The authors prove some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space PN(C)with two families of moving targets,and the results obtained improve some earlier...The authors prove some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space PN(C)with two families of moving targets,and the results obtained improve some earlier work.展开更多
In this article, some uniqueness theorems of meromorphic mappings in sev- eral complex variables sharing hyperplanes in general position are proved with truncated multiplicities.
Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were appli...Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.展开更多
This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N（C） with truncated multiplicities, and our results improve some earlier work.
In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractiona...In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.展开更多
The uniqueness theorem and the theorem of reciprocity in the linearized porous piezoelectricity are established under the assumption of positive definiteness of elastic and electric fields. General theorems in the lin...The uniqueness theorem and the theorem of reciprocity in the linearized porous piezoelectricity are established under the assumption of positive definiteness of elastic and electric fields. General theorems in the linear theory of porous piezoelectric materials are proved for the quasi-static electric field approximation. The uniqueness theorem is also proved without using the positive definiteness of the elastic field. An eigenvalue problem associated with free vibrations of a porous piezoelectric body is stud- ied using the abstract formulation. Some properties of operators are also proved. The problem of frequency shift due to small disturbances, based on an abstract formulation, is studied using a variational and operator approach. A perturbation analysis of a special ease is also given.展开更多
In this paper,we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces(totally geodesic hypersurfaces with respect to a meromorphic connection) ...In this paper,we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces(totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space P^(k).This is a generalization of Cartan’s Second Main Theorem.As a consequence,we establish a uniqueness theorem for holomorphic mappings which intersect O(k^(3)) many totally geodesic hypersurfaces.展开更多
In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spe...In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.展开更多
In this paper we present a correction of the proofofa strong uniqueness theorem given by H.Strauss in 1992 on approximation by reciprocals of functions of an n-dimensional space span (u_1,…,u_n) satisfying coefficien...In this paper we present a correction of the proofofa strong uniqueness theorem given by H.Strauss in 1992 on approximation by reciprocals of functions of an n-dimensional space span (u_1,…,u_n) satisfying coefficient constraints.展开更多
In this paper we present a correction of the proof of u strong uniqueness theorem given by H. Struuss [1] in 1992 on approximation by reciprocals of functions uf an n-dimensional space (u,…un) satisfying coefficient ...In this paper we present a correction of the proof of u strong uniqueness theorem given by H. Struuss [1] in 1992 on approximation by reciprocals of functions uf an n-dimensional space (u,…un) satisfying coefficient constraints.展开更多
The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a u...The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a uniqueness result and a reciprocal theorem.The proof of the reciprocal theorem avoids both using the Laplace transform and incorporating the initial conditions into the equations of motion.The uniqueness theorem is derived with no definiteness assumption on the elastic constitutive coefficients.Then the continuous dependence theorem is discussed upon two external data systems.Finally,the variational principle of Hamilton type which fully characterizes the solution of the mixed boundary-initial-value problem（mixed problem） is obtained.These theorems lay a solid foundation for further theoretical and numerical studies on microstretch thermomagnetoelectroelastic materials.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are gi...The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are given.The single-layer and double-layer thermoelastic potentials are constructed and their basic properties are established.The integral representation of general solutions is obtained.The existence of regular solutions of the BVPs is proved by means of the potential method(boundary integral method)and the theory of singular integral equations.展开更多
In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is fir...This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.展开更多
This paper deals with the problem of uniqueness of meromorphic functions, and gets the following result: There exists a set S with 13 elements such that any two non-constant meromorphic functions / and g satisfying E(...This paper deals with the problem of uniqueness of meromorphic functions, and gets the following result: There exists a set S with 13 elements such that any two non-constant meromorphic functions / and g satisfying E(S,f) = E(S,g) and E({∞},f) = E({∞},g) must be identical. This is the best result on this question until now.展开更多
In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by ...In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.展开更多
In this article, we prove that viscosity solutions of the parabolic inhomogeneous equationsn＋p/put-△p^Nu=f（x,t）can be characterized using asymptotic mean value properties for all p ≥ 1, including p = 1 and p = ∞...In this article, we prove that viscosity solutions of the parabolic inhomogeneous equationsn＋p/put-△p^Nu=f（x,t）can be characterized using asymptotic mean value properties for all p ≥ 1, including p = 1 and p = ∞. We also obtain a comparison principle for the non-negative or non-positive inhomogeneous term f for the corresponding initial-boundary value problem and this in turn implies the uniqueness of solutions to such a problem.展开更多
基金the National Natural Science Foundation of China(Nos.10971156,11271291)
文摘The authors prove some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space PN(C)with two families of moving targets,and the results obtained improve some earlier work.
基金the National Natural Science Foundation of China (No. 10571135)the Doctoral Program Foundation of the Ministry of Education of China (No. 20050240711)the Foundation of theCommittee of Science and Technology of Shanghai (No. 03JC14027)
文摘In this article, some uniqueness theorems of meromorphic mappings in sev- eral complex variables sharing hyperplanes in general position are proved with truncated multiplicities.
