Eco-township is of great significance for constructing beautiful countryside and accomplishing regional coordinated development between rural and urban areas to protect and improve environment in towns and villages in...Eco-township is of great significance for constructing beautiful countryside and accomplishing regional coordinated development between rural and urban areas to protect and improve environment in towns and villages in accordance with Envi- ronment Planning and Guidance of Townlets. The research took national eco-town- ship in Luoshi Town, Xinluo County, Jiangxi Province as an example and analyzed major environmental problems and causes by collecting natural, social and environ- ment information, from the perspectives of surveying on pollution source and envi- ronment quality. Finally, the research conducted regionalization of environment func- tion zones, determined environment quality protection objectives, and formulated en- vironment protection countermeasures, providing references for eco-township develop- ment in underdeveloped areas.展开更多
In unconventional reservoirs, small faults allow the flow ofoil and gas as well as act as obstacles to exploration; for, (1) fracturing facilitates fluid migration, (2) reservoir flooding, and (3) triggering of ...In unconventional reservoirs, small faults allow the flow ofoil and gas as well as act as obstacles to exploration; for, (1) fracturing facilitates fluid migration, (2) reservoir flooding, and (3) triggering of small earthquakes. These small faults are not generally detected because of the low seismic resolution. However, such small faults are very active and release sufficient energy to initiate a large number of microseismic events (MEs) during hydraulic fracturing. In this study, we identified microfractures (MF) from hydraulic fracturing and natural small faults based on microseismicity characteristics, such as the time-space distribution, source mechanism, magnitude, amplitude, and frequency. First, I identified the mechanism of small faults and MF by reservoir stress analysis and calibrated the ME based on the microseismic magnitude. The dynamic characteristics (frequency and amplitude) of MEs triggered by natural faults and MF were analyzed; moreover, the geometry and activity types of natural fault and MF were grouped according to the source mechanism. Finally, the differences among time-space distribution, magnitude, source mechanism, amplitude, and frequency were used to differentiate natural faults and manmade fractures.展开更多
In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of ...In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.展开更多
This paper uses three size metrics,which are collectable during the design phase,to analyze the potentially confounding effect of class size on the associations between object-oriented(OO)metrics and maintainability...This paper uses three size metrics,which are collectable during the design phase,to analyze the potentially confounding effect of class size on the associations between object-oriented(OO)metrics and maintainability.To draw as many general conclusions as possible,the confounding effect of class size is analyzed on 127 C++ systems and 113 Java systems.For each OO metric,the indirect effect that represents the distortion of the association caused by class size and its variance for individual systems is first computed.Then,a statistical meta-analysis technique is used to compute the average indirect effect over all the systems and to determine if it is significantly different from zero.The experimental results show that the confounding effects of class size on the associations between OO metrics and maintainability generally exist,regardless of whatever size metric is used.Therefore,empirical studies validating OO metrics on maintainability should consider class size as a confounding variable.展开更多
Targeting modernization, we should keep to the Chinese-style path of car- rying out industrialization in a new way and advancing IT application, urbanization, and agricultural modernization. In the research, the scien...Targeting modernization, we should keep to the Chinese-style path of car- rying out industrialization in a new way and advancing IT application, urbanization, and agricultural modernization. In the research, the scientific concepts of IT applica- tion, urbanization, agricultural modernization and industrialization were illustrated and the interrelations were analyzed, with measures on harmonized development pro- posed based on existing problems.展开更多
ln the research, an empirical analysis was performed on production per-formance and influential factors of rice in Changsha County and Liling City. The re-sults showed that production scale has been closely linked to ...ln the research, an empirical analysis was performed on production per-formance and influential factors of rice in Changsha County and Liling City. The re-sults showed that production scale has been closely linked to age and education level of farmers. The larger scale, the higher comprehensive performance, but rele-vant efficiency tends to be lower. Sowing area and yield per unit area are major in-fluential factors of production performance of double-cropping rice, but the rest influ-ential factors are different upon production scale. Final y, developmental strategies are proposed for development of double-cropping rice.展开更多
