In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t0,limt→∞x(t)=ψ0,lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t0,limt→∞x(t)=ψ0,limt→∞x′(t)et=0,where t0 and ψ0 are real constants,φ(s)=s/√1−s2,s∈R with s∈(−1,1),f:[t0,∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
In this article,we investigate the uniqueness of solutions for the two-species chemotaxis model with two chemicals in two-dimensional space by hyper-contractivity estimates and semigroup theory.Mainly,we prove that as...In this article,we investigate the uniqueness of solutions for the two-species chemotaxis model with two chemicals in two-dimensional space by hyper-contractivity estimates and semigroup theory.Mainly,we prove that as long as the solution exists,it must be unique.Specifically,we first derive Lp hyper-contractivity estimates of solutions,then establish refined hyper-contractivity estimates,and finally complete the proof of solution uniqueness by combining semigroup theory.展开更多
In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|αueu^(2),in B1,u=0,onδB1ueu2;in B1;u=0;on@B1;whereλ>0,α>-2;B1denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|αueu^(2),in B1,u=0,onδB1ueu2;in B1;u=0;on@B1;whereλ>0,α>-2;B1denotes the unit disk in R2:By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B1,the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.展开更多
In this paper,we investigate the uniqueness of meromorphic functions and their derivatives in the unit disc and consider the relations between the Borel points and the shared-values of meromorphic functions in an angu...In this paper,we investigate the uniqueness of meromorphic functions and their derivatives in the unit disc and consider the relations between the Borel points and the shared-values of meromorphic functions in an angular domain by Nevanlinna value distribution theory.An admissible meromorphic function with orde or precise order has Borel point and shares IM common values with its derivative in an angular domain of the unit disc,then the meromorphic function and its derivative are unique.The obtained results improve and generalize some existing results and enrich the uniqueness theory of meromorphic functions.展开更多
We consider a constrained minimization problem arising in the fractional Schrödinger equation with a trapping potential.By exploring some delicate energy estimates and studying decay properties of solution sequen...We consider a constrained minimization problem arising in the fractional Schrödinger equation with a trapping potential.By exploring some delicate energy estimates and studying decay properties of solution sequences,we obtain the concentration behavior of each minimizer of the fractional Schrödinger energy functional when a↗a*:=‖Q‖22s,where Q is the unique positive radial solution of (-△)su+su-|u|2su=0 in R2.Based on the discussion of the concentration phenomenon,we prove the local uniqueness of minimizers by establishing a local Poho zaev identity and studying the blow-up estimates to the nonlocal operator(-△)s.展开更多
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 Lηnf=Σk=0nakf (z+kη)+a-1f′.These results lead to a refined characterization of f (z)≡Lηnf (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.展开更多
In this paper,we consider the reconstruction of a locally rough sur-face from phaseless near-field data generated by the incident electric dipoles.To obtain the uniqueness for this inverse problem,we use the superposi...In this paper,we consider the reconstruction of a locally rough sur-face from phaseless near-field data generated by the incident electric dipoles.To obtain the uniqueness for this inverse problem,we use the superposition of point sources as the incident waves.These point sources lie on an admissi-ble surface.The measured data are collected from another admissible surface above this locally rough surface.We derive the Rellich's lemma and the reci-procity relation for the electric total fields.Based on them,we establish the uniqueness in phaseless inverse electromagnetic scattering by locally rough surfaces.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
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>0,10 is a parameter.Under some assumptions on Q(x),we show the existence and local uniquene...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>0,10 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 first visits uniqueness, scale, and resolution issues in groundwater flow forward modeling problems. It then makes the point that non-unique solutions to groundwater flow inverse problems arise from a lack ...This paper first visits uniqueness, scale, and resolution issues in groundwater flow forward modeling problems. It then makes the point that non-unique solutions to groundwater flow inverse problems arise from a lack of information necessary to make the problems well defined. Subsequently, it presents the necessary conditions for a well-defined inverse problem. They are full specifications of (1) flux boundaries and sources/sinks, and (2) heads everywhere in the domain at at least three times (one of which is t = 0), with head change everywhere at those times being nonzero for transient flow. Numerical experiments are presented to corroborate the fact that, once the necessary