In this paper we study the degenerate differential system with delay:E(t)=Ax(t)+Bx(t-1)+f(t),give the canonical form of this systems and study this form of degeneration system with delay,have some results for the so...In this paper we study the degenerate differential system with delay:E(t)=Ax(t)+Bx(t-1)+f(t),give the canonical form of this systems and study this form of degeneration system with delay,have some results for the solvability of such systems and the uniqueness of their solutions.展开更多
A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are p...A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.展开更多
The solvability of nonlinear elliptic equation with boundary perturbation is consid- ered. The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.
The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the correspondi...The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.展开更多
The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using t...The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.展开更多
Considering both the effect of nonisothermal nature of the solid/liquid interface and the microscopic solvability theory (MicST), a further improved version of free dendritic growth model for pure materials was propos...Considering both the effect of nonisothermal nature of the solid/liquid interface and the microscopic solvability theory (MicST), a further improved version of free dendritic growth model for pure materials was proposed. Model comparison indicates that there is a higher temperature at the tip of dendrite predicted by the present model compared with the corresponding model with the isothermal solid/liquid interface assumption. This is attributed to the sidewise thermal diffusion, i.e. the gradient of temperature along the nonisothermal interface. Furthermore, it is indicated that the distinction between the stability criteria from MicST and marginal stability theory (MarST) is more significant with the increase of bath undercoolings. Model test also indicates that the present model can give an agreement with the available experimental data. It is finally concluded that the nonisothermal nature of the solid/liquid interface and the stability criterion from MicST should be taken into account in modeling free dendritic growth.展开更多
Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some eq...Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some equivalent system,,; are given. Using them the paper shows how to state properly initial and boundary conditions for these DAEs. The existence and uniqueness theory of the solution of the initial and boundary value problems for higher index DAEs are proposed.展开更多
Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In ...Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space, we prove the uniqueness of the weak solution. This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals, and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.展开更多
The approximation solvability of the abstract differential inclusion du/dt∈f(t,u)is presented.The convergence of the approximation solution and the existence of the solution for abstract evolution multivalued problem...The approximation solvability of the abstract differential inclusion du/dt∈f(t,u)is presented.The convergence of the approximation solution and the existence of the solution for abstract evolution multivalued problem are discussed.展开更多
Let Mn be the algebra of all n × n complex matrices and gl（n, C） be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ ： gl（n, C） → gl（n, C） preserves solvability in both directions...Let Mn be the algebra of all n × n complex matrices and gl（n, C） be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ ： gl（n, C） → gl（n, C） preserves solvability in both directions if both φ and φ-1 map every solvable Lie subalgebra of gl（n, C） to some solvable Lie subalgebra. In this paper we classify the invertible linear maps preserving solvability on gl（n, C） in both directions. As a sequence, such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.展开更多
Applying constructed homotopy and its properties,we gel some sufficient conditions for the solvability of algebraic inverse eigenvalue problems,which are better than that of the paper [4] in some cases. Inverse eigenv...Applying constructed homotopy and its properties,we gel some sufficient conditions for the solvability of algebraic inverse eigenvalue problems,which are better than that of the paper [4] in some cases. Inverse eigenvalue problems,solvability,sufficient conditions.展开更多
This paper discusses problem IEP:Given n×m matrix X and m×m diagonal matrix A, find an n×n matrix A such that AX=XA.The new solvablily conditions for the problem IEP are obtained. The eigenvalue dislrib...This paper discusses problem IEP:Given n×m matrix X and m×m diagonal matrix A, find an n×n matrix A such that AX=XA.The new solvablily conditions for the problem IEP are obtained. The eigenvalue dislribulaion of the solutions for the problem IEP are described in detail.展开更多
We study the solvability of two classes of Diophantine equations by using some new methods and new results in this paper. Let p be an odd prime and B n denote nth Bernoulli number. We prove that if p≡1(mod 4) and p...We study the solvability of two classes of Diophantine equations by using some new methods and new results in this paper. Let p be an odd prime and B n denote nth Bernoulli number. We prove that if p≡1(mod 4) and pB (p-1)/2 , then the equation x p+2 2m n 4=p ky 2, m,n,k∈[FK(W+3mm\.3mm][TPP107A,+3mm?3mm,BP], k>1, gcd (x,py)=1, and the equation x p+y 2=p kz 4, k∈[FK(W+3mm\.3mm][TPP107A,+3mm?3mm,BP], gcd (x,y)=1, k>1, 2|y have no integral solutions respectively.展开更多
In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth funct...In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.展开更多
Based on the nullor equivalent model of the ideal op amp, the solvability of RLC op amp networks are discussed and some practical problems are analyzed. Then several necessary and sufficient topological conditions for...Based on the nullor equivalent model of the ideal op amp, the solvability of RLC op amp networks are discussed and some practical problems are analyzed. Then several necessary and sufficient topological conditions for unique solvability are given and their proofs are shown in detail.These conditions have great applications in the analysis, synthesis and diagnosis of networks. Finally the solvability of an illustrative network are analyzed as an example.展开更多
The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonline...The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution if the integration of the limit growth function has an appropriate value.展开更多
We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obt...We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.展开更多
In this paper, the nonlinear reaction diffusion equation with boundary perturbation is considered. Using discussions on solvability, the perturbed solution of original problem is obtained, and the uniform validity of ...In this paper, the nonlinear reaction diffusion equation with boundary perturbation is considered. Using discussions on solvability, the perturbed solution of original problem is obtained, and the uniform validity of the solution is proved.展开更多
文摘In this paper we study the degenerate differential system with delay:E(t)=Ax(t)+Bx(t-1)+f(t),give the canonical form of this systems and study this form of degeneration system with delay,have some results for the solvability of such systems and the uniqueness of their solutions.