A new limited memory symmetric rank one algorithm is proposed. It combines a modified self-scaled symmetric rank one (SSR1) update with the limited memory and nonmonotone line search technique. In this algorithm, th...A new limited memory symmetric rank one algorithm is proposed. It combines a modified self-scaled symmetric rank one (SSR1) update with the limited memory and nonmonotone line search technique. In this algorithm, the descent search direction is generated by inverse limited memory SSR1 update, thus simplifying the computation. Numerical comparison of the algorithm and the famous limited memory BFGS algorithm is given. Comparison results indicate that the new algorithm can process a kind of large-scale unconstrained optimization problems.展开更多
A generalized Drinfel'd Sokolov-Wilson (DSW) equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spect...A generalized Drinfel'd Sokolov-Wilson (DSW) equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spectral problems, from which a Darboux transformation for the DSW equation is obtained through a reduction technique. As an application of the Darboux transformations, we give some explicit solutions of the generalized DSW equation and DEW equation such as rational solutions, soliton solutions, periodic solutions.展开更多
The properties and some equivalent characterizations of equal projection( EP), normal and Hermitian elements in a ring are studied by the generalized inverse theory. Some equivalent conditions that an element is EP ...The properties and some equivalent characterizations of equal projection( EP), normal and Hermitian elements in a ring are studied by the generalized inverse theory. Some equivalent conditions that an element is EP under the existence of core inverses are proposed. Let a∈R , then a is EP if and only if aa a^# = a^#aa . At the same time, the equivalent characterizations of a regular element to be EP are discussed.Let a∈R, then there exist b∈R such that a = aba and a is EP if and only if a∈R , a = a ba. Similarly, some equivalent conditions that an element is normal under the existence of core inverses are proposed. Let a∈R , then a is normal if and only if a^*a = a a^*. Also, some equivalent conditions of normal and Hermitian elements in rings with involution involving powers of their group and Moore-Penrose inverses are presented. Let a∈R ∩R^#, n∈N, then a is normal if and only if a^* a^+( a^#) n = a^# a*( a^+) ^n. The results generalize the conclusions of Mosiet al.展开更多
In the framework of topcolor-assisted technicolor model we calculate the contributions from the pseudo Goldstone bosons and new gauge bosons to . We find that for reasonable ranges of the parameters, the pseudo Goldst...In the framework of topcolor-assisted technicolor model we calculate the contributions from the pseudo Goldstone bosons and new gauge bosons to . We find that for reasonable ranges of the parameters, the pseudo Goldstone bosons afford dominate contribution, the correction arising from new gauge bosons is negligibly small, the maximum of the relative corrections is with the center-of-mass energy ; whereas in the case of , the relative corrections could be up to 16%. Thus large new physics might be observable at the experiments of next-generation linear colliders.展开更多
A hybrid distributed virtual environment (DVE) architecture is presented by importing a peer-to-peer (P2P) idea into the traditional client/server (C/S) architecture to improve the DVE system's scalability. The...A hybrid distributed virtual environment (DVE) architecture is presented by importing a peer-to-peer (P2P) idea into the traditional client/server (C/S) architecture to improve the DVE system's scalability. The mathematical model of the overload of the center server was built and a series of simulation experiments were performed to validate the conclusions. When the client number increases to a certain value, the hybrid architecture can reduce server overload with some special clients (temp servers) selected with a certain heuristic strategy. With this architecture, the DVE system can support more system clients with the same server hardware than the C/S architecture can. The server overload "pulse" phenomena causing by the exiting of the temp server can be resolved by adopting a more optimized temp server selecting strategy and by reducing the child client capability of the temp server. By combining the advantages of the C/S architecture and the P2P architecture, the hybrid DVE architecture can effectively improve the scalability of the DVE system. This is validated by theoretical analysis and simulation experiments.展开更多
By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algor...By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm is globally convergent under suitable assumptions.展开更多
The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1...The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1×δ-1)2, the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.展开更多
Dense-medium cyclones have been used for beneficiation of fine particles of coal. In this study, the usability of cyclones in the beneficiation of tailings of a coal preparation plant was investigated. For this purpos...Dense-medium cyclones have been used for beneficiation of fine particles of coal. In this study, the usability of cyclones in the beneficiation of tailings of a coal preparation plant was investigated. For this purpose, separation tests were conducted using spiral concentrator and heavy medium cyclones with the specific weight of medium 1.3-1.8 (g/cm^3) on different grading fractions of tailing in an industrial scale (the weight of tail sample was five tons). Spiral concentrator was utilized to beneficiate particles smaller than 1 mm. In order to evaluate the efficiency of cyclones, sink and float experiments using a specific weight of 1.3, 1.5, 1.7 and 1.9 g/cm^3, were conducted on a pilot scale. Based on the obtained results, the recovery of floated materials in cyclones with the specific weight of 1.40, 1.47 and 1.55 g/cm^3 are 17.75%, 33.80%, and 50%, respectively. Also, the cut point (Pso), which is the relative density at which particles report equally to the both products are 1.40, 1.67 and 1.86 g/cm^3. The probable errors of separation for defined specific weights for cyclones are 0.080, 0.085 and 0.030, respectively. Also, the coefficients of variation was calculated to be 0.20, 0.12 and 0.03. Finally, it could be said that the performance of a cyclone with a heavy medium of 1.40 g/cm^3 specific weight is desirable compared with other specific weights.展开更多
