We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable mo...We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson （G J） hierarchy whose Hamiltonian structure can also be derived by using the trace identity. This provides a much simplier construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra gN. As an application, we apply the loop algebra E of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell （KN） hierarchy which, consisting of two arbitrary parameters a and β, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations.展开更多
A new method of system failure analysis was proposed. First, considering the relationships between the failure subsystems,the decision making trial and evaluation laboratory(DEMATEL) method was used to calculate the d...A new method of system failure analysis was proposed. First, considering the relationships between the failure subsystems,the decision making trial and evaluation laboratory(DEMATEL) method was used to calculate the degree of correlation between the failure subsystems, analyze the combined effect of related failures, and obtain the degree of correlation by using the directed graph and matrix operations. Then, the interpretative structural modeling(ISM) method was combined to intuitively show the logical relationship of many failure subsystems and their influences on each other by using multilevel hierarchical structure model and obtaining the critical subsystems. Finally, failure mode effects and criticality analysis(FMECA) was used to perform a qualitative hazard analysis of critical subsystems, determine the critical failure mode, and clarify the direction of reliability improvement.Through an example, the result demonstrates that the proposed method can be efficiently applied to system failure analysis problems.展开更多
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A m...In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.展开更多
The double Wronskian solutions whose entries satisfy matrix equation for a （2＋1）-dimensional breaking soliton equation （（2＋ 1）DBSE） associated with the ZS-AKNS hierarchy are derived through the Wronskian techn...The double Wronskian solutions whose entries satisfy matrix equation for a （2＋1）-dimensional breaking soliton equation （（2＋ 1）DBSE） associated with the ZS-AKNS hierarchy are derived through the Wronskian technique. Rational and periodic solutions for （2＋1）DBSE are obtained by taking special eases in general double Wronskian solutions.展开更多
Cyber security lacks comprehensive theoretical guidance. General security theory, as a set of basic security theory concepts, is intended to guide cyber security and all the other security work. The general theory of ...Cyber security lacks comprehensive theoretical guidance. General security theory, as a set of basic security theory concepts, is intended to guide cyber security and all the other security work. The general theory of security aims to unify the main branches of cyber security and establish a unified basic theory. This paper proposal an overview on the general theory of security, which is devoted to constructing a comprehensive model of network security. The hierarchical structure of the meridian-collateral tree is described. Shannon information theory is employed to build a cyberspace security model. Some central concepts of security, i.e., the attack and defense, are discussed and several general theorems on security are presented.展开更多
Based on the analytic property of the symmetric q-exponent e_q(x),a new symmetric q-deformed Kadomtsev-Petviashvili(q-KP for short) hierarchy associated with the symmetric q-derivative operator α_q is constructed.Fur...Based on the analytic property of the symmetric q-exponent e_q(x),a new symmetric q-deformed Kadomtsev-Petviashvili(q-KP for short) hierarchy associated with the symmetric q-derivative operator α_q is constructed.Furthermore,the symmetric q-CKP hierarchy and symmetric q-BKP hierarchy are defined.The authors also investigate the additional symmetries of the symmetric q-KP hierarchy.展开更多
A problem of a hierarchy structure optimization is considered.Hierarchical structures arewidely used in the Analytic Hierarchy Process,conjoint analysis,and various other methods of multiplecriteria decision making.Th...A problem of a hierarchy structure optimization is considered.Hierarchical structures arewidely used in the Analytic Hierarchy Process,conjoint analysis,and various other methods of multiplecriteria decision making.The problem consists in finding a structure that needs a minimum number ofpair comparisons for a given total number of the alternatives.For an optimal hierarchy,the minimumefforts are needed for eliciting data and synthesizing the local preferences across the hierarchy to getthe global priorities or utilities.Special estimation techniques are developed and numerical simulationsperformed.Analytical and numerical results suggest optimal ways of priority evaluations for practicalmanagerial decisions in a complex environment.展开更多
This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al...This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al.,2022),this paper studies the source of longitudinal field at solid boundary,caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes.We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless pressure P and temperature T.The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface.We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound,and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur symmetrically"at the samc level,but appears along a zigzag route.At the first level,it is the pressure gradient that generates vorticity unidirectionally;while at the second level,it is the vorticity that generates dilatation unidirectionally.展开更多
Abstract We investigated the social relationships among adult females in two multimale-multifemale groups of black howler monkeys Alouatta pigra during a 14-month study in Palenque National Park, Mexico. Based on over...Abstract We investigated the social relationships among adult females in two multimale-multifemale groups of black howler monkeys Alouatta pigra during a 14-month study in Palenque National Park, Mexico. Based on over 900 focal hours and over 5400 scan samples recording neighboring group members, we found that females very rarely engaged in agonistic interactions and no dominance hierarchy could be discerned. Relationships among resident females were primarily affiliative, but females of one study group spent a higher proportion of time in close proximity and engaged in affiliative interactions with one another at higher rates than females in the other study group. The strength of female relationships increased with the birth of an infant. Al- though no females immigrated during the study period, the temporary association of three extragroup females with our study groups implies that the social system of black howler monkeys is more dynamic than previously suggested. These findings sug- gest that female black howler monkeys behave more similarly to female red howler monkeys A. seniculus than to female mantled howler monkeys A. palliata展开更多
基金Supported by a Research Grant from the CityU Strategic Research under Grant No. 7002564
文摘We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson （G J） hierarchy whose Hamiltonian structure can also be derived by using the trace identity. This provides a much simplier construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra gN. As an application, we apply the loop algebra E of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell （KN） hierarchy which, consisting of two arbitrary parameters a and β, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations.
