Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was...Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was determined. Results and Conclusion The equations a Lie algebraic structure if any nonpotential generalized force doesn't exist while while the equations possess a Lie-admissible algebraic structure if nonpotential generalized forces exist .展开更多
In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained ...In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.展开更多
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations...We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.
An improved algebraic reconstruction technique（ART） combined with tunable diode laser absorption spectroscopy（TDLAS） is presented in this paper for determining two-dimensional（2D） distribution of H2O concentrati...An improved algebraic reconstruction technique（ART） combined with tunable diode laser absorption spectroscopy（TDLAS） is presented in this paper for determining two-dimensional（2D） distribution of H2O concentration and temperature in a simulated combustion flame.This work aims to simulate the reconstruction of spectroscopic measurements by a multi-view parallel-beam scanning geometry and analyze the effects of projection rays on reconstruction accuracy.It finally proves that reconstruction quality dramatically increases with the number of projection rays increasing until more than 180 for 20 × 20 grid,and after that point,the number of projection rays has little influence on reconstruction accuracy.It is clear that the temperature reconstruction results are more accurate than the water vapor concentration obtained by the traditional concentration calculation method.In the present study an innovative way to reduce the error of concentration reconstruction and improve the reconstruction quality greatly is also proposed,and the capability of this new method is evaluated by using appropriate assessment parameters.By using this new approach,not only the concentration reconstruction accuracy is greatly improved,but also a suitable parallel-beam arrangement is put forward for high reconstruction accuracy and simplicity of experimental validation.Finally,a bimodal structure of the combustion region is assumed to demonstrate the robustness and universality of the proposed method.Numerical investigation indicates that the proposed TDLAS tomographic algorithm is capable of detecting accurate temperature and concentration profiles.This feasible formula for reconstruction research is expected to resolve several key issues in practical combustion devices.展开更多
This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. ...This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.展开更多
The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic f...The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.展开更多
The algebraic energy method （AEM） is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states： a^3∑＋ state of NaK, X^2∑＋ state of XeBr, X^2∑＋ state of HgI, X^1...The algebraic energy method （AEM） is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states： a^3∑＋ state of NaK, X^2∑＋ state of XeBr, X^2∑＋ state of HgI, X^1∑＋ state of LiH, A3∏（1） state of IC1, X^1∑＋ state of CsH, A（3∏1） and B0＋（3∏） states of CIF, 21∏ state of KRb, X^1∑＋ state of CO, and c^3∑＋ state of NaK molecule. The results show that the values of De computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable De within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature展开更多
The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theore...The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.展开更多
We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the resul...We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.展开更多
This paper give the algebraic criteria for all delay stability of two dimensional degenerate differential systems with delays and give two examples to illustrate the use of them.
Cloud storage is one of the main application of the cloud computing.With the data services in the cloud,users is able to outsource their data to the cloud,access and share their outsourced data from the cloud server a...Cloud storage is one of the main application of the cloud computing.With the data services in the cloud,users is able to outsource their data to the cloud,access and share their outsourced data from the cloud server anywhere and anytime.However,this new paradigm of data outsourcing services also introduces new security challenges,among which is how to ensure the integrity of the outsourced data.Although the cloud storage providers commit a reliable and secure environment to users,the integrity of data can still be damaged owing to the carelessness of humans and failures of hardwares/softwares or the attacks from external adversaries.Therefore,it is of great importance for users to audit the integrity of their data outsourced to the cloud.In this paper,we first design an auditing framework for cloud storage and proposed an algebraic signature based remote data possession checking protocol,which allows a third-party to auditing the integrity of the outsourced data on behalf of the users and supports unlimited number of verifications.Then we extends our auditing protocol to support data dynamic operations,including data update,data insertion and data deletion.The analysis and experiment results demonstrate that our proposed schemes are secure and efficient.展开更多