A novel mathematical model for single particle slurry propylene polymerization rising heterogeneous Ziegler-Natta catalysts has been developed to describe the kinetic behavior, the molecular weight-distribution, the m...A novel mathematical model for single particle slurry propylene polymerization rising heterogeneous Ziegler-Natta catalysts has been developed to describe the kinetic behavior, the molecular weight-distribution, the monomer concentration, the degree of polymerization, the polydispersity index (PDI), etc. This model provides a more valid mathematical description by accounting for the monomer diffusion phenomena at two levels as multigrai model counts, and obtains results that are more applicable to the conditions existing in most polymerizations of industrial interest. Considering that some models on the mesoscale phenomena are so complex that some existingmodeling aspects have to be simplified or even neglected to make the model convenient for use in interesting engineering studies, it is very important to put some effort into determining what sort of numerical analysis works bestfor these problems. For this reason, special attentionis.paid to these studies to explorean efficient algorithm usingadaptive grid-point spacing in a tlnlte-ditterence technique to tlgure out more practical mass transport models andconvection-diffusion models efficiently. The reasonable outcomes, as well as the significant computation time saving, have been achieved, thereby displaying the advantage of this calculation method.展开更多
We introduce the sequence of spontaneous symmetry breaking of a coupling between Pati-Salam and electroweak symmetries SU( 4 )PS × SU( 4 )EW in order to establish a mathematically consistent relation among th...We introduce the sequence of spontaneous symmetry breaking of a coupling between Pati-Salam and electroweak symmetries SU( 4 )PS × SU( 4 )EW in order to establish a mathematically consistent relation among the coupling constants at grand unification energy scale. With the values of baryon minus lepton quantum numbers of known quarks and leptons, by including right-handed neutrinos, we can lind the mixing angle relations at different energy levels up to the electromagnetic U(1)EM scale.展开更多
A hierarchy of nonlinear lattice soliton equations is derived from a new discrete spectral problem. The Hamiltonian structure of the resulting hierarchy is constructed by using a trace identity formula. Moreover, a Da...A hierarchy of nonlinear lattice soliton equations is derived from a new discrete spectral problem. The Hamiltonian structure of the resulting hierarchy is constructed by using a trace identity formula. Moreover, a Darboux transformation is established with the help of gauge transformations of Lax pairs for the typical lattice soliton equations. The exact solutions are given by applying the Darboux transformation.展开更多
基金Supported by Humanities and Social Sciences of Jiangxi General Colleges and Universities(JC1434)"Twelfth Five-year Plan"of Jiangxi Provincial Social Sciences Program(14SH05)Jiangxi Art Science Planning Program(YG2014113)~~
文摘Eco-township is of great significance for constructing beautiful countryside and accomplishing regional coordinated development between rural and urban areas to protect and improve environment in towns and villages in accordance with Envi- ronment Planning and Guidance of Townlets. The research took national eco-town- ship in Luoshi Town, Xinluo County, Jiangxi Province as an example and analyzed major environmental problems and causes by collecting natural, social and environ- ment information, from the perspectives of surveying on pollution source and envi- ronment quality. Finally, the research conducted regionalization of environment func- tion zones, determined environment quality protection objectives, and formulated en- vironment protection countermeasures, providing references for eco-township develop- ment in underdeveloped areas.
基金supported by the National Key Research and Development Project of China(No.2016ZX05023-004)
文摘In unconventional reservoirs, small faults allow the flow ofoil and gas as well as act as obstacles to exploration; for, (1) fracturing facilitates fluid migration, (2) reservoir flooding, and (3) triggering of small earthquakes. These small faults are not generally detected because of the low seismic resolution. However, such small faults are very active and release sufficient energy to initiate a large number of microseismic events (MEs) during hydraulic fracturing. In this study, we identified microfractures (MF) from hydraulic fracturing and natural small faults based on microseismicity characteristics, such as the time-space distribution, source mechanism, magnitude, amplitude, and frequency. First, I identified the mechanism of small faults and MF by reservoir stress analysis and calibrated the ME based on the microseismic magnitude. The dynamic characteristics (frequency and amplitude) of MEs triggered by natural faults and MF were analyzed; moreover, the geometry and activity types of natural fault and MF were grouped according to the source mechanism. Finally, the differences among time-space distribution, magnitude, source mechanism, amplitude, and frequency were used to differentiate natural faults and manmade fractures.
