So the intereection point equation van proposed, wbich was used to prodict the retention valu, the result was satisfactory.展开更多
The local minimax method(LMM)proposed by Li and Zhou(2001,2002)is an efficient method to solve nonlinear elliptic partial differential equations(PDEs)with certain variational structures for multiple solutions.The stee...The local minimax method(LMM)proposed by Li and Zhou(2001,2002)is an efficient method to solve nonlinear elliptic partial differential equations(PDEs)with certain variational structures for multiple solutions.The steepest descent direction and the Armijo-type step-size search rules are adopted in Li and Zhou(2002)and play a significant role in the performance and convergence analysis of traditional LMMs.In this paper,a new algorithm framework of the LMMs is established based on general descent directions and two normalized(strong)Wolfe-Powell-type step-size search rules.The corresponding algorithm framework,named the normalized Wolfe-Powell-type LMM(NWP-LMM),is introduced with its feasibility and global convergence rigorously justified for general descent directions.As a special case,the global convergence of the NWP-LMM combined with the preconditioned steepest descent(PSD)directions is also verified.Consequently,it extends the framework of traditional LMMs.In addition,conjugate-gradient-type(CG-type)descent directions are utilized to speed up the NWP-LMM.Finally,extensive numerical results for several semilinear elliptic PDEs are reported to profile their multiple unstable solutions and compared with different algorithms in the LMM’s family to indicate the effectiveness and robustness of our algorithms.In practice,the NWP-LMM combined with the CG-type direction performs much better than its known LMM companions.展开更多
文摘Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.
文摘In this paper, a linear relationship between the logarithm of capacity factor k and normal boiling point to of the homologues has been derived, based on the basic retention equation of liquid chromatography according to statistical thermodyoamics proposed by professor Ln Peizhang and others, This equation has been verified by a large number of experimental data, all the strsight lines of lnk- of bumologues for different mobile phass coaiposltion cross each other at the same point, So the intereection point equation van proposed, wbich was used to prodict the retention valu, the result was satisfactory.
基金supported by National Natural Science Foundation of China(Grant Nos.12171148 and 11771138)the Construct Program of the Key Discipline in Hunan Province.Wei Liu was supported by National Natural Science Foundation of China(Grant Nos.12101252 and 11971007)+2 种基金supported by National Natural Science Foundation of China(Grant No.11901185)National Key Research and Development Program of China(Grant No.2021YFA1001300)the Fundamental Research Funds for the Central Universities(Grant No.531118010207).
文摘The local minimax method(LMM)proposed by Li and Zhou(2001,2002)is an efficient method to solve nonlinear elliptic partial differential equations(PDEs)with certain variational structures for multiple solutions.The steepest descent direction and the Armijo-type step-size search rules are adopted in Li and Zhou(2002)and play a significant role in the performance and convergence analysis of traditional LMMs.In this paper,a new algorithm framework of the LMMs is established based on general descent directions and two normalized(strong)Wolfe-Powell-type step-size search rules.The corresponding algorithm framework,named the normalized Wolfe-Powell-type LMM(NWP-LMM),is introduced with its feasibility and global convergence rigorously justified for general descent directions.As a special case,the global convergence of the NWP-LMM combined with the preconditioned steepest descent(PSD)directions is also verified.Consequently,it extends the framework of traditional LMMs.In addition,conjugate-gradient-type(CG-type)descent directions are utilized to speed up the NWP-LMM.Finally,extensive numerical results for several semilinear elliptic PDEs are reported to profile their multiple unstable solutions and compared with different algorithms in the LMM’s family to indicate the effectiveness and robustness of our algorithms.In practice,the NWP-LMM combined with the CG-type direction performs much better than its known LMM companions.
