Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three d...Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.展开更多
The marine green algae genus Chaetomorpha is a common source of“green tide”and is widespread on coasts around the world.In this study,based on invasive Chaetomorpha valida collected from the Shandong Peninsula,the m...The marine green algae genus Chaetomorpha is a common source of“green tide”and is widespread on coasts around the world.In this study,based on invasive Chaetomorpha valida collected from the Shandong Peninsula,the morphogenesis and reproductive characteristics of two strains that are morphologically different from each other,were observed using experimental biology methods.The main results are as follows:(1)significant difference in the size of reproductive cells produced by Strains 1 and 2;(2)gametes produced by Strain 2 are isogamous and same gametangial during the binding process of gametes,whereas those of Strain 1 are isogamous but hetero-cystic;(3)progeny from Strain 1 has rhizoidal holdfast,whereas that of Strain 2 has discoid holdfast;(4)gametophytic“branching”was found in Strain 1.These results could validate the high phenotypic plasticity of macroalgae and offered an interpretation of habitat adaptation.Furthermore,this study innovatively provided fundamental research on the selection of macroalgal traits and explored competitive strategies for the dominant survival of macroalgae from a new perspective.展开更多
The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak so...The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.展开更多
In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system fo...In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.展开更多
The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from ...The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.展开更多
Aim To prove the uniqueness of the viscosity solutions for the initial value problems of one type of second order parabolic partial differential equations: Methods Using comparison theorem. Results and Conclusion If u...Aim To prove the uniqueness of the viscosity solutions for the initial value problems of one type of second order parabolic partial differential equations: Methods Using comparison theorem. Results and Conclusion If u0 is uniform continuousfunction in RN , F is continuous function in RNx(N) and F is degenerate elliptic, then thisequation has the sole viscosity solution.展开更多
Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact con...Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.展开更多
We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional sto...We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional stochastic differential equations driven by Poisson processes. After that, we give a simplified Engelbert theorem for the stochastic differential equations of this type.展开更多
The reverse analysis provides a convenient method to determine four elastic-plastic parameters through an indentation curve such as Young s modulus E, hardness H, yield strength σy and strain hardening exponent n. In...The reverse analysis provides a convenient method to determine four elastic-plastic parameters through an indentation curve such as Young s modulus E, hardness H, yield strength σy and strain hardening exponent n. In this paper, mathematical analysis on a reverse algorithm from Dao model （Dao et al., Acta Mater., 2001, 49, 3899） was carried out, which thought that only when 20 ≤E＊/σ0.033≤ 26 and 0.3n≤ 0.5, the reverse algorithm would yield two solutions of n by dimensionless function Π2. It is shown that, however, there are also two solutions of n when 20≤E＊/σ0.033≤ 26 and 0≤n0.1. A unique n can be obtained by dimensionless function Π3 instead of Π2 in these two ranges. E and H can be uniquely determined by a full indentation curve, and σy can be determined if n is unique. Furthermore, sensitivity analysis on obtaining n from dimensionless function Π3 or Π2 has been made.展开更多
We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H...We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].展开更多
In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existenc...In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.展开更多
This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition.We will show that the penetrable scatterer can be uniquely determined by its far-field pa...This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition.We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number.In the first part of this paper,adequate preparations for the main uniqueness result are made.We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves.Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method.Finally,the a priori estimates of solutions to the general transmission problem with boundary data in L^(p)(δΩ)(1<p<2)are proven by the boundary integral equation method.In the second part of this paper,we give a novel proof on the uniqueness of the inverse conductive scattering problem.展开更多
In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic fu...In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.展开更多
In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
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
We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential p...We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential polynomials of entire functions sharing a common value.展开更多
The differential evolution(DE)algorithm was deployed to calibrate microparameters of the DEM cohesive granular material.4 macroparameters,namely,uniaxial compressive strength,direct tensile strength,Young’s modulus a...The differential evolution(DE)algorithm was deployed to calibrate microparameters of the DEM cohesive granular material.4 macroparameters,namely,uniaxial compressive strength,direct tensile strength,Young’s modulus and Poisson’s ratio,can be calibrated to high accuracy.The best calibration accuracy could reach the sum of relative errors RE_(sum)<0.1%.Most calibrations can be achieved with RE_(sum)<5%within hours or RE_(sum)<1%within 2 days.Based on the calibrated results,microparameters uniqueness analysis was carried out to reveal the correlation between microparameters and the macroscopic mechanical behaviour of material:(1)microparameters effective modulus,tensile strength and normal-to-shear stiffness ratio control the elastic behaviour and stable crack growth,(2)microparameters cohesion and friction angles present a negative linear correlation that controls the axial strain and lateral strain prior to the peak stress,and(3)microparameters friction coefficient controls shear crack friction and slip mainly refers to the unstable crack behaviour.Consideration of more macroparameters to regulate the material mechanical behaviour that is dominated by shear crack and slip motion is highlighted for future study.The DE calibration method is expected to serve as an alternative method to calibrate the DEM cohesive granular material to its peak strength.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.12161074)the Talent Introduction Research Foundation of Suqian University (Grant No.106-CK00042/028)+1 种基金Suqian Sci&Tech Program (Grant No.M202206)Sponsored by Qing Lan Project of Jiangsu Province and Suqian Talent Xiongying Plan of Suqian。
文摘Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.
