Integrating Chinese culture into college English can not only enhance students’humanities literacy and cultivate their cultural confidence,but also facilitate the inheritance and international dissemination of Chines...Integrating Chinese culture into college English can not only enhance students’humanities literacy and cultivate their cultural confidence,but also facilitate the inheritance and international dissemination of Chinese culture.Taking Tyler’s curriculum framework as the starting point,this paper analyzes some factors that affect the integration of Chinese culture into the college English teaching and proposes some strategies for the integration of Chinese culture into college English teaching by innovating teaching objectives,enriching teaching contents,transforming modes of course delivery,and reconstructing the assessment system.展开更多
The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we ca...The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the standard Schrodinger equation. In this paper, we have given the generalized Hamilton principle, which can describe the heat exchange system, and the nonconservative force system. On this basis, we have further given their generalized Lagrange functions and Hamilton functions. With the Feynman path integration, we have given the generalized Schrodinger equation of nonconservative force system and the heat exchange system.展开更多
This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we ex...This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we explore the implications for black hole thermodynamics, astrophysics, astronomy, information theory, and the search for new laws of nature. The result includes an estimation of the number of bits stored in a black hole (less than 1.4 × 10<sup>30</sup> bits/m<sup>3</sup>), enhancing our understanding of information storage in extreme gravitational environments. This integration offers valuable insights into the fundamental nature of information and energy, impacting scientific advancements in multiple disciplines.展开更多
In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equa...In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton's principle. Finally, the Hamilton's principle of high-order Lagrangian function is given.展开更多
In this paper, the shallow water problem is discussed. By treating the incompressible condition as the constraint, a constrained Hamilton variational principle is presented for the shallow water problem. Based on the ...In this paper, the shallow water problem is discussed. By treating the incompressible condition as the constraint, a constrained Hamilton variational principle is presented for the shallow water problem. Based on the constrained Hamilton variational principle, a shallow water equation based on displacement and pressure (SWE-DP) is developed. A hybrid numerical method combining the finite element method for spa- tial discretization and the Zu-class method for time integration is created for the SWE- DP. The correctness of the proposed SWE-DP is verified by numerical comparisons with two existing shallow water equations (SWEs). The effectiveness of the hybrid numerical method proposed for the SWE-DP is also verified by numerical experiments. Moreover, the numerical experiments demonstrate that the Zu-class method shows excellent perfor- mance with respect to simulating the long time evolution of the shallow water.展开更多
A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hy...A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.展开更多
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo(1987), some uncon ventional Hamilton-type variational principles for dyn...According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo(1987), some uncon ventional Hamilton-type variational principles for dynamics of Reissner sandwich plate can be established systematically. The unconventional Hamilton-type variation principle can fully characterize the initial boundary value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work in dynamics of Reissner sandwich plate, but also to derive systematically the complementary functionals for fivefield, two-field and one-field unconventional Hamilton-type variational principles by the generalized Legender transformations. Furthermore, with this approach, the intrinsic relationship among the various principles can be explained clearly.展开更多
By introducing the Hamilton theory and algorithms into the problems of laminated composite plates andshells, the Hamiltion type generalized variational principle is established, and the Hamilton canonical equations an...By introducing the Hamilton theory and algorithms into the problems of laminated composite plates andshells, the Hamiltion type generalized variational principle is established, and the Hamilton canonical equations andthe boundary conditions for the static and elastoplastic analysis of composite plates are presented. With thetransformation of phase variables, the Hamilton canonical equations and their boundary conditions for thecylindrical shells and doubly curved shells in the curvilinear coordinate are given.展开更多
According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrica...According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An ifnportant integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper, Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.展开更多
Spin-polarized periodic density functional theory was performed to characterize H2S adsorp- tion and dissociation on graphene oxides (GO) surface. The comprehensive reaction network of H2S oxidation with epoxy and h...Spin-polarized periodic density functional theory was performed to characterize H2S adsorp- tion and dissociation on graphene oxides (GO) surface. The comprehensive reaction network of H2S oxidation with epoxy and hydroxyl groups of GO was discussed. It is shown that the reduction reaction is mainly governed by epoxide ring opening and hydroxyl hydrogenation which is initiated by H transfer from H2S or its derivatives, hlrthermore, the presence of another OH group at the opposite side relative to the adsorbed H2S activates the oxygen group to facilitate epoxide ring opening and hydroxyl hydrogenation. For H2S interaction with -O and -OH groups adsorption on each side of graphene, the pathway is a favorable reaction path by the introduction of intermediate states, the predicted energy barriers are 3.2 and 10.4 kcal/mol, respectively, the second H transfer is tile rate-determining step in the whole reaction process. In addition, our calculations suggest that both epoxy and hydroxyl groups can enhance tile binding of S to the C-C bonds and the effect of hydroxyl group is more local than that of the epoxy.展开更多
