关于一个素数和一个素数的k次方和问题

设k≥2,Hk表示一个正整数n的集合,使对任意的正整数q,同余方程a+b2三n(modq)在模q的既约剩余系中有解a,b.Dk(N)表示n≤N,n∈Hk,但不能表成p1+p22=n的数的个数,其中p1,p2表示素数.则在GRH下,Dk(N)<<N1-1/k(h(k)+1)+ε,这里k=2,3;h(2)=2,h(3)=8.     

Discrete dihedral-angle modulation in porphyrin wheels adsorbed on Cu(1 0 0) observed by scanning tunneling microscopy

Conformations of two dodecameric porphyrin wheels adsorbed on a Cu(1 0 0) were probed by using scanning tunneling microscopy (STM). Whereas a wheel consisting of six meso-meso linked diporphyrins was detected as uniform ring structure, several different images with three discrete molecular heights were detected for a wheel consisting of six meso-meso, β-β,β-β triply-linked planar diporphyrins. These results indicate that the former has a conformation similar to that in a free space, while the latter has various conformations with respect to orientation of planar diporphyrin units toward the metal surface. Several discrete STM images of the latter have been interpreted in terms of possible eight conformations, which vary as to relative orientation of neighboring diporphyrin units.     

Experimental determination of rheological properties of polydimethylsiloxane

A series of linear polydimethylsiloxane of different molecular weight and with reduced polydispersity were prepared by partial fractionation of commercial products. The rheological functions, i.e. zero shear viscosity (η₀), first and second normal stress coefficients (Ψ₁₀ and Ψ₂₀), of the materials were experimentally measured by conventional rotational rheometers and by a rotation rod apparatus. The relationships between molecular structure (molecular weight and polydispersity index) and rheological functions are presented and discussed on the basis of equations proposed in the literature. Zero shear viscosity data conform to the well-known dependence on a power 3.5 of molecular weight. However, a consistently stronger influence of molecular weight over Ψ₁₀ and Ψ₂₀ is found. The influence of polydispersity over Ψ₁₀ is also analyzed.     

Molecular recognition of ammonium ion by tetrahomodioxacalix[4]biscrown

The first theoretical study on the conformational features and the complexation behaviors upon ammonium ion binding of tetrahomodioxacalix[4]biscrown-4 has been performed using molecular dynamic simulations and density functional theory. The conformational analyses show that the relative stability and the geometry of the ammonium ion complexes are directly contributed by the number of putative hydrogen bonds between oxygen lone pairs and ammonium hydrogens.     

Ar-buffer-assisted deposition of Cu13 on Cu(1 1 1) surfaces

In this paper, the deposition of Cu₁₃ onto Cu(1 1 1) surface through argon buffer layers was investigated by molecular dynamics (MD) simulations. The interactions between Cu-Cu, Cu-Ar, and Ar-Ar were described by Finnis-Sinclair (FS) tight-binding potential and L-J potential, respectively. The impact energy was chosen to be 2-6 eV/atom in order to compare with experimental results. It was observed that with Ar-buffer layers, the Cu cluster deposited on the surface may retain its free cluster symmetry (I_h). Whereas, on originally bare Cu surface, the deposited Cu cluster lost its original symmetry completely and was recrystalized to have the same fcc structure as the substrate. The Ar-buffer dissipates most of the translational energy of the incident cluster. Therefore, it prevents the cluster from being overheated upon impinging. Furthermore, the interaction between Ar and Cu benefits the confinement of the cluster structure. Our study shows that with Ar-buffer layers, the lateral spread of deposited clusters is 20% smaller than that on the bare Cu surface. This is consistent with the experimental findings.     