基金Project(51275205)supported by the National Natural Science Foundation of China
文摘A new method of system failure analysis was proposed. First, considering the relationships between the failure subsystems,the decision making trial and evaluation laboratory(DEMATEL) method was used to calculate the degree of correlation between the failure subsystems, analyze the combined effect of related failures, and obtain the degree of correlation by using the directed graph and matrix operations. Then, the interpretative structural modeling(ISM) method was combined to intuitively show the logical relationship of many failure subsystems and their influences on each other by using multilevel hierarchical structure model and obtaining the critical subsystems. Finally, failure mode effects and criticality analysis(FMECA) was used to perform a qualitative hazard analysis of critical subsystems, determine the critical failure mode, and clarify the direction of reliability improvement.Through an example, the result demonstrates that the proposed method can be efficiently applied to system failure analysis problems.
文摘In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.
基金Supported by the National Natural Science Foundation of China under Grant No. 10671121
文摘The double Wronskian solutions whose entries satisfy matrix equation for a （2＋1）-dimensional breaking soliton equation （（2＋ 1）DBSE） associated with the ZS-AKNS hierarchy are derived through the Wronskian technique. Rational and periodic solutions for （2＋1）DBSE are obtained by taking special eases in general double Wronskian solutions.
基金supported by the National Key R&D Program of China (2016YFF0204001)the National Key Technology Support Program (2015BAH08F02)+3 种基金the CCF-Venustech Hongyan Research Initiative (2016-009)the PAPD fundthe CICAEET fundthe Guizhou Provincial Key Laboratory of Public Big Data Program
文摘Cyber security lacks comprehensive theoretical guidance. General security theory, as a set of basic security theory concepts, is intended to guide cyber security and all the other security work. The general theory of security aims to unify the main branches of cyber security and establish a unified basic theory. This paper proposal an overview on the general theory of security, which is devoted to constructing a comprehensive model of network security. The hierarchical structure of the meridian-collateral tree is described. Shannon information theory is employed to build a cyberspace security model. Some central concepts of security, i.e., the attack and defense, are discussed and several general theorems on security are presented.
基金supported by the National Natural Science Foundation of China(Nos.11201451,11271210,11371278,11431010)the Erasmus Mundus Action 2 EXPERTS,the SMSTC grant(No.12XD1405000)Fundamental Research Funds for the Central Universities
文摘Based on the analytic property of the symmetric q-exponent e_q(x),a new symmetric q-deformed Kadomtsev-Petviashvili(q-KP for short) hierarchy associated with the symmetric q-derivative operator α_q is constructed.Furthermore,the symmetric q-CKP hierarchy and symmetric q-BKP hierarchy are defined.The authors also investigate the additional symmetries of the symmetric q-KP hierarchy.
文摘A problem of a hierarchy structure optimization is considered.Hierarchical structures arewidely used in the Analytic Hierarchy Process,conjoint analysis,and various other methods of multiplecriteria decision making.The problem consists in finding a structure that needs a minimum number ofpair comparisons for a given total number of the alternatives.For an optimal hierarchy,the minimumefforts are needed for eliciting data and synthesizing the local preferences across the hierarchy to getthe global priorities or utilities.Special estimation techniques are developed and numerical simulationsperformed.Analytical and numerical results suggest optimal ways of priority evaluations for practicalmanagerial decisions in a complex environment.
基金supported by the National Natural Science Foundation of China(Grant Nos.12102365,91752202,11472016,11621202,and 12272371).
文摘This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al.,2022),this paper studies the source of longitudinal field at solid boundary,caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes.We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless pressure P and temperature T.The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface.We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound,and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur symmetrically"at the samc level,but appears along a zigzag route.At the first level,it is the pressure gradient that generates vorticity unidirectionally;while at the second level,it is the vorticity that generates dilatation unidirectionally.
基金Acknowledgement We thank the Mexican government （CONANP） for research permission to work at Palenque National Park granted to AE. Our research was supported by grants from the National Science Foundation （DDIG 0622386）, the L.S.B. Leakey Foundation, the Department of Zoology, University of Wisconsin-Madison, and the Pittsburgh Zoo Conservation Fund. All animal care regulations and applicable national laws were followed. M. Marroquin, R. MacDonald, G. Campbell, J.M. Jose Dominguez, C. Hauglustaine, E Gimmie, and A. Herbert provided support in the field. C. Snowdon, T. Ziegler, J. Lambert, and two anonymous reviewers provided helpful comments on an earlier version of this manuscript.
文摘Abstract We investigated the social relationships among adult females in two multimale-multifemale groups of black howler monkeys Alouatta pigra during a 14-month study in Palenque National Park, Mexico. Based on over 900 focal hours and over 5400 scan samples recording neighboring group members, we found that females very rarely engaged in agonistic interactions and no dominance hierarchy could be discerned. Relationships among resident females were primarily affiliative, but females of one study group spent a higher proportion of time in close proximity and engaged in affiliative interactions with one another at higher rates than females in the other study group. The strength of female relationships increased with the birth of an infant. Al- though no females immigrated during the study period, the temporary association of three extragroup females with our study groups implies that the social system of black howler monkeys is more dynamic than previously suggested. These findings sug- gest that female black howler monkeys behave more similarly to female red howler monkeys A. seniculus than to female mantled howler monkeys A. palliata