The investigation of novel signal processing tools is one of the hottest research topics in modern signal processing community. Among them, the algebraic and geometric signal processing methods are the most powerful t...The investigation of novel signal processing tools is one of the hottest research topics in modern signal processing community. Among them, the algebraic and geometric signal processing methods are the most powerful tools for the representation of the classical signal processing method. In this paper, we provide an overview of recent contributions to the algebraic and geometric signal processing. Specifically, the paper focuses on the mathematical structures behind the signal processing by emphasizing the algebraic and geometric structure of signal processing. The two major topics are discussed. First, the classical signal processing concepts are related to the algebraic structures, and the recent results associated with the algebraic signal processing theory are introduced. Second, the recent progress of the geometric signal and information processing representations associated with the geometric structure are discussed. From these discussions, it is concluded that the research on the algebraic and geometric structure of signal processing can help the researchers to understand the signal processing tools deeply, and also help us to find novel signal processing methods in signal processing community. Its practical applications are expected to grow significantly in years to come, given that the algebraic and geometric structure of signal processing offer many advantages over the traditional signal processing.展开更多
A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transform...A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space.Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves,the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves,the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.展开更多
The algebraic collapsing acceleration(ACA)technique maximizes the use of geometric flexibility of the method of characteristics(MOC).The spatial grids for loworder ACA are the same as the high-order transport,which ma...The algebraic collapsing acceleration(ACA)technique maximizes the use of geometric flexibility of the method of characteristics(MOC).The spatial grids for loworder ACA are the same as the high-order transport,which makes the numerical solution of ACA equations costly,especially for large-size problems.To speed-up the MOC transport iterations effectively for general geometry,a coarse-mesh ACA method that involves selectively merging fine-mesh cells with identical materials,called material-mesh ACA(MMACA),is presented.The energy group batching(EGB)strategy in the tracing process is proposed to increase the parallel efficiency for microscopic crosssection problems.Microscopic and macroscopic crosssection benchmark problems are used to validate and analyse the accuracy and efficiency of the MMACA method.The maximum errors in the multiplication factor and pin power distributions are from the VERA-4 B-2 D case with silver-indium-cadmium(AIC)control rods inserted and are 104 pcm and 1.97%,respectively.Compared with the single-thread ACA solution,the maximum speed-up ratio reached 25 on 12 CPU cores for microscopic cross-section VERA-4-2 D problem.For the C5 G7-2 D and LRA-2 D benchmarks,the MMACA method can reduce the computation time by approximately one half.The present work proposes the MMACA method and demonstrates its ability to effectively accelerate MOC transport iterations.展开更多
This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in ...This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.展开更多
This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
The dynamical correlation between quantum entanglement and intramolecular energy in realistic molecular vibrations is explored using the Lie algebraic approach. The explicit expression of entanglement measurement can ...The dynamical correlation between quantum entanglement and intramolecular energy in realistic molecular vibrations is explored using the Lie algebraic approach. The explicit expression of entanglement measurement can be achieved using algebraic operations. The common and different characteristics of dynamical entanglement in different molecular vibrations are also provided. The dynamical study of quantum entanglement and intramolecular energy in small molecular vibrations can be helpful for controlling the entanglement and further understanding the intramolecular dynamics.展开更多
Let P-n be an algebraic polynomial of degree n with real coefficients. We study the extremal properties of the integral integral(-1)(1)(P ''(n) (x))(2)dx and integral(-1)(1) (1-x(2))1/2(P ''(n)(x))(2)d...Let P-n be an algebraic polynomial of degree n with real coefficients. We study the extremal properties of the integral integral(-1)(1)(P ''(n) (x))(2)dx and integral(-1)(1) (1-x(2))1/2(P ''(n)(x))(2)dx subject to the constraint max \P-n(x)\less than or equal to 1.展开更多
文摘Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was determined. Results and Conclusion The equations a Lie algebraic structure if any nonpotential generalized force doesn't exist while while the equations possess a Lie-admissible algebraic structure if nonpotential generalized forces exist .
文摘In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.
基金supported by the Natural Science Foundationof China (10471065)the Natural Science Foundation of Guangdong Province (N04010474)
文摘We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.