By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variatio...By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland's variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346(2008), 9-16] are weakened or even completely relieved.展开更多
The paper posits that kin sociality and eusociality are derived from the handicap-care principles based on the need-based care to the handicappers from the caregivers for the self-interest of the caregivers. In this p...The paper posits that kin sociality and eusociality are derived from the handicap-care principles based on the need-based care to the handicappers from the caregivers for the self-interest of the caregivers. In this paper, handicap is defined as the difficulty to survive and reproduce independently. Kin sociality is derived from the childhood handicap-care principle where the children are the handicapped children who receive the care from the kin caregivers in the inclusive kin group to survive. The caregiver gives care for its self-interest to reproduce its gene. The individual’s gene of kin sociality contains the handicapped childhood and the caregiving adulthood. Eusociality is derived from the adulthood handicap-care principle where responsible adults are the handicapped adults who give care and receive care at the same time in the interdependent eusocial group to survive and reproduce its gene. Queen bees reproduce, but must receive care from worker bees that work but must rely on queen bees to reproduce. A caregiver gives care for its self-interest to survive and reproduce its gene. The individual’s gene of eusociality contains the handicapped childhood-adulthood and the caregiving adulthood. The chronological sequence of the sociality evolution is individual sociality without handicap, kin sociality with handicapped childhood, and eusociality with handicapped adulthood. Eusociality in humans is derived from bipedalism and the mixed habitat. The chronological sequence of the eusocial human evolution is 1) the eusocial early hominins with bipedalism and the mixed habitat, 2) the eusocial early Homo species with bipedalism, the larger brain, and the open habitat, 3) the eusocial late Homo species with bipedalism, the largest brain, and the unstable habitat, and 4) extended eusocial Homo sapiens with bipedalism, the shrinking brain, omnipresent imagination, and the harsh habitat. The omnipresence of imagination in human culture converts eusociality into extended eusociality with both perception and omnipresent imagination.展开更多
This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian m...This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian mechanics and Birkhoffian mechanics as three research frames,we introduce Herglotz’s generalized variational principle,dynamical equations of Herglotz type,Noether symmetry and conserved quantities,and their generalization to time-delay dynamics,fractional dynamics and time-scale dynamics,and put forward some problems as suggestions for future research.展开更多
The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is nece...The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system.Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations.The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics.Here,the fractional Pfaff-Birkhoff variational problem is presented and studied.The definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly given.Secondly,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively.Finally,an example is given to illustrate the application of the results.展开更多
In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we der...In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.展开更多
The radiation fields generated when a charged particle is incident on or moving away from a perfectly conducting plane are obtained. These fields are known in the literature as transition radiation. The field equation...The radiation fields generated when a charged particle is incident on or moving away from a perfectly conducting plane are obtained. These fields are known in the literature as transition radiation. The field equations derived thus are used to evaluate the energy, momentum and the action associated with the radiation. The results show that for a charged particle moving with speed ν, the longitudinal momentum associated with the transition radiation is approximately equal to ΔU/c for values of ?1- ν/c smaller than about 10-3 where ΔU is the total radiated energy dissipated during the interaction and cis the speed of light in free space. The action of the radiation, defined as the product of the total energy dissipated and the duration of the emission, increases as 1- ν/c decreases and, for an electron, it becomes equal to h/4π when ν = c - νm where νm is the speed pertinent to the lowest possible momentum associated with a particle confined inside the universe and?h is the Planck constant. Combining these results with Heisenberg’s uncertainty principle, an expression that predicts the value of the elementary charge is derived.展开更多
Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhed...Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhedral scatterers.展开更多
Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous...Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.展开更多
Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the gene...Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isopaxametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which axe often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.展开更多
基金supported by Program of curriculum ideological and political education teaching reform,Zhoukou Normal University-Research on the Path of Ideological and Political Construction of College English Course in local universities from the perspective of cultural confidence(Fund No.SZJG-2022004)Program of Educational Curriculum Reform Henan Province-The exploration of the cultivation of the mentors in normal universities under the background of teacher professional certification(Fund No.2022-JSJYZD-028)+1 种基金the research and practice program of teaching and learning in Zhoukou Normal University(Fund No.JF2021016)achievements of the training program for young and middle-aged key teachers at Zhoukou Normal University in 2021.
