Zigzag graphene nanoribbons: Flexible and robust transparent conductors

We report the effect of bending deformation on the optical and transport properties of zigzag graphene nanoribbons (ZGNRs) induced by the uniaxial strain using the first-principles method combined with non-equilibrium Green's function. The optical properties of ZGNRs in the region of visible light are almost unchanged under the uniaxial strain, whereas an absorption peak occurs at the infrared region for the bent ZGNRs under the transverses strain. The transport properties of ZGNRs under the transverses strain with the bending angle up to 65° remain almost the same as those of the flat one. The transmission coefficients around the Fermi level only slightly decrease when the bending angle further increases to 72.5°. Moreover, ZGNRs under the longitudinal strain show the same transmission conductance around the Fermi level as that of the flat one. The edge states of ZGNRs still behave as excellent ballistic transport channels under bending deformation, which makes them promising flexible and robust transparent conductors.     

喷雾干燥法制备Li_(1.2)Mn_(0.4+x)Ni_xCr_(0.4-2x)O_2及其结构与电化学特征

利用喷雾干燥法合成了富锂三元正极材料Li1.2Mn0.4+xNixCr0.4-2xO2(x=0,0.05,0.10,0.15,0.20,以下简称为SD1~SD5),并利用XRD,XPS,ICP,TEM,SEM等手段对材料进行结构,元素价态,形貌及电化学性能等方面的表征。SD1~SD5系列样品都具有层状结构,其所含的Cr元素为Cr6+和Cr3+共存,而Ni元素价态为+2.5价,Mn元素为+4价。SD1~SD4样品中由于存在非晶态的Li2CrO4,导致样品表现出强烈的吸湿性。这个问题可通过水洗处理来解决,且水洗处理对于改善该系列材料的电化学性能有明显的效果。SD1~SD5系列样品中,SD1与SD4样品电化学性能较好,以20 mA.g-1的放电电流密度,在4.8~2.0 V电压区间内,首次放电比容量分别为247和220 mA.h.g-1,经过20次充放电循环后,容量保持率分别为73%和78%。高温条件下SD1和SD4样品的首次放电比容量分别增大为256和237 mA.h.g-1,经过20次充放电循环后容量保持率分别为83%和99%。将充放电电压扩展为5.0~2.0 V时,SD4样品首次放电比容量可以达到307 mA.h.g-1。     

Supersymmetric extensions of Schrödinger-invariance

The set of dynamic symmetries of the scalar free Schrödinger equation in d space dimensions gives a realization of the Schrödinger algebra that may be extended into a representation of the conformal algebra in $d+2$ dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-$\frac{1}{2}$ Lévy-Leblond equation. An $N=2$ supersymmetric extension of these equations leads, respectively, to a ‘super-Schrödinger’ model and to the $(3|2)$-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras $\mathfrak{osp}(2|2)⋉\mathfrak{sh}(2|2)$ and $\mathfrak{osp}(2|4)$, respectively. The Schrödinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schrödinger–Neveu–Schwarz algebra ${\mathfrak{sns}}^{(N)}$ with N supercharges. Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of $\mathfrak{osp}(2|4)$. If one includes both $N=2$ supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values.     

Luminescent 2-D double-layered polymer, [(CuI)4(CH3SCH3)3]infinity, containing helical chains constructed by flower-basket-shaped Cu4I4 clusters

A new route for the synthesis of coordination compounds with dimethyl sulfide ligand is reported; the prepared compound is a novel 2-D framework with a 1-D right-handed and left-handed helical structure, which is unique in the sense that the fundamental units are unusual Cu4I4 clusters.     

六棱柱型金属团簇化合物W2Ag4S8(dppy)4的纳秒光限幅特性

新合成了一种金属团簇化合物W2Ag4S8(dppy)4,(分子式为C68H56Ag4N4P4S8W2)并用X-射线单晶衍射结构分析方法测定了其晶体结构.单晶X-射线衍射数据表明这种金属团簇化合物具有六棱柱型.在纳秒激光脉冲作用下研究了W2Ag4S8(dppy)4的二甲基甲酰胺(DMF)溶液的光限幅特性.实验结果表明W2Ag4S8(dppy)4的DMF溶液在放置一段时间后光限幅特性明显优于新配制的DMF溶液,其光限幅特性明显强于C60甲苯溶液,表现出其具有较强的光限幅特性.为了研究W2Ag4S8(dppy)4的光限幅机制及光限幅特性在放置一段时间后发生变化的原因,又做了非线性散射和泵浦探测实验,并对其光限幅机制和光限幅特性在放置一段时间后发生变化的原因进行了分析.     

双调和方程特征值问题

该文讨论Navier边值条件下的双调和特征值问题 Δ²u=λa(x)u+f(x, u), x∈ Ω, u=Δu=0, x∈ Ω, 解的存在性, 其中Ω R^N(N ≥ 5)是有界光滑区域, Δ²为双调和算子, 权函数a(x)> 0 a. e. 于Ω, 且 a(x)∈L^r(Ω) (r ≥ N/4). 应用变分方法, 得出了在f(x, u)=0的情况下方程的第二特征值, 并研究了它的结构. 同时在f(x, u) 满足一定的条件下, 得出了共振与非共振情形下方程非零解的存在性 .     

关于广义分次局部上同调的tame性的一个结果

设R=＋n∈N0Rn（R=R0[R1]）是分次Noether交换环,（R0,m0）是一个局部环,R＋=＋n∈NRn;设N是一个有限生成Z-分次R-模,这里N、N0、Z分别表示全体正整数、全体非负整数和全体格致所构成的集合．令h=sup{i∈Z｜HR＋^i（N）不是Artin模}．Dibaei和Nazari证明了HR＋^h（N）是tame模．我们将该结果推广到了广义分次局部上同调模的情形．     

Duality and Penalization in Optimization via an Augmented Lagrangian Function with Applications

This paper aims to establish duality and exact penalization results for the primal problem of minimizing an extended real-valued function in a reflexive Banach space in terms of a valley-at-0 augmented Lagrangian function. It is shown that every weak limit point of a sequence of optimal solutions generated by the valley-at-0 augmented Lagrangian problems is a solution of the original problem. A zero duality gap property and an exact penalization representation between the primal problem and the valley-at-0 augmented Lagrangian dual problem are obtained. These results are then applied to an inequality and equality constrained optimization problem in infinite-dimensional spaces and variational problems in Sobolev spaces, respectively. The first author was supported by the Research Committee of Hong Kong Polytechnic University, by Grant 10571174 from the National Natural Science Foundation of China and Grant 08KJB11009 from the Jiangsu Education Committee of China. The second author was supported by Grant BQ771 from the Research Grants Council of Hong Kong. We are grateful to the referees for useful suggestions which have contributed to the final presentation of the paper.     

Some classes of analytic and multivalent functions involving a linear operator

By using a linear operator, which is defined here by means of the Hadamard product (or convolution), the authors introduce some new classes of analytic and multivalent functions in the open unit disk and investigate their inclusion relationships and convolution properties. Integral transforms of functions in these classes are also discussed.