文摘In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.
基金The National Natural Science Foundation of China(No.60425206,60633010)
文摘This paper uses three size metrics,which are collectable during the design phase,to analyze the potentially confounding effect of class size on the associations between object-oriented(OO)metrics and maintainability.To draw as many general conclusions as possible,the confounding effect of class size is analyzed on 127 C++ systems and 113 Java systems.For each OO metric,the indirect effect that represents the distortion of the association caused by class size and its variance for individual systems is first computed.Then,a statistical meta-analysis technique is used to compute the average indirect effect over all the systems and to determine if it is significantly different from zero.The experimental results show that the confounding effects of class size on the associations between OO metrics and maintainability generally exist,regardless of whatever size metric is used.Therefore,empirical studies validating OO metrics on maintainability should consider class size as a confounding variable.
文摘Targeting modernization, we should keep to the Chinese-style path of car- rying out industrialization in a new way and advancing IT application, urbanization, and agricultural modernization. In the research, the scientific concepts of IT applica- tion, urbanization, agricultural modernization and industrialization were illustrated and the interrelations were analyzed, with measures on harmonized development pro- posed based on existing problems.
基金Supported by Key Financial Program of Hunan Province([2014]74)National Natural Science Foundation of China(41601097)Science&Technology Innovation Project of Hunan Academy of Agriculture Sciences(2016JC08)~~
文摘ln the research, an empirical analysis was performed on production per-formance and influential factors of rice in Changsha County and Liling City. The re-sults showed that production scale has been closely linked to age and education level of farmers. The larger scale, the higher comprehensive performance, but rele-vant efficiency tends to be lower. Sowing area and yield per unit area are major in-fluential factors of production performance of double-cropping rice, but the rest influ-ential factors are different upon production scale. Final y, developmental strategies are proposed for development of double-cropping rice.
基金the National Natural Science Foundation of China(10471062)the Natural Science Foundation of Jiangsu Province(BK2006184)~~
文摘A new limited memory symmetric rank one algorithm is proposed. It combines a modified self-scaled symmetric rank one (SSR1) update with the limited memory and nonmonotone line search technique. In this algorithm, the descent search direction is generated by inverse limited memory SSR1 update, thus simplifying the computation. Numerical comparison of the algorithm and the famous limited memory BFGS algorithm is given. Comparison results indicate that the new algorithm can process a kind of large-scale unconstrained optimization problems.
基金Supported by National Natural Science Foundation of China under Grant No.10871182Innovation Scientists and Technicians Troop Construction Projects of Henan Province
文摘A generalized Drinfel'd Sokolov-Wilson (DSW) equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spectral problems, from which a Darboux transformation for the DSW equation is obtained through a reduction technique. As an application of the Darboux transformations, we give some explicit solutions of the generalized DSW equation and DEW equation such as rational solutions, soliton solutions, periodic solutions.
基金The National Natural Science Foundation of China(No.11371089)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)the Natural Science Foundation of Jiangsu Province(No.BK20141327)
文摘The properties and some equivalent characterizations of equal projection( EP), normal and Hermitian elements in a ring are studied by the generalized inverse theory. Some equivalent conditions that an element is EP under the existence of core inverses are proposed. Let a∈R , then a is EP if and only if aa a^# = a^#aa . At the same time, the equivalent characterizations of a regular element to be EP are discussed.Let a∈R, then there exist b∈R such that a = aba and a is EP if and only if a∈R , a = a ba. Similarly, some equivalent conditions that an element is normal under the existence of core inverses are proposed. Let a∈R , then a is normal if and only if a^*a = a a^*. Also, some equivalent conditions of normal and Hermitian elements in rings with involution involving powers of their group and Moore-Penrose inverses are presented. Let a∈R ∩R^#, n∈N, then a is normal if and only if a^* a^+( a^#) n = a^# a*( a^+) ^n. The results generalize the conclusions of Mosiet al.
文摘In the framework of topcolor-assisted technicolor model we calculate the contributions from the pseudo Goldstone bosons and new gauge bosons to . We find that for reasonable ranges of the parameters, the pseudo Goldstone bosons afford dominate contribution, the correction arising from new gauge bosons is negligibly small, the maximum of the relative corrections is with the center-of-mass energy ; whereas in the case of , the relative corrections could be up to 16%. Thus large new physics might be observable at the experiments of next-generation linear colliders.