文摘Integrating Chinese culture into college English can not only enhance students’humanities literacy and cultivate their cultural confidence,but also facilitate the inheritance and international dissemination of Chinese culture.Taking Tyler’s curriculum framework as the starting point,this paper analyzes some factors that affect the integration of Chinese culture into the college English teaching and proposes some strategies for the integration of Chinese culture into college English teaching by innovating teaching objectives,enriching teaching contents,transforming modes of course delivery,and reconstructing the assessment system.
文摘The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the standard Schrodinger equation. In this paper, we have given the generalized Hamilton principle, which can describe the heat exchange system, and the nonconservative force system. On this basis, we have further given their generalized Lagrange functions and Hamilton functions. With the Feynman path integration, we have given the generalized Schrodinger equation of nonconservative force system and the heat exchange system.
文摘This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we explore the implications for black hole thermodynamics, astrophysics, astronomy, information theory, and the search for new laws of nature. The result includes an estimation of the number of bits stored in a black hole (less than 1.4 × 10<sup>30</sup> bits/m<sup>3</sup>), enhancing our understanding of information storage in extreme gravitational environments. This integration offers valuable insights into the fundamental nature of information and energy, impacting scientific advancements in multiple disciplines.
基金the Natural Science Foundation of Jiangxi Provincethe Foundation of Education Department of Jiangxi Province under Grant No.[2007]136
文摘In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton's principle. Finally, the Hamilton's principle of high-order Lagrangian function is given.
基金Project supported by the National Natural Science Foundation of China(No.11472067)
文摘In this paper, the shallow water problem is discussed. By treating the incompressible condition as the constraint, a constrained Hamilton variational principle is presented for the shallow water problem. Based on the constrained Hamilton variational principle, a shallow water equation based on displacement and pressure (SWE-DP) is developed. A hybrid numerical method combining the finite element method for spa- tial discretization and the Zu-class method for time integration is created for the SWE- DP. The correctness of the proposed SWE-DP is verified by numerical comparisons with two existing shallow water equations (SWEs). The effectiveness of the hybrid numerical method proposed for the SWE-DP is also verified by numerical experiments. Moreover, the numerical experiments demonstrate that the Zu-class method shows excellent perfor- mance with respect to simulating the long time evolution of the shallow water.
基金supported by the National Natural Science Foundation of China (10872108,10876100)the Program for New Century Excellent Talents in University (NCET-07-0477)the National Basic Research Program of China (2010CB832701)
文摘A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.
基金Project supported by the National Natural Science Foundation of China(No.10172097)the Doctoral Foundation of Ministry of Education of China(No.20030558025)
文摘According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo(1987), some uncon ventional Hamilton-type variational principles for dynamics of Reissner sandwich plate can be established systematically. The unconventional Hamilton-type variation principle can fully characterize the initial boundary value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work in dynamics of Reissner sandwich plate, but also to derive systematically the complementary functionals for fivefield, two-field and one-field unconventional Hamilton-type variational principles by the generalized Legender transformations. Furthermore, with this approach, the intrinsic relationship among the various principles can be explained clearly.
文摘By introducing the Hamilton theory and algorithms into the problems of laminated composite plates andshells, the Hamiltion type generalized variational principle is established, and the Hamilton canonical equations andthe boundary conditions for the static and elastoplastic analysis of composite plates are presented. With thetransformation of phase variables, the Hamilton canonical equations and their boundary conditions for thecylindrical shells and doubly curved shells in the curvilinear coordinate are given.
基金Project supported by the National Natural Science Foundation of China(No.10172097)the Doctoral Foundation of Ministry of Education of China(No.20030558025)
文摘According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An ifnportant integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper, Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.
基金This work was supported by the National Natu- ral Science Foundation of China (No.21004009) and the Foundation of Jiangxi Educational Committee (No.G J J13447 and No.G J J14485). We are grateful to High Performance Computer Center of State Key Lab- oratory of Physical Chemistry of Solid Surface (Xiamen University).
