某类解析函数的Fekete-Szego¨不等式

作者引入一个新的解析函数类B（λ，α，σ，β），我们讨论了B（λ，α，σ，β）的Ｆｅｋｅｔｅ-Ｓｚｅｇ¨ｏ 不等式，得到了准确结果，从而推广了一些作者的相关结果。     

Theoretical study on the reaction mechanism of the alcoholysis of isocyanates

In this paper, the reactions of HNCO or CH₃NCO with methanol have been studied using the ab initio MO method. The geometries of the reactants and products have been optimized by the energy gradient method. The calculated results are in accordance with experiment. Using Powell's method, by the minimization of the Euclidean norm σ of the gradient, the structures of the transition state (TS ) for the two reactions were obtained. The structures have been further confirmed as TS by finding that there is one and only one negative eigenvalue for their force constant matrix. The imaginary vibration mode corresponding to the TS was also discussed. The calculated activation barriers of these two reactions are 96.02 and 95.13 kJ/mol, respectively. It can be concluded that the alcoholysis reaction of isocyanate is a nucleophilic addition reaction with methanol as an electronic donor and isocyanate as an acceptor and that the hydroxyl hydrogen of CH₃OH plays an important role in the reaction.     

Evolution of spin-dependent atomic wave packets in a harmonic potential

We have investigated theoretically the evolution of spin-dependent atomic wave packets in a harmonic magnetic trapping potential. For a Bose-condensed gas, which undergoes a Mott insulator transition and a spin-dependent transport, the atomic wavefunction can be described by an entangled single-atom state. Due to the confinement of the harmonic potential, the density distributions exhibit periodic decay and revival, which is different from the case of free expansion after switching off the combined harmonic and optical lattice potential.     

Dnd点群的几点释疑

Point group in crystallography is one of the important subjects in structural chemistry.Some topics are very difficult to understand.To name a few, why does point group of D_2d belong to tetragonal? Why are D_4d and D_6d not included in 32 kinds of crystallographic point groups? The two questions are easy to answer if we understand the following topic:for the D_nd point group, when n is odd, it contains an I_n symmetry axis; when n is even, it contains an I_2n symmetry axis.In this work, graphic method and matrix method are adopted to clarify why the D_nd point group includes an S_2n axis, and thus give explanations that D_2d belongs to tetragonal as well as D_4d and D_6d are not included in 32 kinds of crystallographic point groups.     

对抛式冷原子陀螺仪中原子运动轨迹的控制

冷原子具有很小的速度,很窄的速度分布以及良好的相干特性,利用冷原子物质波干涉特性可实现原子干涉仪,具有萨格奈克效应的原子干涉仪即原子陀螺仪,可精密测量转动速率. 冷原子轨迹的精确控制对提高冷原子陀螺仪的测量精度有着重要的意义,文章报道了利用直接数字频率综合器,实现对双向对抛冷原子运动轨迹的精确控制. 关键词： 冷原子 原子陀螺仪 直接数字频率综合器     

复杂网络局部结构的涌现:共同邻居驱动网络演化

在对真实网络的小世界和无标度特性进行了大量深入考量之后,最近的研究热点开始转移到更加细致的局部结构.实证数据显示,大量真实网络具有幂律的低阶集团度分布.这一普适的规律,无法由富者愈富以及熟人推荐的网络生长机理再现.本文提出一种由共同邻居驱动的网络演化模型,该模型能够重现实证研究所观察到的幂律集团度分布,暗示共同邻居驱动是复杂网络局部结构涌现形成的内在机理. 关键词： 复杂网络 演化模型 集团度分布 共同邻居     

6,7-二氰基联吡啶喹喔啉的Eu~Ⅲ、Tb~Ⅲ配合物的合成和晶体结构(英文)

6,7-二氰基联吡啶喹喔啉(DICNQ)分别与Eu(NO3)3.6H2O、Tb(NO3)3.6H2O水热反应产生两个新的三价稀土金属-有机配合物[Eu(DICNQ)2(NO3)3].(CH3CN)2(1)和[Tb(DICNQ)(NO3)3]2(2)。X射线单晶衍射研究表明化合物1结晶于单斜晶系,Cc无心空间群,晶胞参数a=1.157 7(6)nm,b=3.193 4(2)nm,c=1.106 6(6)nm,β=97.633(2)°,V=4.055(4)nm3,Z=4,Mr=984.63,Dc=1.613 g.cm-3,μ=1.623 mm-1,F(000)=1 952,S=1.035,T=293(2)K。最终精修结果为:R=0.033 5,wR=0.078 1,I>2σ(I)的点为6 467个。化合物2结晶于三斜晶系,P1空间群,晶胞参数a=0.871 1(3)nm,b=0.890 8(3)nm,c=1.544 9(5)nm,α=80.852(9)°,β=84.217(9)°,γ=65.475(7)°,V=1.076 0(6)nm3,Z=1,Mr=1 254.44,Dc=1.936 g.cm-3,μ=3.356 mm-1,F(000)=604,S=1.026,T=293(2)K。最终精修结果为:R=0.036 8,wR=0.095 6,I>2σ(I)的点为3 697个。化合物1中孤立中性分子之间具有C-H…O氢键作用,而化合物2的晶体结构既包含配体间的π…π堆积作用又有分子间C-H…N和分子内C-H…O氢键作用。     