conditions are met, the inverse problem has a unique solution. We also demonstrate that measurement noise, instability, and sensitivity are issues related to solution techniques rather than the inverse problems themselves. In addition, we show that a mathematically well-defined inverse problem, based on an equivalent homogeneous or a layered conceptual model, may yield physically incorrect and scenario-dependent parameter values. These issues are attributed to inconsistency between the scale of the head observed and that implied by these models. Such issues can be reduced only if a sufficiently large number of observation wells are used in the equivalent homogeneous domain or each layer. With a large number of wells, we then show that increase in parameterization can lead to a higher-resolution depiction of heterogeneity if an appropriate inverse methodology is used. Furthermore, we illustrate that, using the same number of wells, a highly parameterized model in conjunction with hydraulic tomography can yield better characterization of the aquifer and minimize the scale and scenario-dependent problems. Lastly, benefits of the highly parameterized model and hydraulic tomography are tested according to their ability to improve predictions of aquifer responses induced by independent stresses not used in the inverse modeling efforts.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 REsum<0.1%.Most calibrations can be achieved with REsum<5%within hours or REsum<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
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 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 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
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
In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases ...In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.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.
We study boundary value problems for fractional integro-differential equations involving Caputo derivative of orderα∈(n-1,n)in Banach spaces.Existence and uniqueness results of solutions are established by virtue of...We study boundary value problems for fractional integro-differential equations involving Caputo derivative of orderα∈(n-1,n)in Banach spaces.Existence and uniqueness results of solutions are established by virtue of the Holder's inequality,a suitable singular Cronwall's inequality and fixed point theorem via a priori estimate method.At last,examples are given to illustrate the results.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
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
摘要In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t0,limt→∞x(t)=ψ0,limt→∞x′(t)et=0,where t0 and ψ0 are real constants,φ(s)=s/√1−s2,s∈R with s∈(−1,1),f:[t0,∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
基金Supported by the National Natural Science Foundation of China(Grant No.12171218)the Natural Science Foundation Program of Liaoning Province(Grant No.2024-MS-002)。
摘要In this article,we investigate the uniqueness of solutions for the two-species chemotaxis model with two chemicals in two-dimensional space by hyper-contractivity estimates and semigroup theory.Mainly,we prove that as long as the solution exists,it must be unique.Specifically,we first derive Lp hyper-contractivity estimates of solutions,then establish refined hyper-contractivity estimates,and finally complete the proof of solution uniqueness by combining semigroup theory.
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
摘要In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|αueu^(2),in B1,u=0,onδB1ueu2;in B1;u=0;on@B1;whereλ>0,α>-2;B1denotes the unit disk in R2:By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B1,the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
摘要In this paper,we investigate the uniqueness of meromorphic functions and their derivatives in the unit disc and consider the relations between the Borel points and the shared-values of meromorphic functions in an angular domain by Nevanlinna value distribution theory.An admissible meromorphic function with orde or precise order has Borel point and shares IM common values with its derivative in an angular domain of the unit disc,then the meromorphic function and its derivative are unique.The obtained results improve and generalize some existing results and enrich the uniqueness theory of meromorphic functions.
基金supported by the Fundamental Research Program of Shanxi Province(202403021222126)supported by the Fundamental Research Program of Shanxi Province(202303021211056)supported by the National Natural Science Foundation of China(12071486)。
摘要We consider a constrained minimization problem arising in the fractional Schrödinger equation with a trapping potential.By exploring some delicate energy estimates and studying decay properties of solution sequences,we obtain the concentration behavior of each minimizer of the fractional Schrödinger energy functional when a↗a*:=‖Q‖22s,where Q is the unique positive radial solution of (-△)su+su-|u|2su=0 in R2.Based on the discussion of the concentration phenomenon,we prove the local uniqueness of minimizers by establishing a local Poho zaev identity and studying the blow-up estimates to the nonlocal operator(-△)s.