Structure, dsingle-particle and many-particle coefficients of Lennard—Jones liquid Al

We investigate the effects of temperature and density on the single-particle and many-particle coefficients as well as on the structures of homogenous systems in which the particles are assumed to interact via a continuous soft sphere potential in the microcanonical ensemble. The pair distribution function and therefore the structures of the systems studied are affected by temperature close to and above the melting point through migrations of atoms from the first shell in the pair distribution function. The dynamics of atomic pairs in the short-time regime in liquid aluminium may be said to be governed by the potential of mean force, which depends on the static structure of liquid Al at all investigated temperatures. A polynomial dependence ofD on density and temperature was observed in contradiction to Arrhenius law. The shear viscosities of the systems studied are largely nonlinear. It was observed that the soft sphere potential used in our calculations overestimates the Stoke-Einstein relation.     

Bandgap engineering of self-assembled InAs quantum dots with a thin AlAs barrier

We investigate the effects of a thin AlAs layer with different position and thickness on the optical properties of InAs quantum dots (QDs) by using transmission electron microscopy and photoluminescence (PL). The energy level shift of InAs QD samples is observed by introducing the thin AlAs layer without any significant loss of the QD qualities. The emission peak from InAs QDs directly grown on the 4 monolayer (ML) AlAs layer is blueshifted from that of reference sample by 219 meV with a little increase in FWHM from 42–47 meV for ground state. In contrast, InAs QDs grown under the 4 ML AlAs layer have PL peak a little redshifted to lower energy by 17 meV. This result is related to the interdiffusion of Al atom at the InAs QDs caused by the annealing effect during growing of InAs QDs on AlAs layer.     

Surface reconstructions and phase transitions on the GaAs(111)B surface

The (111)B surface of GaAs has been investigated using scanning tunneling microscopy (STM) and a number of different reconstructions have been found at different surface stoichiometries. In accordance with electron diffraction studies, we find the series (2 × 2), (1 × 1)_LT, ( ) and (1 × 1)_HT with increasing annealing temperature, corresponding to decreasing surface As concentration. The (1 × 1)_LT is of particular interest, since it only occurs in a narrow temperature window between the two more established reconstructions, the (2 × 2) and the ( ). We find the (1 × 1)_LT to take the form of a mixture of the local structures of both the (2 × 2) and ( ) phases, rather than having a distinct structure. This is behaviour consistent with a kinetically limited system, dominated by the supply of As adatoms to the surface, and may be an example of a continuous phase transition. Above the (1 × 1)_LT transition, atomic resolution images of the ( ) surface reveal only a three-fold symmetry of the hexagonal structural units, brought about by inequivalent surface bonding due to the 23.4° rotation of the surface unit cell relative to the substrate. This is responsible for the disorder found in the ( ) reconstruction, since the structure may form in one of two domains. At lower surface As concentration, the (1 × 1)_HT surface adopts a structure combining small domains of a 19.1° structure and random disorder. There is no apparent similarity between the (1 × 1)_LT and (1 × 1)_HT structures, which may be due to our measurements being conducted at room temperature and without an As flux to control the surface As concentration.     

Molecular Recognition with Model Systems

How structures fit together is the principal domain of molecular recognition, and current studies are evolving from the host–guest chemistry of ions to interactions between two molecules. Recent advances in the synthesis of sizable concave molecules, especially those featuring convergent functional groups, make it possible to bind smaller convex structures with considerable selectivity. One result is that hydrogen bonding can be addressed in model systems. The present review emphasizes the use of cleftlike structures as a means of probing the forces involved in nucleic acid recognition. The application of such molecules to the catalysis of chemical reactions, particularly those involved in self-replicating systems, is also described. Some implications for future pharmaceutical agents are suggested as a result of access to synthetic receptors for biologically relevant targets.     

分子结构振动固有频率与链烷烃热力学性质的定量关系

用分子结构固有频率和分子中的甲基数作为分子结构信息指数,建立链烷烃分子结构与热力学性质的双参数QSPR模型.该模型用于18种链烷烃分子的标准生成焓、标准熵和标准生成自由能实验值的回归分析,得到相关程度大于0.999的标准生成焓、标准熵回归方程和相关程度大于0.99的标准生成自由能回归方程.所得方程用于67种链烷烃的标准生成焓、标准熵和标准生成自由能预测,结果与实验值的相关程度均大于0.9950.