文摘Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.
基金supported in part by the National Natural Science Foundation of China(10971156,11271291)
文摘This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N（C） with truncated multiplicities, and our results improve some earlier work.
基金the Council of Scientific and Industrial Research(CSIR),India
文摘In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.
基金Project supported by NSFC(10571135)Doctoral Program Foundation of the Ministry of Education of China(20050240771)Funds of the Science and Technology Committee of Shanghai(03JC14027)
文摘In this article, two uniqueness theorems of meromorphic mappings on moving targets with truncated multiplicities are proved.
基金the University Grant Commission for providing the financial support for this work (No. 8(42)/2010 (MRP/NRCB))
文摘The uniqueness theorem and the theorem of reciprocity in the linearized porous piezoelectricity are established under the assumption of positive definiteness of elastic and electric fields. General theorems in the linear theory of porous piezoelectric materials are proved for the quasi-static electric field approximation. The uniqueness theorem is also proved without using the positive definiteness of the elastic field. An eigenvalue problem associated with free vibrations of a porous piezoelectric body is stud- ied using the abstract formulation. Some properties of operators are also proved. The problem of frequency shift due to small disturbances, based on an abstract formulation, is studied using a variational and operator approach. A perturbation analysis of a special ease is also given.
基金partially supported by a graduate studentship of HKU,the RGC grant(1731115)the National Natural Science Foundation of China(11701382)partially supported by the RGC grant(1731115 and 17307420)。
文摘In this paper,we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces(totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space P^(k).This is a generalization of Cartan’s Second Main Theorem.As a consequence,we establish a uniqueness theorem for holomorphic mappings which intersect O(k^(3)) many totally geodesic hypersurfaces.
基金Supported by the National Natural Science Foundation of China(11171152)the Jiangsu Natural Science Foundation of China(BK2010489)
文摘In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.
文摘In this paper we present a correction of the proofofa strong uniqueness theorem given by H.Strauss in 1992 on approximation by reciprocals of functions of an n-dimensional space span (u_1,…,u_n) satisfying coefficient constraints.
文摘In this paper we present a correction of the proof of u strong uniqueness theorem given by H. Struuss [1] in 1992 on approximation by reciprocals of functions uf an n-dimensional space (u,…un) satisfying coefficient constraints.
基金Project supported by the National Natural Science Fundation of China(Nos.11572358 and 11272223)the Training Program for Leading Talent in University Innovative Research Team in Hebei Province(No.LJRC006)
文摘The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a uniqueness result and a reciprocal theorem.The proof of the reciprocal theorem avoids both using the Laplace transform and incorporating the initial conditions into the equations of motion.The uniqueness theorem is derived with no definiteness assumption on the elastic constitutive coefficients.Then the continuous dependence theorem is discussed upon two external data systems.Finally,the variational principle of Hamilton type which fully characterizes the solution of the mixed boundary-initial-value problem（mixed problem） is obtained.These theorems lay a solid foundation for further theoretical and numerical studies on microstretch thermomagnetoelectroelastic materials.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
文摘The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are given.The single-layer and double-layer thermoelastic potentials are constructed and their basic properties are established.The integral representation of general solutions is obtained.The existence of regular solutions of the BVPs is proved by means of the potential method(boundary integral method)and the theory of singular integral equations.
基金supported by NSFC (10871076,10771011)SRFDP (20050574002)NKBRP (2005CB321902)
文摘In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.
基金the first author (XL) was supported by the China Postdoctoral Science Foundation (20100480494)the NSF of China (11101412)+1 种基金K.C. Wong Education Foundation, Hong Kongthe second author (BZ) was supported by the NSF of China (11071244,11161130002)
文摘This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.
基金Project Supported by the Natural Science Foundation of Shandongthe National Natural Science Foundation of China.
文摘This paper deals with the problem of uniqueness of meromorphic functions, and gets the following result: There exists a set S with 13 elements such that any two non-constant meromorphic functions / and g satisfying E(S,f) = E(S,g) and E({∞},f) = E({∞},g) must be identical. This is the best result on this question until now.
基金Supported by the National Natural Science Foundation of China(Grant No.11126327)the Natural Science Foundation of Guangdong Province(Nos.2016A030313002+1 种基金2015A030313644)the Training Plan for the Outstanding Young Teachers in Higher Education of Guangdong Province(Grant No.Yq2013159)
文摘In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.
基金supported by the National Natural Science Foundation of China(11071119,11171153)
文摘In this article, we prove that viscosity solutions of the parabolic inhomogeneous equationsn＋p/put-△p^Nu=f（x,t）can be characterized using asymptotic mean value properties for all p ≥ 1, including p = 1 and p = ∞. We also obtain a comparison principle for the non-negative or non-positive inhomogeneous term f for the corresponding initial-boundary value problem and this in turn implies the uniqueness of solutions to such a problem.