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。
摘要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 Lηnf=Σk=0nakf (z+kη)+a-1f′.These results lead to a refined characterization of f (z)≡Lηnf (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(Grant No.12271209)by the Natural Science Foundation of Jilin Province(Grant 20240101311JC).
摘要In this paper,we consider the reconstruction of a locally rough sur-face from phaseless near-field data generated by the incident electric dipoles.To obtain the uniqueness for this inverse problem,we use the superposition of point sources as the incident waves.These point sources lie on an admissi-ble surface.The measured data are collected from another admissible surface above this locally rough surface.We derive the Rellich's lemma and the reci-procity relation for the electric total fields.Based on them,we establish the uniqueness in phaseless inverse electromagnetic scattering by locally rough surfaces.
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)
摘要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 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)。
摘要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>0,10 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.
基金supported by the Strategic Environmental Research and Development Program(Grant No.ER-1365)the Environmental Security and Technology Certification Program(Grant No.ER201212)the Earth Sciences of the National Science Foundation(Grant No.1014594)
摘要This paper first visits uniqueness, scale, and resolution issues in groundwater flow forward modeling problems. It then makes the point that non-unique solutions to groundwater flow inverse problems arise from a lack of information necessary to make the problems well defined. Subsequently, it presents the necessary conditions for a well-defined inverse problem. They are full specifications of (1) flux boundaries and sources/sinks, and (2) heads everywhere in the domain at at least three times (one of which is t = 0), with head change everywhere at those times being nonzero for transient flow. Numerical experiments are presented to corroborate the fact that, once the necessary conditions are met, the inverse problem has a unique solution. We also demonstrate that measurement noise, instability, and sensitivity are issues related to solution techniques rather than the inverse problems themselves. In addition, we show that a mathematically well-defined inverse problem, based on an equivalent homogeneous or a layered conceptual model, may yield physically incorrect and scenario-dependent parameter values. These issues are attributed to inconsistency between the scale of the head observed and that implied by these models. Such issues can be reduced only if a sufficiently large number of observation wells are used in the equivalent homogeneous domain or each layer. With a large number of wells, we then show that increase in parameterization can lead to a higher-resolution depiction of heterogeneity if an appropriate inverse methodology is used. Furthermore, we illustrate that, using the same number of wells, a highly parameterized model in conjunction with hydraulic tomography can yield better characterization of the aquifer and minimize the scale and scenario-dependent problems. Lastly, benefits of the highly parameterized model and hydraulic tomography are tested according to their ability to improve predictions of aquifer responses induced by independent stresses not used in the inverse modeling efforts.
摘要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 REsum<0.1%.Most calibrations can be achieved with REsum<5%within hours or REsum<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.
基金the Council of Scientific and Industrial Research(CSIR),India
摘要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 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
摘要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)
摘要In this article, two uniqueness theorems of meromorphic mappings on moving targets with truncated multiplicities are proved.
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
摘要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.
基金supported by the NSFC(11026110,11101201)the NSF of Jiangxi(2010GQS0144)
摘要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.
基金supported by JSPS Grant-in-Aid for Scientific Research(C)(15K04970)
摘要In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.
基金supported in part by the National Natural Science Foundation of China(10971156,11271291)
摘要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supported by Grant In Aid research fund of Virginia Military Instittue,USA
摘要We study boundary value problems for fractional integro-differential equations involving Caputo derivative of orderα∈(n-1,n)in Banach spaces.Existence and uniqueness results of solutions are established by virtue of the Holder's inequality,a suitable singular Cronwall's inequality and fixed point theorem via a priori estimate method.At last,examples are given to illustrate the results.
基金Supported by the National Natural Science Foundation of China(Nos.32270219,31970216)。
摘要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.