基金The project Supported by NNSF of China(19971052)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.61205151)the National Key Scientific Instrument and Equipment Development Project of China(Grant No.2014YQ060537)the National Basic Research Program,China(Grant No.2013CB632803)
文摘An improved algebraic reconstruction technique（ART） combined with tunable diode laser absorption spectroscopy（TDLAS） is presented in this paper for determining two-dimensional（2D） distribution of H2O concentration and temperature in a simulated combustion flame.This work aims to simulate the reconstruction of spectroscopic measurements by a multi-view parallel-beam scanning geometry and analyze the effects of projection rays on reconstruction accuracy.It finally proves that reconstruction quality dramatically increases with the number of projection rays increasing until more than 180 for 20 × 20 grid,and after that point,the number of projection rays has little influence on reconstruction accuracy.It is clear that the temperature reconstruction results are more accurate than the water vapor concentration obtained by the traditional concentration calculation method.In the present study an innovative way to reduce the error of concentration reconstruction and improve the reconstruction quality greatly is also proposed,and the capability of this new method is evaluated by using appropriate assessment parameters.By using this new approach,not only the concentration reconstruction accuracy is greatly improved,but also a suitable parallel-beam arrangement is put forward for high reconstruction accuracy and simplicity of experimental validation.Finally,a bimodal structure of the combustion region is assumed to demonstrate the robustness and universality of the proposed method.Numerical investigation indicates that the proposed TDLAS tomographic algorithm is capable of detecting accurate temperature and concentration profiles.This feasible formula for reconstruction research is expected to resolve several key issues in practical combustion devices.
文摘This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.
基金Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China （Grant Nos 10471145 and 10372053） and the Natural Science Foundation of Henan Provincial Government of China （Grant Nos 0311011400 and 0511022200）.
文摘The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.
基金Project supported by the Science Foundation of China West Normal University （Grant No 05B016） and the Science Foundation of Sichuan province Educational Bureau of China （Grant No 2006A080）.
文摘The algebraic energy method （AEM） is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states： a^3∑＋ state of NaK, X^2∑＋ state of XeBr, X^2∑＋ state of HgI, X^1∑＋ state of LiH, A3∏（1） state of IC1, X^1∑＋ state of CsH, A（3∏1） and B0＋（3∏） states of CIF, 21∏ state of KRb, X^1∑＋ state of CO, and c^3∑＋ state of NaK molecule. The results show that the values of De computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable De within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature
基金Supported by Guangdong Natural Science Foundation(2015A030313628,S2012010010376)Training plan for Distinguished Young Teachers in Higher Education of Guangdong(Yqgdufe1405)+1 种基金Guangdong Education Science Planning Project(2014GXJK091,GDJG20142304)the National Natural Science Foundation of China(11301140,11101096)
文摘The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.
文摘We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.
文摘This paper give the algebraic criteria for all delay stability of two dimensional degenerate differential systems with delays and give two examples to illustrate the use of them.
基金The authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped improve the quality of this paper. This work is supported by National Natural Science Foundation of China （No： 61379144）, Foundation of Science and Technology on Information Assurance Laboratory （No： KJ-13-002） and the Graduate Innovation Fund of the National University of Defense Technology.
文摘Cloud storage is one of the main application of the cloud computing.With the data services in the cloud,users is able to outsource their data to the cloud,access and share their outsourced data from the cloud server anywhere and anytime.However,this new paradigm of data outsourcing services also introduces new security challenges,among which is how to ensure the integrity of the outsourced data.Although the cloud storage providers commit a reliable and secure environment to users,the integrity of data can still be damaged owing to the carelessness of humans and failures of hardwares/softwares or the attacks from external adversaries.Therefore,it is of great importance for users to audit the integrity of their data outsourced to the cloud.In this paper,we first design an auditing framework for cloud storage and proposed an algebraic signature based remote data possession checking protocol,which allows a third-party to auditing the integrity of the outsourced data on behalf of the users and supports unlimited number of verifications.Then we extends our auditing protocol to support data dynamic operations,including data update,data insertion and data deletion.The analysis and experiment results demonstrate that our proposed schemes are secure and efficient.
