In this article, we discuss nonsymmetric solutions of the colored Yang-Baxter equation dependent on spectral as well as colored parameters and give all seven-vertex solutions by Wu＇s method. It is also proved that th...In this article, we discuss nonsymmetric solutions of the colored Yang-Baxter equation dependent on spectral as well as colored parameters and give all seven-vertex solutions by Wu＇s method. It is also proved that the solutions are composed of six groups of basic solutions up to five solution transformations. Moreover, al l solutions can be classified into two categories called Baxter type and free-fermion type.展开更多
In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-...In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.展开更多
In this paper, the relationship between solutions of the Quantum Yang-Baxter Equation and quantum comodules, and some properties of the quantum comodule category are characterized here. These results make it possible ...In this paper, the relationship between solutions of the Quantum Yang-Baxter Equation and quantum comodules, and some properties of the quantum comodule category are characterized here. These results make it possible to give some set-theoretical solutions of the Quantum Yang-Baxter Equation.展开更多
In these two papers (Ⅰ) and (Ⅱ),the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given.In the Paper (Ⅱ),we give the general solutions of the Yang-Baxter equation in this ...In these two papers (Ⅰ) and (Ⅱ),the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given.In the Paper (Ⅱ),we give the general solutions of the Yang-Baxter equation in this case.展开更多
In this note a simple extension of the complex algebra to higher dimension is proposed. Using the proposed algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there ...In this note a simple extension of the complex algebra to higher dimension is proposed. Using the proposed algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra where the associative nature can be recovered.展开更多
This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an...This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an efficient procedure based on the modified Adomian decomposition method to obtain closed-form solutions of the Laguerre’s and the associated Laguerre’s differential equations. The proposed technique makes sense as the attitudes of the acquired solutions towards the neighboring singular points are correctly taken care of.展开更多
This paper studies the local solvability of the differental equations associated to unsolvable inhomogeneous left invariant differential operators on the Heisenberg group.It is provedthat for a class of inhomogeneous ...This paper studies the local solvability of the differental equations associated to unsolvable inhomogeneous left invariant differential operators on the Heisenberg group.It is provedthat for a class of inhomogeneous left invariant differental operators on the Heisenberg group,the local solvability of the corresponding equations is equivalent to the local sovability of the equations associated to their highest order terms.Then,under certain conditions on the highest order term,we obtain the necessary and sufficient conditions for the functon f to satisfy ill order for the differential equation Lu=f to be locally solvable展开更多
Encouraged by the wide spectrum of novel applications of gas hydrates,e.g.,energy recovery,gas separation,gas storage,gas transportation,water desalination,and hydrogen hydrate as a green energy resource,as well as CO...Encouraged by the wide spectrum of novel applications of gas hydrates,e.g.,energy recovery,gas separation,gas storage,gas transportation,water desalination,and hydrogen hydrate as a green energy resource,as well as CO2 capturing,many scientists have focused their attention on investigating this important phenomenon.Of course,from an engineering viewpoint,the mathematical modeling of gas hydrates is of paramount importance,as anticipation of gas hydrate stability conditions is effective in the design and control of industrial processes.Overall,the thermodynamic modeling of gas hydrate can be tackled as an equilibration of three phases,i.e.,liquid,gas,and solid hydrate.The inseparable component in all hydrate systems,water,is highly polar and non-ideal,necessitating the use of more advanced equation of states(EoSs) that take into account more intermolecular forces for thermodynamic modeling of these systems.Motivated by the ever-increasing number of publications on this topic,this study aims to review the application of associating EoSs for the thermodynamic modeling of gas hydrates.Three most important hydrate-based models available in the literature including the van der Waals-Platteeuw(vdW-P) model,Chen-Guo model,and Klauda-Sandler model coupled with and SAFT EoSs were investigated and compared with cubic EoSs.It was concluded that the CPA and SAFT EoSs gave very accurate results for hydrate systems as they take into account the association interactions,which are very crucial in gas hydrate systems in which water,methanol,glycols,and other types of associating compounds are available.Moreover,it was concluded that the CPA EoS is easier to use than the SAFT-type EoSs and our suggestion for the gas hydrate systems is the CPA EoS.展开更多
Based on the statistical theory for chemical association,equations of state for hard-spherechain fluids(HSCFs)and square-well chain fluids(SWCFs)can be derived through the n-particlecavity correlation function(CCF)of ...Based on the statistical theory for chemical association,equations of state for hard-spherechain fluids(HSCFs)and square-well chain fluids(SWCFs)can be derived through the n-particlecavity correlation function(CCF)of the corresponding reference system,where n is the chain lengthor the number of segments of a chain molecule.The reference system is a fluid composed of only cor-responding monomers.In this work,the n-particle CCF is approximated by a product of effectivetwo-particle CCFs which accounts for correlations in nearest-neighbour and next-to-nearest-neighboursegment pairs.The CCFs for SWCFs may be expressed by a product of the corresponding functionfor HSCFs and a perturbation term originated from the square-well attractive potential.All these ef-fective two-particle CCFs and perturbation terms are density dependent.The dependence is determinedmainly by using computer-simulation results.The obtained equations can excellently describecompressibility factors and second Virial coefficients for展开更多
In these two papers (I) and (II), the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper (I), we give the Yang-Baxter equation and give the general solutions o...In these two papers (I) and (II), the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper (I), we give the Yang-Baxter equation and give the general solutions of some function equations for the next paper.展开更多
This article provides a closed form solution to the telegrapher’s equation with three space variables defined on a subset of a sphere within two radii, two azimuthal angles and one polar angle. The Dirichlet problem ...This article provides a closed form solution to the telegrapher’s equation with three space variables defined on a subset of a sphere within two radii, two azimuthal angles and one polar angle. The Dirichlet problem for general boundary conditions is solved in detail, on the basis of which Neumann and Robin conditions are easily handled. The solution to the simpler problem in cylindrical coordinates is also provided. Ways to efficiently implement the formulae are explained. Minor adjustments result in solutions to the wave equation and to the heat equation on the same domain as well, since the latter are particular cases of the more general telegrapher’s equation.展开更多
In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equation...In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.展开更多
The solutions of the Laplace equation in n-dimensional space are studied.The angular eigenfunctions have the form of associated Jacobi polynomials.The radial solution of the Helmholtz equation is derived.
