Some Theorems on Leibniz n-Algebras from the Category Un(Lb)

We study the Leibniz n-algebra Un(∑),whose multiplication is defined viathe bracket of a Leibniz algebra ∑ as[x1,...,xn]=[x1,[...,[xn-2,[xn-1,xn]]...]].Weshow that Un(∑) is simple if and only if ∑ is a simple Lie algebra.An analog of Levi'stheorem for Leibniz algebras in Un(Lb) is established and it is proven that the Leibnizn-kernel of Un(Σ) for any semisimple Leibniz algebra Σ is the n-algebra Un(Σ).     

ON GENERALIZED COMPLETE(p,q)-ELLIPTIC INTEGRALS

In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generalized convexity and concavity of these functions.In particular,some Turán type inequalities are given.Finally,we also show some new series representations of these functions by applying Alzer and Richard's methods.     

对氯苯甲酸构筑的铜(Ⅱ)配合物的合成、HSA结合及细胞毒性

本文合成了配合物[Cu(pcba)₂·(phen)(H₂O)] (pcba =对氯苯甲酸,phen = 1,10-邻菲罗啉),该配合物属于三斜晶系,P1空间群,晶胞参数为a=0.790 98(2) nm,b=1.072 40(4) nm,c=1.487 19(6) nm,α=100.613(3)°,β=95.239(3)°,γ=108.334(3)°,Z=2,D_c=1.638 g·cm^-3,F(000)=582,最终结构残差因子R₁=0.035 9,wR₂=0.089 1。采用紫外及荧光研究了配合物和人血清蛋白(HSA)的相互作用方式。结果表明,配合物静态猝灭HSA荧光,可求得配合物与HSA的猝灭常数K_sv=2.35×10⁵ L·mol^-1,猝灭速率常数K_q=2.35×10¹³ L·mol^-1·s^-1,结合常数为K_a=2.14×10¹³ L·mol^-1,结合位点n=2.37。同时,研究了配合物对胃癌细胞A549、宫颈癌细胞Hela和肝癌细胞HepG2的抗增殖能力。     

算子代数上2-局部Lie三重导子的结构

设X是维数大于2的Banach空间,映射δ:B(X)→B(X)是2-局部Lie三重导子,则对所有A∈B(X)有δ(A)=[A,T]+φ(A),这里T∈B(X),φ是从B(X)到FI的齐次映射且满足对所有A,B∈B(X)有φ(A+B)=φ(A),其中B是交换子的和.     

偏缠绕模的Frobenius性质

主要给出了偏缠绕模的Frobenius性质，推广了缠绕模相应的性质。     

Examples of compactλ-hypersurfaces in Euclidean spaces

In this paper,we first construct compact embeddedλ-hypersurfaces with the topology of torus which are calledλ-torus in Euclidean spaces?n^+1.Then,we give many compact immersedλ-hypersurfaces in Euclidean spaces?n^+1.     

A New Sufficient Degree Condition for a Graphic Sequence to Be Forcibly k-Edge-Connected

A graphic sequence π =(d₁, d₂,..., d_n) is said to be forcibly k-edge-connected if every realization of π is k-edge-connected. In this paper, we obtain a new sufficient degree condition for π to be forcibly k-edgeconnected. We also show that this new sufficient degree condition implies a strongest monotone degree condition for π to be forcibly 2-edge-connected and a conjecture about a strongest monotone degree condition for π to be forcibly 3-edge-connected due to...     

CCSD(T) study on the structures and chemical bonds of AnO molecules (An = Bk–Lr)

The molecular geometries and dissociation energies of AnO (An = Bk–Lr) molecules were first obtained at thecoupled-cluster single-, double-, and perturbative triple-excitations [CCSD(T)] level of theory. Four hybrid functionals,B3LYP, M06-2X, TPSSh, and PBE0, were also employed in the calculations for the sake of comparison. In comparison ofthe CCSD(T) results, B3LYP, TPSSh, and PBE0 functionals can obtain more appropriate results than M06-2X and MP2.The analyses on molecular orbitals show that the 7s, 6d, and 5f atomic orbitals of actinide (An) atoms participate in thebonding of An–O bonds. The partial covalent nature between An and O atoms is revealed by QTAIM analyses.     

Copper-catalyzed diversified annulations between α-diketones and alkynyl α-diketones

Copper-catalyzed divergent annulations between α-diketones and alkynyl α-diketones have been achieved, delivering a series of highly functionalized and biologically important cis-hexahydro-2Hcyclopenta[b]furan(HCPF) and 2-hydroxydihydrofuran-3(2H)-one(HDFO) products with high levels of stereoselectivity under identical conditions. The protocol features the use of earth-abundant copper catalyst, mild conditions, shortening synthetic routes in constructing different molecular frameworks, and reduc...