基金Supported by the National Natural Science Foundation of China(Nos.32270219,31970216)。
文摘The marine green algae genus Chaetomorpha is a common source of“green tide”and is widespread on coasts around the world.In this study,based on invasive Chaetomorpha valida collected from the Shandong Peninsula,the morphogenesis and reproductive characteristics of two strains that are morphologically different from each other,were observed using experimental biology methods.The main results are as follows:(1)significant difference in the size of reproductive cells produced by Strains 1 and 2;(2)gametes produced by Strain 2 are isogamous and same gametangial during the binding process of gametes,whereas those of Strain 1 are isogamous but hetero-cystic;(3)progeny from Strain 1 has rhizoidal holdfast,whereas that of Strain 2 has discoid holdfast;(4)gametophytic“branching”was found in Strain 1.These results could validate the high phenotypic plasticity of macroalgae and offered an interpretation of habitat adaptation.Furthermore,this study innovatively provided fundamental research on the selection of macroalgal traits and explored competitive strategies for the dominant survival of macroalgae from a new perspective.
基金partially supported by NSFC(11831003,12031012)the Institute of Modern Analysis-A Frontier Research Center of Shanghai。
文摘The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.
文摘In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.
文摘The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.
文摘Aim To prove the uniqueness of the viscosity solutions for the initial value problems of one type of second order parabolic partial differential equations: Methods Using comparison theorem. Results and Conclusion If u0 is uniform continuousfunction in RN , F is continuous function in RNx(N) and F is degenerate elliptic, then thisequation has the sole viscosity solution.
基金The National Natural Science Foundation of China(No.10672039)the Key Project of Ministry of Education of China(No.105083)
文摘Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.
文摘We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional stochastic differential equations driven by Poisson processes. After that, we give a simplified Engelbert theorem for the stochastic differential equations of this type.
基金supported by the National Natural Science Foundation of China (Nos. 11002121, 11002122,and 10828205)the Natural Science Foundation of Hu-nan Province for Innovation Group (No. 09JJ7004)+2 种基金the Key Special Program for Science and Technology of Hu-nan Province (No. 2009FJ1002)and the Natural Science Foundation of Xiangtan University (No. 09XZX04)One of the authors (C. Lu) is also grateful to the support from the Australian Research Council (No. DP0985450)
文摘The reverse analysis provides a convenient method to determine four elastic-plastic parameters through an indentation curve such as Young s modulus E, hardness H, yield strength σy and strain hardening exponent n. In this paper, mathematical analysis on a reverse algorithm from Dao model （Dao et al., Acta Mater., 2001, 49, 3899） was carried out, which thought that only when 20 ≤E＊/σ0.033≤ 26 and 0.3n≤ 0.5, the reverse algorithm would yield two solutions of n by dimensionless function Π2. It is shown that, however, there are also two solutions of n when 20≤E＊/σ0.033≤ 26 and 0≤n0.1. A unique n can be obtained by dimensionless function Π3 instead of Π2 in these two ranges. E and H can be uniquely determined by a full indentation curve, and σy can be determined if n is unique. Furthermore, sensitivity analysis on obtaining n from dimensionless function Π3 or Π2 has been made.
基金supported by NSF of Fujian Province,China(S0750013),supported by NSF of Fujian Province,China(2008J0190)the Research Foundation of Ningde Normal University(2008J001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].
基金supported by Natural Science Foundation of China(11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT 17R46financially supported by funding for basic research business in Central Universities(innovative funding projects)(2018CXZZ090)。
文摘In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.
文摘This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition.We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number.In the first part of this paper,adequate preparations for the main uniqueness result are made.We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves.Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method.Finally,the a priori estimates of solutions to the general transmission problem with boundary data in L^(p)(δΩ)(1<p<2)are proven by the boundary integral equation method.In the second part of this paper,we give a novel proof on the uniqueness of the inverse conductive scattering problem.
基金Supported by the NNSFC (10671109)the NSFFC(2008J0190)+1 种基金the Research Fund for Talent Introduction of Ningde Teachers College (2009Y019)the Scitific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.
文摘In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
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supported by the NSFC(11026110,11101201)the NSF of Jiangxi(2010GQS0144)
文摘We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential polynomials of entire functions sharing a common value.
文摘The differential evolution(DE)algorithm was deployed to calibrate microparameters of the DEM cohesive granular material.4 macroparameters,namely,uniaxial compressive strength,direct tensile strength,Young’s modulus and Poisson’s ratio,can be calibrated to high accuracy.The best calibration accuracy could reach the sum of relative errors RE_(sum)<0.1%.Most calibrations can be achieved with RE_(sum)<5%within hours or RE_(sum)<1%within 2 days.Based on the calibrated results,microparameters uniqueness analysis was carried out to reveal the correlation between microparameters and the macroscopic mechanical behaviour of material:(1)microparameters effective modulus,tensile strength and normal-to-shear stiffness ratio control the elastic behaviour and stable crack growth,(2)microparameters cohesion and friction angles present a negative linear correlation that controls the axial strain and lateral strain prior to the peak stress,and(3)microparameters friction coefficient controls shear crack friction and slip mainly refers to the unstable crack behaviour.Consideration of more macroparameters to regulate the material mechanical behaviour that is dominated by shear crack and slip motion is highlighted for future study.The DE calibration method is expected to serve as an alternative method to calibrate the DEM cohesive granular material to its peak strength.
