The aim of this paper is to define the notions of generalized （m, n）-derivations and generalized （m, n）：Jordan derivations and to prove two theorems involving these map- pings.
Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A^2) = 2 mAδ(A) + 2nδ(A)A for every ...Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A^2) = 2 mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every(m, n)-Jordan derivation with m = n from a C*-algebra into its Banach bimodule is zero. An additive mappingδ from R into M is called a(m, n)-Jordan derivable mapping at W in R if(m + n)δ(AB + BA) =2mδ(A)B + 2 mδ(B)A + 2 nAδ(B) + 2 nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left(right) separating set generated algebraically by all idempotents in A, then every(m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital(A, B)-bimodule and U = [A M N B] is a generalized matrix algebra, then every(m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.展开更多
设R是一个环,M是一个R-双边模,m和n是两个非负整数满足m+n≠0,如果δ是一个从R到M的可加映射满足对任意A∈R,(m+n)δ(A^2)=2mAδ(A)+2nδ(A)A,则称δ是一个(m,n)-Jordan导子.本文证明了,如果R是一个单位环,M是一个单位R-双边模含有一个...设R是一个环,M是一个R-双边模,m和n是两个非负整数满足m+n≠0,如果δ是一个从R到M的可加映射满足对任意A∈R,(m+n)δ(A^2)=2mAδ(A)+2nδ(A)A,则称δ是一个(m,n)-Jordan导子.本文证明了,如果R是一个单位环,M是一个单位R-双边模含有一个由R中幂等元代数生成的左(右)分离集,那么,当m,n>0且m≠n时,每一个从R到M的(m,n)-Jordan导子恒等于零.还证明了,如果A和B是两个单位环,M是一个忠实的单位(A,B)-双边模(N是一个忠实的单位(B,A)-双边模),m,n>0且m≠n,U=[A N M B]是一个|mn(m-n)(m+n)|-无挠的广义矩阵环,那么每一个从U到自身的(m,n)-Jordan导子恒等于零.展开更多
Concerning the stability problem of functional equations, we introduce a general （m, n）- Cauchy-Jensen functional equation and establish new theorems about the Hyers-Ulam stability of general （m, n）-Cauchy Jensen ...Concerning the stability problem of functional equations, we introduce a general （m, n）- Cauchy-Jensen functional equation and establish new theorems about the Hyers-Ulam stability of general （m, n）-Cauchy Jensen additive mappings in C^＊-algebras, which generalize the result＇s obtained for Cauchy-Jensen type additive mappings.展开更多
文摘采用自主研发的多源多宿GNSS-R(Global Navigation Satellite System-Reflections,全球导航卫星系统反射信号)海洋环境遥感探测系统,在天津渤海湾特定区域进行了3次机载校飞试验,获得了大量有效GNSS-R信号数据,对自然条件下的海面有效波高进行了反演处理。该系统通过对接收的GNSS直达信号和海面反射信号进行相关运算处理,可以获得DDM(Delay-Doppler Mapping,时延—多普勒映射)图谱,再利用DCF(Derivative of the Correlation Function,相关函数的导数)在DDM图谱基础上进行相关功率波形的计算,进而通过计算DCF的函数波形宽度得到海面有效波高,验证了该方法的可行性。该方法具有全天时、全天候、高分辨率、低成本等优点,对全球范围内中小尺度海洋状态和物理现象的监测具有重要意义。
文摘The aim of this paper is to define the notions of generalized （m, n）-derivations and generalized （m, n）：Jordan derivations and to prove two theorems involving these map- pings.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11801342 and 11801005)
文摘Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A^2) = 2 mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every(m, n)-Jordan derivation with m = n from a C*-algebra into its Banach bimodule is zero. An additive mappingδ from R into M is called a(m, n)-Jordan derivable mapping at W in R if(m + n)δ(AB + BA) =2mδ(A)B + 2 mδ(B)A + 2 nAδ(B) + 2 nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left(right) separating set generated algebraically by all idempotents in A, then every(m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital(A, B)-bimodule and U = [A M N B] is a generalized matrix algebra, then every(m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.
文摘设R是一个环,M是一个R-双边模,m和n是两个非负整数满足m+n≠0,如果δ是一个从R到M的可加映射满足对任意A∈R,(m+n)δ(A^2)=2mAδ(A)+2nδ(A)A,则称δ是一个(m,n)-Jordan导子.本文证明了,如果R是一个单位环,M是一个单位R-双边模含有一个由R中幂等元代数生成的左(右)分离集,那么,当m,n>0且m≠n时,每一个从R到M的(m,n)-Jordan导子恒等于零.还证明了,如果A和B是两个单位环,M是一个忠实的单位(A,B)-双边模(N是一个忠实的单位(B,A)-双边模),m,n>0且m≠n,U=[A N M B]是一个|mn(m-n)(m+n)|-无挠的广义矩阵环,那么每一个从U到自身的(m,n)-Jordan导子恒等于零.
文摘Concerning the stability problem of functional equations, we introduce a general （m, n）- Cauchy-Jensen functional equation and establish new theorems about the Hyers-Ulam stability of general （m, n）-Cauchy Jensen additive mappings in C^＊-algebras, which generalize the result＇s obtained for Cauchy-Jensen type additive mappings.