基金Sponsored by Program for Changjiang Scholars and Innovative Research Team in University ( IRT1005 )the National Natural Science Founda-tions of China ( 61171195 and 61179031)Program for New Century Excellent Talents in University ( NCET-12-0042)
文摘The investigation of novel signal processing tools is one of the hottest research topics in modern signal processing community. Among them, the algebraic and geometric signal processing methods are the most powerful tools for the representation of the classical signal processing method. In this paper, we provide an overview of recent contributions to the algebraic and geometric signal processing. Specifically, the paper focuses on the mathematical structures behind the signal processing by emphasizing the algebraic and geometric structure of signal processing. The two major topics are discussed. First, the classical signal processing concepts are related to the algebraic structures, and the recent results associated with the algebraic signal processing theory are introduced. Second, the recent progress of the geometric signal and information processing representations associated with the geometric structure are discussed. From these discussions, it is concluded that the research on the algebraic and geometric structure of signal processing can help the researchers to understand the signal processing tools deeply, and also help us to find novel signal processing methods in signal processing community. Its practical applications are expected to grow significantly in years to come, given that the algebraic and geometric structure of signal processing offer many advantages over the traditional signal processing.
基金Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project,China(Grant No.2012010)the National Natural Science Foundation of China(Grant Nos.41205082 and 41476019)+1 种基金the Special Funds for Theoretical Physics of the National Natural Science Foundation of China(Grant No.11447205)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD),China
文摘A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space.Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves,the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves,the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.
基金supported by the Chinese TMSR Strategic Pioneer Science and Technology Project(No.XDA02010000)the Frontier Science Key Program of the Chinese Academy of Sciences(No.QYZDY-SSW-JSC016)。
文摘The algebraic collapsing acceleration(ACA)technique maximizes the use of geometric flexibility of the method of characteristics(MOC).The spatial grids for loworder ACA are the same as the high-order transport,which makes the numerical solution of ACA equations costly,especially for large-size problems.To speed-up the MOC transport iterations effectively for general geometry,a coarse-mesh ACA method that involves selectively merging fine-mesh cells with identical materials,called material-mesh ACA(MMACA),is presented.The energy group batching(EGB)strategy in the tracing process is proposed to increase the parallel efficiency for microscopic crosssection problems.Microscopic and macroscopic crosssection benchmark problems are used to validate and analyse the accuracy and efficiency of the MMACA method.The maximum errors in the multiplication factor and pin power distributions are from the VERA-4 B-2 D case with silver-indium-cadmium(AIC)control rods inserted and are 104 pcm and 1.97%,respectively.Compared with the single-thread ACA solution,the maximum speed-up ratio reached 25 on 12 CPU cores for microscopic cross-section VERA-4-2 D problem.For the C5 G7-2 D and LRA-2 D benchmarks,the MMACA method can reduce the computation time by approximately one half.The present work proposes the MMACA method and demonstrates its ability to effectively accelerate MOC transport iterations.
基金Project supported by the National Natural Science Foundation of China （Grant No 1057009）.
文摘This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.
基金Supported by the Natural Science Foundation of Guangdong Province（04010474） Supported by the Foundation of the Education Department of Anhui Province for Outstanding Young Teachers in University（2011SQRL172）
文摘This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
基金supported by the National Natural Science Foundation of China(Grant Nos.11147019 and 91021009)
文摘The dynamical correlation between quantum entanglement and intramolecular energy in realistic molecular vibrations is explored using the Lie algebraic approach. The explicit expression of entanglement measurement can be achieved using algebraic operations. The common and different characteristics of dynamical entanglement in different molecular vibrations are also provided. The dynamical study of quantum entanglement and intramolecular energy in small molecular vibrations can be helpful for controlling the entanglement and further understanding the intramolecular dynamics.
文摘Let P-n be an algebraic polynomial of degree n with real coefficients. We study the extremal properties of the integral integral(-1)(1)(P ''(n) (x))(2)dx and integral(-1)(1) (1-x(2))1/2(P ''(n)(x))(2)dx subject to the constraint max \P-n(x)\less than or equal to 1.