文摘Spin-polarized periodic density functional theory was performed to characterize H2S adsorp- tion and dissociation on graphene oxides (GO) surface. The comprehensive reaction network of H2S oxidation with epoxy and hydroxyl groups of GO was discussed. It is shown that the reduction reaction is mainly governed by epoxide ring opening and hydroxyl hydrogenation which is initiated by H transfer from H2S or its derivatives, hlrthermore, the presence of another OH group at the opposite side relative to the adsorbed H2S activates the oxygen group to facilitate epoxide ring opening and hydroxyl hydrogenation. For H2S interaction with -O and -OH groups adsorption on each side of graphene, the pathway is a favorable reaction path by the introduction of intermediate states, the predicted energy barriers are 3.2 and 10.4 kcal/mol, respectively, the second H transfer is tile rate-determining step in the whole reaction process. In addition, our calculations suggest that both epoxy and hydroxyl groups can enhance tile binding of S to the C-C bonds and the effect of hydroxyl group is more local than that of the epoxy.
基金Supported by the National Natural Science Foundation of China(10871141)
文摘By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland's variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346(2008), 9-16] are weakened or even completely relieved.
文摘The paper posits that kin sociality and eusociality are derived from the handicap-care principles based on the need-based care to the handicappers from the caregivers for the self-interest of the caregivers. In this paper, handicap is defined as the difficulty to survive and reproduce independently. Kin sociality is derived from the childhood handicap-care principle where the children are the handicapped children who receive the care from the kin caregivers in the inclusive kin group to survive. The caregiver gives care for its self-interest to reproduce its gene. The individual’s gene of kin sociality contains the handicapped childhood and the caregiving adulthood. Eusociality is derived from the adulthood handicap-care principle where responsible adults are the handicapped adults who give care and receive care at the same time in the interdependent eusocial group to survive and reproduce its gene. Queen bees reproduce, but must receive care from worker bees that work but must rely on queen bees to reproduce. A caregiver gives care for its self-interest to survive and reproduce its gene. The individual’s gene of eusociality contains the handicapped childhood-adulthood and the caregiving adulthood. The chronological sequence of the sociality evolution is individual sociality without handicap, kin sociality with handicapped childhood, and eusociality with handicapped adulthood. Eusociality in humans is derived from bipedalism and the mixed habitat. The chronological sequence of the eusocial human evolution is 1) the eusocial early hominins with bipedalism and the mixed habitat, 2) the eusocial early Homo species with bipedalism, the larger brain, and the open habitat, 3) the eusocial late Homo species with bipedalism, the largest brain, and the unstable habitat, and 4) extended eusocial Homo sapiens with bipedalism, the shrinking brain, omnipresent imagination, and the harsh habitat. The omnipresence of imagination in human culture converts eusociality into extended eusociality with both perception and omnipresent imagination.
基金supported by the National Natural Science Foundations of China (Nos. 11972241,11572212,11272227)the Natural Science Foundation of Jiangsu Province(No. BK20191454).
文摘This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian mechanics and Birkhoffian mechanics as three research frames,we introduce Herglotz’s generalized variational principle,dynamical equations of Herglotz type,Noether symmetry and conserved quantities,and their generalization to time-delay dynamics,fractional dynamics and time-scale dynamics,and put forward some problems as suggestions for future research.
基金Supported by the National Natural Science Foundation of China(10972151,11272227)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province(CXZZ11_0949)the Innovation Program for Postgraduate of Suzhou University of Science and Technology(SKCX11S_050)
文摘The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system.Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations.The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics.Here,the fractional Pfaff-Birkhoff variational problem is presented and studied.The definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly given.Secondly,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively.Finally,an example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (11061023)
文摘In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.
文摘The radiation fields generated when a charged particle is incident on or moving away from a perfectly conducting plane are obtained. These fields are known in the literature as transition radiation. The field equations derived thus are used to evaluate the energy, momentum and the action associated with the radiation. The results show that for a charged particle moving with speed ν, the longitudinal momentum associated with the transition radiation is approximately equal to ΔU/c for values of ?1- ν/c smaller than about 10-3 where ΔU is the total radiated energy dissipated during the interaction and cis the speed of light in free space. The action of the radiation, defined as the product of the total energy dissipated and the duration of the emission, increases as 1- ν/c decreases and, for an electron, it becomes equal to h/4π when ν = c - νm where νm is the speed pertinent to the lowest possible momentum associated with a particle confined inside the universe and?h is the Planck constant. Combining these results with Heisenberg’s uncertainty principle, an expression that predicts the value of the elementary charge is derived.
基金supported by NSF grant,FRG DMS 0554571supported substantially by Hong Kong RGC grant (Project 404407)partially by Cheung Kong Scholars Programme through Wuhan University,China.
文摘Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhedral scatterers.
文摘Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.
基金Project supported by the National Natural Science Foundation of China(No.50276041)
文摘Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isopaxametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which axe often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.