YBE associated with the scattering from kaleidoscopes of Sutherland has been found. The reflection behaviour at the Dynkin diagram and its physical meaning are explored.
With the statistical mechanical theory for square-well-chain fluids as the basic princi-ples,a molecular thermodynamic model including expressions for the Helmholtz function and thecompressibility factor for associate...With the statistical mechanical theory for square-well-chain fluids as the basic princi-ples,a molecular thermodynamic model including expressions for the Helmholtz function and thecompressibility factor for associated square-well-chain fluids has been developed.Employment ofthe shield-sticky concept enables the corporation of association bonds between in the model.Good agreement with computer-simulation results for dimer-linear quadrimer systems is obtained.Satisfactory correlation for vapor pressures and saturated liquid volumes of pure substances con-taining associated molecules(such as carboxylic acids,alcohols,amines,water,etc.)with four mo-lecular parameters indicates the applicability of the model.展开更多
基金supported by NKBRPC(2004CB31800, 2006CB805905)Knowledge Innovation Funds of CAS (KJCX3-SYW-S03)
文摘In this article, we discuss nonsymmetric solutions of the colored Yang-Baxter equation dependent on spectral as well as colored parameters and give all seven-vertex solutions by Wu＇s method. It is also proved that the solutions are composed of six groups of basic solutions up to five solution transformations. Moreover, al l solutions can be classified into two categories called Baxter type and free-fermion type.
基金The NSF(11047030 and 11771122) of Chinathe Science and Technology Program(152300410061) of Henan Province
文摘In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.
文摘In this paper, the relationship between solutions of the Quantum Yang-Baxter Equation and quantum comodules, and some properties of the quantum comodule category are characterized here. These results make it possible to give some set-theoretical solutions of the Quantum Yang-Baxter Equation.
文摘In these two papers (Ⅰ) and (Ⅱ),the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given.In the Paper (Ⅱ),we give the general solutions of the Yang-Baxter equation in this case.
文摘In this note a simple extension of the complex algebra to higher dimension is proposed. Using the proposed algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra where the associative nature can be recovered.
文摘This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an efficient procedure based on the modified Adomian decomposition method to obtain closed-form solutions of the Laguerre’s and the associated Laguerre’s differential equations. The proposed technique makes sense as the attitudes of the acquired solutions towards the neighboring singular points are correctly taken care of.
文摘This paper studies the local solvability of the differental equations associated to unsolvable inhomogeneous left invariant differential operators on the Heisenberg group.It is provedthat for a class of inhomogeneous left invariant differental operators on the Heisenberg group,the local solvability of the corresponding equations is equivalent to the local sovability of the equations associated to their highest order terms.Then,under certain conditions on the highest order term,we obtain the necessary and sufficient conditions for the functon f to satisfy ill order for the differential equation Lu=f to be locally solvable
文摘Encouraged by the wide spectrum of novel applications of gas hydrates,e.g.,energy recovery,gas separation,gas storage,gas transportation,water desalination,and hydrogen hydrate as a green energy resource,as well as CO2 capturing,many scientists have focused their attention on investigating this important phenomenon.Of course,from an engineering viewpoint,the mathematical modeling of gas hydrates is of paramount importance,as anticipation of gas hydrate stability conditions is effective in the design and control of industrial processes.Overall,the thermodynamic modeling of gas hydrate can be tackled as an equilibration of three phases,i.e.,liquid,gas,and solid hydrate.The inseparable component in all hydrate systems,water,is highly polar and non-ideal,necessitating the use of more advanced equation of states(EoSs) that take into account more intermolecular forces for thermodynamic modeling of these systems.Motivated by the ever-increasing number of publications on this topic,this study aims to review the application of associating EoSs for the thermodynamic modeling of gas hydrates.Three most important hydrate-based models available in the literature including the van der Waals-Platteeuw(vdW-P) model,Chen-Guo model,and Klauda-Sandler model coupled with and SAFT EoSs were investigated and compared with cubic EoSs.It was concluded that the CPA and SAFT EoSs gave very accurate results for hydrate systems as they take into account the association interactions,which are very crucial in gas hydrate systems in which water,methanol,glycols,and other types of associating compounds are available.Moreover,it was concluded that the CPA EoS is easier to use than the SAFT-type EoSs and our suggestion for the gas hydrate systems is the CPA EoS.