Diversity of lanthanide(III)-organic extended frameworks with a 4,8-disulfonyl-2,6-naphthalenedicarboxylic acid ligand: syntheses, structures, and magnetic and luminescent properties

A sulfonate-carboxylate ligand, 4,8-disulfonyl-2,6-naphthalenedicarboxylic acid (H(4)-DSNDA), and eight new lanthanide coordination polymers {[Pr(4)(OH)(4)(DSNDA)(2)(H(2)O)(12)](H(2)O)(10)}(n) (1), [Ln(H(2)-DSNDA)(0.5)(DSNDA)(0.5)(H(2)O)(5)](n) (Ln = La(2), Nd(3), Sm(4), Eu(5), Gd(6), and Dy(7)), and {[Er(H-DSNDA)(H(2)O)(4)](H(2)O)}(n) (8) have been synthesized. Detailed crystal structures of these compounds have been investigated. Compound 1 has a 3D framework featuring the unique cubane-shaped [Pr(4)(μ(3)-OH)(4)] clusters and is a binodal 4,8-connected network with (4(16)·6(12))(4(4)·6(2))(2) topology. Compounds 2-7 are isostructural and have 2D layered structures. Compound 8 is also a 2D layer but belongs to different structural types. The luminescence behavior of compound Eu(5) shows that the π-rich aromatic organic ligands efficiently transfer the absorbed light energy to the Eu(III) ions, thus enhancing the overall luminescent properties of compound Eu(5). The magnetic properties of all compounds except for the diamagnetic La(2) compound have been investigated. In addition, elemental analysis, IR spectra, and thermogravimetric analysis of these compounds are also described.     

Effects of irradiation on epidermis ultrastructure of fresh day-lily flowers

Effects of gamma irradiation on epidermis ultrastructure of fresh day-lily (Hemerocallis fulva L.) flowers were studied by scanning electron microscopy. Damaged cells of petal epidermis were found in the day-lily flowers irradiated with 1.0 or more kGy. The cells damaged by irradiation broke and lost cytoplasm, and therefore, showed a serious shrinkage. The compartment of the cells disappeared in injury. With 1.0 or more kGy irradiation, the damaged cells were also observed on the epidermis of the sepal and receptacle cells. The injury was found in a small spot or area on the epidermis of the sepal as well as the petal. The injury spot of the sepal epidermis was shown to resemble ashes and no cell wall of the epidermis was found. On the other hand, the epidermis of the receptacle was torn away with 1.0 or more kGy irradiation. The damaged spots of the receptacle epidermis also appeared after irradiation. Irradiation was not recommended for treating the fresh day-lily flowers as vegetables since the dosage (2.0 or more kGy) needed for inhibiting the flower blooming as shown in our previous works, caused injury on the epidermis of the flowers.     

Preference of online users and personalized recommendations

In a recent work [T. Zhou, Z. Kuscsik, J.-G. Liu, M. Medo, J.R. Wakeling, Y.-C. Zhang, Proc. Natl. Acad. Sci. 107 (2010) 4511], a personalized recommendation algorithm with high performance in both accuracy and diversity is proposed. This method is based on the hybridization of two single algorithms called probability spreading and heat conduction, which respectively are inclined to recommend popular and unpopular products. With a tunable parameter, an optimal balance between these two algorithms in system level is obtained. In this paper, we apply this hybrid method in individual level, namely each user has his/her own personalized hybrid parameter to adjust. Interestingly, we find that users are quite different in personalized hybrid parameters and the recommendation performance can be significantly improved if each user is assigned with his/her optimal personalized hybrid parameter. Furthermore, we find that users’ personalized parameters are negatively correlated with users’ degree but positively correlated with the average degree of the items collected by each user. With these understandings, we propose a strategy to assign users with suitable personalized parameters, which leads to a further improvement of the original hybrid method. Finally, our work highlights the importance of considering the heterogeneity of users in recommendation.