In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. ...In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. The solutions of the dynamical systems are obtained by utilizing the method of Laplace transform technique and are based on the formula of the Laplace transform of the Mittag-Leffler function in two parameters. Next, we present the existence and uniqueness of solutions for nonlinear sequential fractional dynamical systems with damping by using fixed point theorems under some appropriate conditions.展开更多
In this paper, we investigate the effect of weight function in the nonlinear part on global solvability of the Cauchy problem for a class of semi-linear hyperbolic equations with damping.
The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert spa...The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.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
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
Nanoparticles provide great advantages but also great risks. Risks associating with nanoparticles are the problem of all technologies, but they increase in many times in nanotechnologies. Adequate methods of outgoing ...Nanoparticles provide great advantages but also great risks. Risks associating with nanoparticles are the problem of all technologies, but they increase in many times in nanotechnologies. Adequate methods of outgoing production inspection are necessary to solve the problem of risks, and the inspection must be based on the safety standard. Existing safety standard results from a principle of “maximum permissible concentrations or MPC”. This principle is not applicable to nanoparticles, but a safety standard reflecting risks inherent in nanoparticles doesn’t exist. Essence of the risks is illustrated by the example from pharmacology, since its safety assurance is conceptually based on MPC and it has already come against this problem. Possible formula of safety standard for nanoparticles is reflected in many publications, but conventional inspection methods cannot provide its realization, and this gap is an obstacle to assumption of similar formulas. Therefore the development of nanoparticle industry as a whole (also development of the pharmacology in particular) is impossible without the creation of an adequate inspection method. There are suggested new inspection methods founded on the new physical principle and satisfying to the adequate safety standard for nanoparticles. These methods demonstrate that creation of the adequate safety standard and the outgoing production inspection in a large-scale manufacturing of nanoparticles are the solvable problems. However there is a great distance between the physical principle and its hardware realization, and a transition from the principle to the hardware demands great intellectual and material costs. Therefore it is desirable to call attention of the public at large to the necessity of urgent expansions of investigations associated with outgoing inspections in nanoparticles technologies. It is necessary also to attract attention, first, of representatives of state structures controlling approvals of the adequate safety standard to this problem, since it is impossible to compel producers providing the safety without the similar standard, and, second, of leaders of pharmacological industry, since their industry already entered into the nanotechnology era, and they have taken an interest in a forthcoming development of inspection methods.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
This paper reinterprets the economic input-output equation as a description of a realized situation without considering decision making. This paper uses the equation that the self-sufficiency rate is added to the Leon...This paper reinterprets the economic input-output equation as a description of a realized situation without considering decision making. This paper uses the equation that the self-sufficiency rate is added to the Leontief type, and discusses its solvability. The equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. This condition means that commodities which a part of the relevant society possesses are not all inputted to its inside. Moreover, if the process of input and output is time irreversible, each part of the relevant society satisfies the space-time openness condition. Therefore, the solvability of the equation is guaranteed by time irreversibility. This proposition seems to be relevant to the grandfather paradox which is a type of time paradox.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
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
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
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 minimax path location problem is to find a path P in a graph G such that the maximum distance d_(G)(v,P)from every vertex v∈V(G)to the path P is minimized.It is a well-known NP-hard problem in network optimizatio...The minimax path location problem is to find a path P in a graph G such that the maximum distance d_(G)(v,P)from every vertex v∈V(G)to the path P is minimized.It is a well-known NP-hard problem in network optimization.This paper studies the fixed-parameter solvability,that is,for a given graph G and an integer k,to decide whether there exists a path P in G such that max v∈V(G)d_(G)(v,P)≤k.If the answer is affirmative,then graph G is called k-path-eccentric.We show that this decision problem is NP-complete even for k=1.On the other hand,we characterize the family of 1-path-eccentric graphs,including the traceable,interval,split,permutation graphs and others.Furthermore,some polynomially solvable special graphs are discussed.展开更多
The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods [1] are considered th...The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods [1] are considered the preferred methods. Selecting an effective preconditioner with appropriate parameters for a specific sparse linear system presents a challenging task for many application scientists and engineers who have little knowledge of preconditioned iterative methods. The purpose of this paper is to predict the parameter solvability space of the preconditioners with two or more parameters. The parameter solvability space is usually irregular, however, in many situations it shows spatial locality, i.e. the parameter locations that are closer in parameter space are more likely to have similar solvability. We propose three spatial data mining methods to predict the solvability of ILUT which make usage of spatial locality in different ways. The three methods are MSC （multi-points SVM classifier）, OSC （overall SVM classifier）, and OSAC （overall spatial autoregressive classifier）. The experimental results show that both MSC and OSAC can obtain 90% accuracy in prediction, but OSAC is much simpler to implement. We focus our work on ILUT preconditioner [2], but the proposed strategies should be applicable to other preconditioners with two or more parameters.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
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 obtain a priori estimates and solvability in Hardy type space in a bounded domain of Rn for second order elliptic equations with coefficients of limited smoothness. Such a result can be served as an endpoint case o...We obtain a priori estimates and solvability in Hardy type space in a bounded domain of Rn for second order elliptic equations with coefficients of limited smoothness. Such a result can be served as an endpoint case of the classical LP（1 〈 p 〈 ∞） theory for second order elliptic equations. Our approach is based on a standard technique of perturbation rather than that of integral representation formula.展开更多
文摘In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. The solutions of the dynamical systems are obtained by utilizing the method of Laplace transform technique and are based on the formula of the Laplace transform of the Mittag-Leffler function in two parameters. Next, we present the existence and uniqueness of solutions for nonlinear sequential fractional dynamical systems with damping by using fixed point theorems under some appropriate conditions.