基金Supported by the National Natural Science Foundation of China （20876041, 20736002）, the National Basic Research Program of China （2009CB219902）, the Program for Changjiang Scholars and Innovative Research Team in University of China （Grant IRT0721） and the Programme of Introducing Talents of Discipline to Universities （Grant B08021） of China.
文摘与一个协会模型一起的状态(曙光女神) 的联合 Peng-Robinson (PR ) 方程由刘等源于盾粘的方法(SSM ) ，一个新 cubic-plus-association (CPA ) 曙光女神被建议描述纯离子的液体(IL ) 和他们的混合物的热力学的性质。为 25 IL 的新分子的参数被在宽温度和压力范围上适合试验性的密度数据获得，并且全面平均偏差是 0.22% 。为相应 IL 的模型参数 b 与他们的分子的团显示出一种好线性关系，因此模型参数的数字有效地被减少。用一温度无关的二进制可调节的参数 kij，为 IL + 的二进制混合物的蒸汽液体 equilibria (VLE ) 的令人满意的关联联系溶剂的非联系的溶剂和 + 与全面一般水准被获得蒸汽压力 2.91% 和 7.01% 的偏差分别地。另外， VLE 为 IL + 结果从 CPA，格子液体(LF ) 和有可变范围(SWCF-VR ) 的方形井的链液体曙光女神的非联系的混合物被比较。
基金Supported by the National Natural Science Foundation of China
文摘Based on the statistical theory for chemical association,equations of state for hard-spherechain fluids(HSCFs)and square-well chain fluids(SWCFs)can be derived through the n-particlecavity correlation function(CCF)of the corresponding reference system,where n is the chain lengthor the number of segments of a chain molecule.The reference system is a fluid composed of only cor-responding monomers.In this work,the n-particle CCF is approximated by a product of effectivetwo-particle CCFs which accounts for correlations in nearest-neighbour and next-to-nearest-neighboursegment pairs.The CCFs for SWCFs may be expressed by a product of the corresponding functionfor HSCFs and a perturbation term originated from the square-well attractive potential.All these ef-fective two-particle CCFs and perturbation terms are density dependent.The dependence is determinedmainly by using computer-simulation results.The obtained equations can excellently describecompressibility factors and second Virial coefficients for
文摘In these two papers (I) and (II), the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper (I), we give the Yang-Baxter equation and give the general solutions of some function equations for the next paper.
文摘This article provides a closed form solution to the telegrapher’s equation with three space variables defined on a subset of a sphere within two radii, two azimuthal angles and one polar angle. The Dirichlet problem for general boundary conditions is solved in detail, on the basis of which Neumann and Robin conditions are easily handled. The solution to the simpler problem in cylindrical coordinates is also provided. Ways to efficiently implement the formulae are explained. Minor adjustments result in solutions to the wave equation and to the heat equation on the same domain as well, since the latter are particular cases of the more general telegrapher’s equation.
基金Project was supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University
文摘In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.
基金Supported by the Nationa1 Natural Science Foundation of China under Grant No.10874018"the Fundamental Research Funds for the Central Universities"
文摘The solutions of the Laplace equation in n-dimensional space are studied.The angular eigenfunctions have the form of associated Jacobi polynomials.The radial solution of the Helmholtz equation is derived.
文摘YBE associated with the scattering from kaleidoscopes of Sutherland has been found. The reflection behaviour at the Dynkin diagram and its physical meaning are explored.
基金Supported by the National Natural Science Foundation of China and the Doctorate Research Foundation sponsored by the National Education Commission of China.
文摘With the statistical mechanical theory for square-well-chain fluids as the basic princi-ples,a molecular thermodynamic model including expressions for the Helmholtz function and thecompressibility factor for associated square-well-chain fluids has been developed.Employment ofthe shield-sticky concept enables the corporation of association bonds between in the model.Good agreement with computer-simulation results for dimer-linear quadrimer systems is obtained.Satisfactory correlation for vapor pressures and saturated liquid volumes of pure substances con-taining associated molecules(such as carboxylic acids,alcohols,amines,water,etc.)with four mo-lecular parameters indicates the applicability of the model.
