In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multipli...In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence.展开更多
Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations an...In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].展开更多
We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provid...We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.展开更多
Compactness of subspaces of a Z<sub>2</sub>-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebr...Compactness of subspaces of a Z<sub>2</sub>-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a Lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced Lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.展开更多
A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-L...A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.展开更多
目的研究百会穴久留针法通过脑源性神经营养因子(BDNF)/酪氨酸受体激酶B(TrkB)通路改善缺血性脑卒中小鼠神经功能的作用及机制。方法选择雄性C57BL/6J小鼠48只,随机分为假手术1组、模型1组、久留针1组、普通留针组,每组12只。后3组采用...目的研究百会穴久留针法通过脑源性神经营养因子(BDNF)/酪氨酸受体激酶B(TrkB)通路改善缺血性脑卒中小鼠神经功能的作用及机制。方法选择雄性C57BL/6J小鼠48只,随机分为假手术1组、模型1组、久留针1组、普通留针组,每组12只。后3组采用线栓法制备缺血性脑卒中模型,手术造模后第1天起久留针1组和普通留针组分别给予百会穴久留针和普通留针治疗,连续14 d。另选择雄性C57BL/6J小鼠40只,随机分为假手术2组、模型2组、久留针2组、久留针3组,每组10只。后3组采用线栓法制备缺血性脑卒中模型,针灸治疗前分别给予腺相关病毒100μl单次尾静脉注射。采用改良神经功能缺损评分(mNSS)及水迷宫实验的逃避潜伏期、目标象限停留时间、穿越原平台次数评价神经功能。结果与假手术1组比较,模型1组mNSS评分、目标象限停留时间、穿越原平台次数及缺血脑组织BDNF、TrkB表达明显降低,细胞凋亡率及裂解型半胱氨酸天冬氨酸蛋白酶3(Caspase-3)表达明显增加,差异有统计学意义(P<0.05);与模型1组比较,久留针1组和普通留针组mNSS评分、目标象限停留时间、穿越原平台次数及缺血脑组织BDNF、TrkB表达明显增加,细胞凋亡率及裂解型Caspase-3表达明显降低,且久留针1组上述变化较普通留针组更为显著,差异有统计学意义(P<0.05)。与久留针2组比较,久留针3组mNSS评分、目标象限停留时间、穿越原平台次数及缺血脑组织中BDNF表达明显降低(P<0.05),细胞凋亡率及裂解型Caspase-3表达明显增加[(16.41±2.25)%vs(7.59±1.09)%;1.46±0.16 vs 0.94±0.12,P<0.05]。结论百会穴久留针治疗对缺血性脑卒中小鼠神经功能的改善作用更为显著,激活BDNF/TrkB通路是其发挥神经保护作用的相关分子机制。展开更多
基金Supported by the National Natural Science Foundation of China(12271319).
文摘In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence.
文摘Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
基金Supported by a grant of National Natural Science Foundation of China(12001243,61976244,12171294,11961016)the Natural Science Basic Research Plan in Shaanxi Province of China(2020JQ-762,2021JQ-580)。
文摘In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].
文摘We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.
文摘Compactness of subspaces of a Z<sub>2</sub>-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a Lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced Lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.
基金Supported by the National Natural Science Foundation of China(11501523,61673320)。
文摘A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.
文摘目的研究百会穴久留针法通过脑源性神经营养因子(BDNF)/酪氨酸受体激酶B(TrkB)通路改善缺血性脑卒中小鼠神经功能的作用及机制。方法选择雄性C57BL/6J小鼠48只,随机分为假手术1组、模型1组、久留针1组、普通留针组,每组12只。后3组采用线栓法制备缺血性脑卒中模型,手术造模后第1天起久留针1组和普通留针组分别给予百会穴久留针和普通留针治疗,连续14 d。另选择雄性C57BL/6J小鼠40只,随机分为假手术2组、模型2组、久留针2组、久留针3组,每组10只。后3组采用线栓法制备缺血性脑卒中模型,针灸治疗前分别给予腺相关病毒100μl单次尾静脉注射。采用改良神经功能缺损评分(mNSS)及水迷宫实验的逃避潜伏期、目标象限停留时间、穿越原平台次数评价神经功能。结果与假手术1组比较,模型1组mNSS评分、目标象限停留时间、穿越原平台次数及缺血脑组织BDNF、TrkB表达明显降低,细胞凋亡率及裂解型半胱氨酸天冬氨酸蛋白酶3(Caspase-3)表达明显增加,差异有统计学意义(P<0.05);与模型1组比较,久留针1组和普通留针组mNSS评分、目标象限停留时间、穿越原平台次数及缺血脑组织BDNF、TrkB表达明显增加,细胞凋亡率及裂解型Caspase-3表达明显降低,且久留针1组上述变化较普通留针组更为显著,差异有统计学意义(P<0.05)。与久留针2组比较,久留针3组mNSS评分、目标象限停留时间、穿越原平台次数及缺血脑组织中BDNF表达明显降低(P<0.05),细胞凋亡率及裂解型Caspase-3表达明显增加[(16.41±2.25)%vs(7.59±1.09)%;1.46±0.16 vs 0.94±0.12,P<0.05]。结论百会穴久留针治疗对缺血性脑卒中小鼠神经功能的改善作用更为显著,激活BDNF/TrkB通路是其发挥神经保护作用的相关分子机制。