文摘In this paper, we investigate the effect of weight function in the nonlinear part on global solvability of the Cauchy problem for a class of semi-linear hyperbolic equations with damping.
文摘The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.
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.
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Nanoparticles provide great advantages but also great risks. Risks associating with nanoparticles are the problem of all technologies, but they increase in many times in nanotechnologies. Adequate methods of outgoing production inspection are necessary to solve the problem of risks, and the inspection must be based on the safety standard. Existing safety standard results from a principle of “maximum permissible concentrations or MPC”. This principle is not applicable to nanoparticles, but a safety standard reflecting risks inherent in nanoparticles doesn’t exist. Essence of the risks is illustrated by the example from pharmacology, since its safety assurance is conceptually based on MPC and it has already come against this problem. Possible formula of safety standard for nanoparticles is reflected in many publications, but conventional inspection methods cannot provide its realization, and this gap is an obstacle to assumption of similar formulas. Therefore the development of nanoparticle industry as a whole (also development of the pharmacology in particular) is impossible without the creation of an adequate inspection method. There are suggested new inspection methods founded on the new physical principle and satisfying to the adequate safety standard for nanoparticles. These methods demonstrate that creation of the adequate safety standard and the outgoing production inspection in a large-scale manufacturing of nanoparticles are the solvable problems. However there is a great distance between the physical principle and its hardware realization, and a transition from the principle to the hardware demands great intellectual and material costs. Therefore it is desirable to call attention of the public at large to the necessity of urgent expansions of investigations associated with outgoing inspections in nanoparticles technologies. It is necessary also to attract attention, first, of representatives of state structures controlling approvals of the adequate safety standard to this problem, since it is impossible to compel producers providing the safety without the similar standard, and, second, of leaders of pharmacological industry, since their industry already entered into the nanotechnology era, and they have taken an interest in a forthcoming development of inspection methods.
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This paper reinterprets the economic input-output equation as a description of a realized situation without considering decision making. This paper uses the equation that the self-sufficiency rate is added to the Leontief type, and discusses its solvability. The equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. This condition means that commodities which a part of the relevant society possesses are not all inputted to its inside. Moreover, if the process of input and output is time irreversible, each part of the relevant society satisfies the space-time openness condition. Therefore, the solvability of the equation is guaranteed by time irreversibility. This proposition seems to be relevant to the grandfather paradox which is a type of time paradox.
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.
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 minimax path location problem is to find a path P in a graph G such that the maximum distance d_(G)(v,P)from every vertex v∈V(G)to the path P is minimized.It is a well-known NP-hard problem in network optimization.This paper studies the fixed-parameter solvability,that is,for a given graph G and an integer k,to decide whether there exists a path P in G such that max v∈V(G)d_(G)(v,P)≤k.If the answer is affirmative,then graph G is called k-path-eccentric.We show that this decision problem is NP-complete even for k=1.On the other hand,we characterize the family of 1-path-eccentric graphs,including the traceable,interval,split,permutation graphs and others.Furthermore,some polynomially solvable special graphs are discussed.
文摘The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods [1] are considered the preferred methods. Selecting an effective preconditioner with appropriate parameters for a specific sparse linear system presents a challenging task for many application scientists and engineers who have little knowledge of preconditioned iterative methods. The purpose of this paper is to predict the parameter solvability space of the preconditioners with two or more parameters. The parameter solvability space is usually irregular, however, in many situations it shows spatial locality, i.e. the parameter locations that are closer in parameter space are more likely to have similar solvability. We propose three spatial data mining methods to predict the solvability of ILUT which make usage of spatial locality in different ways. The three methods are MSC （multi-points SVM classifier）, OSC （overall SVM classifier）, and OSAC （overall spatial autoregressive classifier）. The experimental results show that both MSC and OSAC can obtain 90% accuracy in prediction, but OSAC is much simpler to implement. We focus our work on ILUT preconditioner [2], but the proposed strategies should be applicable to other preconditioners with two or more parameters.
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.
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.
基金Supported by NNSF of China Grant No.10571084NNSF of China Grant No.10771097
文摘We obtain a priori estimates and solvability in Hardy type space in a bounded domain of Rn for second order elliptic equations with coefficients of limited smoothness. Such a result can be served as an endpoint case of the classical LP（1 〈 p 〈 ∞） theory for second order elliptic equations. Our approach is based on a standard technique of perturbation rather than that of integral representation formula.