文摘A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.
基金Supported by the National Natural Science Foundation of China(40676016,10471039)National Key Project for Basic Research(2004CB418304)+1 种基金Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)
文摘The solvability of nonlinear elliptic equation with boundary perturbation is consid- ered. The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.
文摘The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.
基金the NNSF of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)part by E-Institutes of Shanghai Municipal Education Commission(E03004)
文摘The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.
基金Project(51671075) supported by the National Natural Science Foundation of ChinaProject(E201446) supported by the Natural Science Foundation of Heilongjiang Province,China+1 种基金Project(SKLSP201606) supported by Fund of the State Key Laboratory of Solidification Processing in NWPU,ChinaProject(2016M590970) supported by China Postdoctoral Science Foundation
文摘Considering both the effect of nonisothermal nature of the solid/liquid interface and the microscopic solvability theory (MicST), a further improved version of free dendritic growth model for pure materials was proposed. Model comparison indicates that there is a higher temperature at the tip of dendrite predicted by the present model compared with the corresponding model with the isothermal solid/liquid interface assumption. This is attributed to the sidewise thermal diffusion, i.e. the gradient of temperature along the nonisothermal interface. Furthermore, it is indicated that the distinction between the stability criteria from MicST and marginal stability theory (MarST) is more significant with the increase of bath undercoolings. Model test also indicates that the present model can give an agreement with the available experimental data. It is finally concluded that the nonisothermal nature of the solid/liquid interface and the stability criterion from MicST should be taken into account in modeling free dendritic growth.
基金Project supported by the National Natural Science Foundation of China by Jiangsu Provincial Natural Science Foundation
文摘Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some equivalent system,,; are given. Using them the paper shows how to state properly initial and boundary conditions for these DAEs. The existence and uniqueness theory of the solution of the initial and boundary value problems for higher index DAEs are proposed.
基金Project supported by the National Natural Science Foundation of China (Nos.10372016 and 10672022)
文摘Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space, we prove the uniqueness of the weak solution. This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals, and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.
基金the National Natural Science Foundation of China(No.19771062)
文摘The approximation solvability of the abstract differential inclusion du/dt∈f(t,u)is presented.The convergence of the approximation solution and the existence of the solution for abstract evolution multivalued problem are discussed.
基金The NSF (2009J05005) of Fujian Provincea Key Project of Fujian Provincial Universities-Information Technology Research Based on Mathematics
文摘Let Mn be the algebra of all n × n complex matrices and gl（n, C） be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ ： gl（n, C） → gl（n, C） preserves solvability in both directions if both φ and φ-1 map every solvable Lie subalgebra of gl（n, C） to some solvable Lie subalgebra. In this paper we classify the invertible linear maps preserving solvability on gl（n, C） in both directions. As a sequence, such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.
文摘Applying constructed homotopy and its properties,we gel some sufficient conditions for the solvability of algebraic inverse eigenvalue problems,which are better than that of the paper [4] in some cases. Inverse eigenvalue problems,solvability,sufficient conditions.
文摘This paper discusses problem IEP:Given n×m matrix X and m×m diagonal matrix A, find an n×n matrix A such that AX=XA.The new solvablily conditions for the problem IEP are obtained. The eigenvalue dislribulaion of the solutions for the problem IEP are described in detail.
文摘We study the solvability of two classes of Diophantine equations by using some new methods and new results in this paper. Let p be an odd prime and B n denote nth Bernoulli number. We prove that if p≡1(mod 4) and pB (p-1)/2 , then the equation x p+2 2m n 4=p ky 2, m,n,k∈[FK(W+3mm\.3mm][TPP107A,+3mm?3mm,BP], k>1, gcd (x,py)=1, and the equation x p+y 2=p kz 4, k∈[FK(W+3mm\.3mm][TPP107A,+3mm?3mm,BP], gcd (x,y)=1, k>1, 2|y have no integral solutions respectively.
文摘In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.
文摘Based on the nullor equivalent model of the ideal op amp, the solvability of RLC op amp networks are discussed and some practical problems are analyzed. Then several necessary and sufficient topological conditions for unique solvability are given and their proofs are shown in detail.These conditions have great applications in the analysis, synthesis and diagnosis of networks. Finally the solvability of an illustrative network are analyzed as an example.
文摘The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution if the integration of the limit growth function has an appropriate value.
文摘We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.
基金Supported by the National Natural Science Foundation of China (40676016 and 40876010)the Knowledge Innovation Project of Chinese Academy of Sciences (KZCX2-YW-Q03-08)Construct Project of E-Institutes of Shanghai Municipal Education Commission (E03004)
文摘In this paper, the nonlinear reaction diffusion equation with boundary perturbation is considered. Using discussions on solvability, the perturbed solution of original problem is obtained, and the uniform validity of the solution is proved.
