Discussion on the Homology Theory of Lie Algebras

Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

MS-222和丁香酚胁迫对四指马鲅幼鱼鳃及肝脏组织微观结构的影响

【目的】探究不同质量浓度的MS-222和丁香酚胁迫对四指马鲅(Eleutheronema tetradactylum)幼鱼鳃和肝脏组织损伤的影响。【方法】设置7个浓度的MS-222(20、30、35、40、45、50、60 mg/L)和7个浓度的丁香酚(5、10、20、25、30、40、50 mg/L),分析不同处理对平均全长4.5(±0.5)cm、平均体质量1.5(±0.5)g的四指马鲅幼鱼的静水麻醉效应。【结果】当MS-222浓度不小于35 mg/L时,麻醉467 s后幼鱼开始出现应激反应;浓度为50 mg/L时可将部分幼鱼诱导进入麻醉期,浓度为60 mg/L时可在293 s后将全部幼鱼诱导进入麻醉期。丁香酚浓度不小于25 mg/L时,麻醉291 s后幼鱼开始出现应激反应;浓度为30 mg/L时可将部分幼鱼诱导进入麻醉期;浓度为40、50 mg/L时,分别可以在194 s和102 s将全部幼鱼诱导进入麻醉期。随着MS-222和丁香酚浓度的升高,幼鱼进入同一麻醉时期的时间显著缩短(P<0.05),高浓度下四指马鲅幼鱼进入麻醉时期的时间过快,超过耐受值可能对鱼体产生一定毒害作用,导致鱼体死亡。观察幼鱼组织病理切片发现,随着MS-222和丁香酚浓度的升高,幼鱼肝细胞出现空泡,排列紊乱,核内可见核溶解,肝板结构不清;鳃小片弯曲,末端肿大,严重者可胀破、脱落。【结论】适度的麻醉剂量可以降低鱼体对外界环境的应激反应,减少耗氧,不同浓度的MS-222和丁香酚(5 mg/L除外)均可在3 min内对四指马鲅幼鱼产生镇静作用,当2种麻醉剂浓度过高、麻醉时间过长以及幼鱼长时间处于应激状态时,会出现死亡现象。

Some results on derivations of MV-algebras

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].

(ρ, τ, σ)-Derivations of Dendriform Algebras

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.

ON SYMMETRIC EXTENDED MS-ALGEBRAS WHOSE CONGRUENCES ARE PERMUTABLE

Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized.

MS-222对墨瑞鳕麻醉效果及血清生化指标的影响

为探索MS-222麻醉剂对墨瑞鳕(734.94±51.36 g)的麻醉效果,在水温18±0.5℃条件下,采用不同浓度(0.10、0.15、0.20、0.30 mg·L^(-1))麻醉剂进行麻醉实验,并分析麻醉复苏后血清生化指标的变化。结果显示,在麻醉及复苏时间效果上,麻醉有效浓度范围为0.185~0.227 mg·L^(-1)。麻醉期间,血清中的葡萄糖、皮质醇含量与对照组相比均存在显著差异(P<0.05),随麻醉剂浓度增加,葡萄糖含量先升高后降低,皮质醇含量先降低再升高;碱性磷酸酶活性和谷丙转氨酶活性仅在0.30 mg·L^(-1)组显著升高(P<0.05);超氧歧化酶活性先降低后升高,过氧化氢酶活性逐渐下降。复苏12 h后,葡萄糖含量、谷丙转氨酶活性、超氧歧化酶活性均恢复到对照组水平,而皮质醇含量除0.10 mg·L^(-1)组、碱性磷酸酶活性及过氧化氢酶活性除0.30 mg·L^(-1)组外,其他组均恢复到对照组水平。综合考虑MS-222麻醉剂的麻醉效果及对墨瑞鳕机体的影响,麻醉剂浓度在0.20 mg·L^(-1)具有最佳效果。研究结果可为MS-222麻醉剂使用安全性及其麻醉机理的分析提供参考依据。

2D Curves in Conformal Hyperquaternion Algebras H⊗2m

The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H⊗2m in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H⊗2m is the object of this work.

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

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.

Root Systems Lie Algebras

A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.

A SPECIAL KIND OF PRINCIPAL CONGRUENCES ON MS-ALGEBRAS

In this article, for any a in the MS-algebra L, the author considers the con- gruence of the form defined by （x,y） ∈θa→←x∧a°° = y ∧a° and x ∨ a°° = y ∨ a°°. A characterization of subdirectly irreducible MS-algebras is given and it is also proved that the union of two principal congruences having this form is a principal congruence if and only if L ∈ K2 ∨ K3.

KERNEL IDEALS AND CONGRUENCES ON MS-ALGEBRAS

In this article, the authors describe the largest congruence induced by a kernel ideal of an MS-algebra and characterize those MS-algebras on which all the congruences are in a one-to-one correspondence with the kernel ideals.

Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra

Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L∞(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L2(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .

Split-Tetraquaternion Algebra and Applications

In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.

The Report of Homological Algebra

The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modules.

Quantum Computingvia Entanglement in Geometric Algebra Approach

The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.

e-FILTERS OF MS-ALGEBRAS

The notion of e-filters is introduced in an MS-algebra and characterized. The concept of D-filters is introduced and a set of equivalent conditions under which every D-filter is an e-filter are given. The properties of the space of all prime e-filters of an MS-algebra are observed. The concept of D-prime filters is introduced and then a set of equivalent conditions axe derived for a prime e-filter to become a D-prime filter in topological terms.

Implicative and Fuzzy Implicative Ideals of Lattice Implication Algebras

In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.

偏序集上的MS-收敛

定义在s_(2)-连续偏序集上的S-极限是一种重要的收敛结构.本文用集族MS代替定向集,将s_(2)-连续和S-极限进行推广,定义了s_(2)MS-连续和MS-极限,并用MS-极限定义了s_(2)MS-α-连续.本文主要结果有:(i)如果L为s_(2)MS-连续偏序集且MS关系具有插入性质,则MS-收敛是拓扑的;(ii)如果L为偏序集,任意的x∈L,α(MS)x∈MS且α(MS)具有插入性质,则MS-收敛为拓扑的当且仅当L为s_(2)MS-α-连续的.

Crossed modules of Lie color algebras

The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.