文摘A hybrid distributed virtual environment (DVE) architecture is presented by importing a peer-to-peer (P2P) idea into the traditional client/server (C/S) architecture to improve the DVE system's scalability. The mathematical model of the overload of the center server was built and a series of simulation experiments were performed to validate the conclusions. When the client number increases to a certain value, the hybrid architecture can reduce server overload with some special clients (temp servers) selected with a certain heuristic strategy. With this architecture, the DVE system can support more system clients with the same server hardware than the C/S architecture can. The server overload "pulse" phenomena causing by the exiting of the temp server can be resolved by adopting a more optimized temp server selecting strategy and by reducing the child client capability of the temp server. By combining the advantages of the C/S architecture and the P2P architecture, the hybrid DVE architecture can effectively improve the scalability of the DVE system. This is validated by theoretical analysis and simulation experiments.
基金Supported by Liu Hui Centre for Applied Mathematics,Nankai University and Tianjin University
文摘By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm is globally convergent under suitable assumptions.
文摘The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1×δ-1)2, the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.
文摘Dense-medium cyclones have been used for beneficiation of fine particles of coal. In this study, the usability of cyclones in the beneficiation of tailings of a coal preparation plant was investigated. For this purpose, separation tests were conducted using spiral concentrator and heavy medium cyclones with the specific weight of medium 1.3-1.8 (g/cm^3) on different grading fractions of tailing in an industrial scale (the weight of tail sample was five tons). Spiral concentrator was utilized to beneficiate particles smaller than 1 mm. In order to evaluate the efficiency of cyclones, sink and float experiments using a specific weight of 1.3, 1.5, 1.7 and 1.9 g/cm^3, were conducted on a pilot scale. Based on the obtained results, the recovery of floated materials in cyclones with the specific weight of 1.40, 1.47 and 1.55 g/cm^3 are 17.75%, 33.80%, and 50%, respectively. Also, the cut point (Pso), which is the relative density at which particles report equally to the both products are 1.40, 1.67 and 1.86 g/cm^3. The probable errors of separation for defined specific weights for cyclones are 0.080, 0.085 and 0.030, respectively. Also, the coefficients of variation was calculated to be 0.20, 0.12 and 0.03. Finally, it could be said that the performance of a cyclone with a heavy medium of 1.40 g/cm^3 specific weight is desirable compared with other specific weights.
基金Supported by the National High Technology Development Program of China (No.2006AA05Z226), Natural Science Foundation of Zhejiang Province (No.Y105370), National HI-TECH Industrialization Program of China (No.2004-2080), and Science Fund for Distinguished Young Scholars of Zhejiang University (No. 111000-581645).
文摘A novel mathematical model for single particle slurry propylene polymerization rising heterogeneous Ziegler-Natta catalysts has been developed to describe the kinetic behavior, the molecular weight-distribution, the monomer concentration, the degree of polymerization, the polydispersity index (PDI), etc. This model provides a more valid mathematical description by accounting for the monomer diffusion phenomena at two levels as multigrai model counts, and obtains results that are more applicable to the conditions existing in most polymerizations of industrial interest. Considering that some models on the mesoscale phenomena are so complex that some existingmodeling aspects have to be simplified or even neglected to make the model convenient for use in interesting engineering studies, it is very important to put some effort into determining what sort of numerical analysis works bestfor these problems. For this reason, special attentionis.paid to these studies to explorean efficient algorithm usingadaptive grid-point spacing in a tlnlte-ditterence technique to tlgure out more practical mass transport models andconvection-diffusion models efficiently. The reasonable outcomes, as well as the significant computation time saving, have been achieved, thereby displaying the advantage of this calculation method.
文摘We introduce the sequence of spontaneous symmetry breaking of a coupling between Pati-Salam and electroweak symmetries SU( 4 )PS × SU( 4 )EW in order to establish a mathematically consistent relation among the coupling constants at grand unification energy scale. With the values of baryon minus lepton quantum numbers of known quarks and leptons, by including right-handed neutrinos, we can lind the mixing angle relations at different energy levels up to the electromagnetic U(1)EM scale.
基金Supported by the National Natural Science Foundation of China under Grant No.10771207
文摘A hierarchy of nonlinear lattice soliton equations is derived from a new discrete spectral problem. The Hamiltonian structure of the resulting hierarchy is constructed by using a trace identity formula. Moreover, a Darboux transformation is established with the help of gauge transformations of Lax pairs for the typical lattice soliton equations. The exact solutions are given by applying the Darboux transformation.