The definitions of generalized pseudoconvex,generalized quasiconvex and its stri ctly generalized convexity were presented for the static programming at locally star -shaped set using the concept of right-upper deriva...The definitions of generalized pseudoconvex,generalized quasiconvex and its stri ctly generalized convexity were presented for the static programming at locally star -shaped set using the concept of right-upper derivative and the concept of sub linear. The sufficient and necessary conditions of the static programming were d erived in terms of a generalized Lemma in this paper. The results obtained are u seful for the further study on the duality of static programming and cover many already known conditions.展开更多
Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the stru...Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered.展开更多
Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф（Xi^△j） is a reduced generalized differential identity for an essential ideal of R, then ф（Zije（△j ）） is a ...Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф（Xi^△j） is a reduced generalized differential identity for an essential ideal of R, then ф（Zije（△j ）） is a generalized polynomial identity for RF, where e（△j） are idempotents in the extended centroid of R determined by △j. Let R be a prime ring and Q be its symmetric Martindale quotient ring. If ф（Xi△j） is a reduced generalized differential identity for a noncommutative Lie ideal of R, then ф（Zij） is a generalized polynomial identity for [R, R]. Moreover, if ф（Xi△j） is a reduced generalized differential identity, with coefficients in Q, for a large right ideal of R, then ф（Zij） is a generalized polynomial identity for Q.展开更多
Let D= {{0},/4, L, M, X} be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X, which satisfies that one of three sums K ＋ L, L＋M and M ＋ K is closed. It is shown that local C...Let D= {{0},/4, L, M, X} be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X, which satisfies that one of three sums K ＋ L, L＋M and M ＋ K is closed. It is shown that local C-derivations and C-derivations at zero point on Alg：D are generalized Ф-derivations.展开更多
基金National Natural Science Foundation ofChina(No.70273029)
文摘The definitions of generalized pseudoconvex,generalized quasiconvex and its stri ctly generalized convexity were presented for the static programming at locally star -shaped set using the concept of right-upper derivative and the concept of sub linear. The sufficient and necessary conditions of the static programming were d erived in terms of a generalized Lemma in this paper. The results obtained are u seful for the further study on the duality of static programming and cover many already known conditions.
基金China NNSF (10726051)Grant in-aid for Scientific Research from Department of Mathematics,Jilin University
文摘Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered.
基金supported by the mathematical Tianyuan Research Foundation of China(10426005)the Basic Research Foundation of Beijing Institute of Technology of China
文摘Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф（Xi^△j） is a reduced generalized differential identity for an essential ideal of R, then ф（Zije（△j ）） is a generalized polynomial identity for RF, where e（△j） are idempotents in the extended centroid of R determined by △j. Let R be a prime ring and Q be its symmetric Martindale quotient ring. If ф（Xi△j） is a reduced generalized differential identity for a noncommutative Lie ideal of R, then ф（Zij） is a generalized polynomial identity for [R, R]. Moreover, if ф（Xi△j） is a reduced generalized differential identity, with coefficients in Q, for a large right ideal of R, then ф（Zij） is a generalized polynomial identity for Q.
基金Supported by the National Natural Science Foundation of China (Grant No.10871224)the Natural Science Young Foundation of Shaanxi Province (Grant No.2010JQ1003)+1 种基金the Natural Science Special Foundation of Education Department of Shaanxi Province (Grant No.08JK344)the Basic Research Foundation of Xi'an University of Architecture and Technology (Grant No.JC1009)
文摘Let D= {{0},/4, L, M, X} be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X, which satisfies that one of three sums K ＋ L, L＋M and M ＋ K is closed. It is shown that local C-derivations and C-derivations at zero point on Alg：D are generalized Ф-derivations.
