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
High-entropy alloys(HEAs),which were introduced as a pioneering concept in 2004,have captured the keen interest of nu-merous researchers.Entropy,in this context,can be perceived as representing disorder and randomness...High-entropy alloys(HEAs),which were introduced as a pioneering concept in 2004,have captured the keen interest of nu-merous researchers.Entropy,in this context,can be perceived as representing disorder and randomness.By contrast,elemental composi-tions within alloy systems occupy specific structural sites in space,a concept referred to as structure.In accordance with Shannon entropy,structure is analogous to information.Generally,the arrangement of atoms within a material,termed its structure,plays a pivotal role in dictating its properties.In addition to expanding the array of options for alloy composites,HEAs afford ample opportunities for diverse structural designs.The profound influence of distinct structural features on the exceptional behaviors of alloys is underscored by numer-ous examples.These features include remarkably high fracture strength with excellent ductility,antiballistic capability,exceptional radi-ation resistance,and corrosion resistance.In this paper,we delve into various unique material structures and properties while elucidating the intricate relationship between structure and performance.展开更多
We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations,with the initial data(u0,B0)being located in the critical Besov space■and the initial densityρ0 being close to a positive co...We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations,with the initial data(u0,B0)being located in the critical Besov space■and the initial densityρ0 being close to a positive constant.By using weighted global estimates,maximal regularity estimates in the Lorentz space for the Stokes system,and the Lagrangian approach,we show that the 2-D MHD equations have a unique global solution.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
An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of...An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.展开更多
The development status and significance of recreational agriculture in Hainan were analyzed.By introducing advantages of Hainan Island in political institution,natural resources and humanistic resources,it was propose...The development status and significance of recreational agriculture in Hainan were analyzed.By introducing advantages of Hainan Island in political institution,natural resources and humanistic resources,it was proposed that special topographical scenery,Qiong Opera(Hainan Opera),tropical plants,rare animal species,customs of Li and Miao nationalities,and agricultural product resources could be applied in the development of recreational agriculture,and many activities of recreational agriculture could be organized.展开更多
In this paper,we prove that there does not exist an r-UPC[2]-graph for each r≥5 and there does not exist an r-UPC[C_t^2]-graph for each r≥3,where t is the number of bridges in a graph and C_t^2 is the number of comb...In this paper,we prove that there does not exist an r-UPC[2]-graph for each r≥5 and there does not exist an r-UPC[C_t^2]-graph for each r≥3,where t is the number of bridges in a graph and C_t^2 is the number of combinations of t bridges taken 2 at a time.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
Objective To observe the clinical effect of blood-letting puncture and cupping at Chōngxiāo（冲霄 Extra） point of Dong＇s unique Extra-ordinary points in the treatment of neck type of cervical spondylosis.Methods S...Objective To observe the clinical effect of blood-letting puncture and cupping at Chōngxiāo（冲霄 Extra） point of Dong＇s unique Extra-ordinary points in the treatment of neck type of cervical spondylosis.Methods Sixty-five patients of neck type of cervical spondylosis were selected and treated with blood-letting puncture and cupping at Chōngxiāo（冲霄 Extra） point once every two or three days,three times constituted one course and two successive courses were given,then the clinical effect was evaluated.Results The curative rate was 69.2%（45/65）,and the total effective rate was 92.3%（60/65）.Conclusion Blood-letting puncture and cupping at Dong＇s Chōngxiāo（冲霄 Extra） point can be used to treat neck type of cervical spondylosis with simple manipulation and obvious efficacy.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
In this paper, we investigate the existence and uniqueness of solutions for a new fourth-order differential equation boundary value problem：{u（4）（t） = f（t, u（t））-b, 0 〈 t 〈 1,u（0） = u′（0） = u′（1） = ...In this paper, we investigate the existence and uniqueness of solutions for a new fourth-order differential equation boundary value problem：{u（4）（t） = f（t, u（t））-b, 0 〈 t 〈 1,u（0） = u′（0） = u′（1） = u（3）（1） = 0,where f ∈ C（[0,1] ×（-∞,＋∞）,（-∞, ＋∞））,b ≥ 0 is a constant. The novelty of this paper is that the boundary value problem is a new type and the method is a new fixed point theorem ofφ-（h,e）-concave operators.展开更多
When initializing cryptographic systems or running cryptographic protocols, the randomness of critical parameters, like keys or key components, is one of the most crucial aspects. But, randomly chosen parameters come ...When initializing cryptographic systems or running cryptographic protocols, the randomness of critical parameters, like keys or key components, is one of the most crucial aspects. But, randomly chosen parameters come with the intrinsic chance of duplicates, which finally may cause cryptographic systems including RSA, ElGamal and Zero-Knowledge proofs to become insecure. When concerning digital identifiers, we need uniqueness in order to correctly identify a specific action or object. Unfortunately we also need randomness here. Without randomness, actions become linkable to each other or to their initiator’s digital identity. So ideally the employed (cryptographic) parameters should fulfill two potentially conflicting requirements simultaneously: randomness and uniqueness. This article proposes an efficient mechanism to provide both attributes at the same time without highly constraining the first one and never violating the second one. After defining five requirements on random number generators and discussing related work, we will describe the core concept of the generation mechanism. Subsequently we will prove the postulated properties (security, randomness, uniqueness, efficiency and privacy protection) and present some application scenarios including system-wide unique parameters, cryptographic keys and components, identifiers and digital pseudonyms.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
In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. ...In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.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(No.52273280)the Creative Research Groups of China(No.51921001).
文摘High-entropy alloys(HEAs),which were introduced as a pioneering concept in 2004,have captured the keen interest of nu-merous researchers.Entropy,in this context,can be perceived as representing disorder and randomness.By contrast,elemental composi-tions within alloy systems occupy specific structural sites in space,a concept referred to as structure.In accordance with Shannon entropy,structure is analogous to information.Generally,the arrangement of atoms within a material,termed its structure,plays a pivotal role in dictating its properties.In addition to expanding the array of options for alloy composites,HEAs afford ample opportunities for diverse structural designs.The profound influence of distinct structural features on the exceptional behaviors of alloys is underscored by numer-ous examples.These features include remarkably high fracture strength with excellent ductility,antiballistic capability,exceptional radi-ation resistance,and corrosion resistance.In this paper,we delve into various unique material structures and properties while elucidating the intricate relationship between structure and performance.
基金supported by the National Natural Science Foundation of China(12371211,12126359)the postgraduate Scientific Research Innovation Project of Hunan Province(XDCX2022Y054,CX20220541).
文摘We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations,with the initial data(u0,B0)being located in the critical Besov space■and the initial densityρ0 being close to a positive constant.By using weighted global estimates,maximal regularity estimates in the Lorentz space for the Stokes system,and the Lagrangian approach,we show that the 2-D MHD equations have a unique global solution.
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.
基金The National Natural Science Foundation of China(No.10971024)the Specialized Research Fund for the Doctoral Program of Higher Education(No.200802860024)the Natural Science Foundation of Jiangsu Province(No.BK2010393)
文摘An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.
基金Supported by the Scientific Research Fund of the College of Applied Science and Technology,Hainan University(yykj-ky-2009-2)~~
文摘The development status and significance of recreational agriculture in Hainan were analyzed.By introducing advantages of Hainan Island in political institution,natural resources and humanistic resources,it was proposed that special topographical scenery,Qiong Opera(Hainan Opera),tropical plants,rare animal species,customs of Li and Miao nationalities,and agricultural product resources could be applied in the development of recreational agriculture,and many activities of recreational agriculture could be organized.
文摘In this paper,we prove that there does not exist an r-UPC[2]-graph for each r≥5 and there does not exist an r-UPC[C_t^2]-graph for each r≥3,where t is the number of bridges in a graph and C_t^2 is the number of combinations of t bridges taken 2 at a time.
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.
文摘Objective To observe the clinical effect of blood-letting puncture and cupping at Chōngxiāo（冲霄 Extra） point of Dong＇s unique Extra-ordinary points in the treatment of neck type of cervical spondylosis.Methods Sixty-five patients of neck type of cervical spondylosis were selected and treated with blood-letting puncture and cupping at Chōngxiāo（冲霄 Extra） point once every two or three days,three times constituted one course and two successive courses were given,then the clinical effect was evaluated.Results The curative rate was 69.2%（45/65）,and the total effective rate was 92.3%（60/65）.Conclusion Blood-letting puncture and cupping at Dong＇s Chōngxiāo（冲霄 Extra） point can be used to treat neck type of cervical spondylosis with simple manipulation and obvious efficacy.
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.
基金Supported by the Shanxi Scholarship Council of China(Grant No.2016-009)the Natural Science Foundation of Shanxi Province(Grant No.201701D121004)
文摘In this paper, we investigate the existence and uniqueness of solutions for a new fourth-order differential equation boundary value problem：{u（4）（t） = f（t, u（t））-b, 0 〈 t 〈 1,u（0） = u′（0） = u′（1） = u（3）（1） = 0,where f ∈ C（[0,1] ×（-∞,＋∞）,（-∞, ＋∞））,b ≥ 0 is a constant. The novelty of this paper is that the boundary value problem is a new type and the method is a new fixed point theorem ofφ-（h,e）-concave operators.
文摘When initializing cryptographic systems or running cryptographic protocols, the randomness of critical parameters, like keys or key components, is one of the most crucial aspects. But, randomly chosen parameters come with the intrinsic chance of duplicates, which finally may cause cryptographic systems including RSA, ElGamal and Zero-Knowledge proofs to become insecure. When concerning digital identifiers, we need uniqueness in order to correctly identify a specific action or object. Unfortunately we also need randomness here. Without randomness, actions become linkable to each other or to their initiator’s digital identity. So ideally the employed (cryptographic) parameters should fulfill two potentially conflicting requirements simultaneously: randomness and uniqueness. This article proposes an efficient mechanism to provide both attributes at the same time without highly constraining the first one and never violating the second one. After defining five requirements on random number generators and discussing related work, we will describe the core concept of the generation mechanism. Subsequently we will prove the postulated properties (security, randomness, uniqueness, efficiency and privacy protection) and present some application scenarios including system-wide unique parameters, cryptographic keys and components, identifiers and digital pseudonyms.
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.
文摘In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.
