线性递归序列模q

设{u_k}_k≥0为一个线性递归序列．序列{u_k(mod q)}_(k≥0)是周期的,很多人都对其周期有过研究．本文应用二次数域中理想的理论,较完全地刻面了二次线性递归序列模q的周期长度,所获结果加强并推广了Engstrom及Wall的结论．     

用自动凯氏定氮仪测定水中氨氮

用MgO控制预蒸馏水中的pH值,以硼酸溶液为吸收液,用稀硫酸进行中和滴定,用自动凯氏定氮仪测试水中的氨氮,检测下限为1mg/L,相对标准偏差在0.32%~1.04%范围内,加标回收率为96%~104%,并将该法与纳氏试剂比色法和离子色谱法进行了比较。     

Bis[1,1′‐bis(diphenylphosphino)ferrocenium] hexadecachlorotetraantimony(III) ethanol solvate

In the title compound, [Fe(C₁₇H₁₄P)₂]₂[Sb₄Cl₁₆]·C₂H₆O, the Fe atoms lie on inversion centres and the pairs of cyclopentadienyl rings are consequently in a fully staggered conformation. The centrosymmetric anionic clusters formed by [Sb₄Cl₁₆]^4? are surrounded by the cations and are held together by weak C—H?Cl interactions. These formations stack along the a axis to form columns, and the columns are interconnected by another weak C—H?Cl interaction along the b axis.     

An insight into the aromaticity of fullerene anions: experimental evidence for diamagnetic ring currents in the five-membered rings of C(60)(6-) and C(70)(6-)

Reduction of the two "closed" [6,6] methanofullerenes, [6,6]C(61)H(2) (1) and [6,6]C(71)H(2) (5), to the corresponding hexaanions with lithium metal causes the bridgehead-bridgehead bonds to open, at least partially, and this change gives rise to diamagnetic ring currents in the resulting homoconjugated six-membered rings (6-MRs). These new ring currents shield the overlying hydrogen atoms on the methylene bridge and induce upfield shifts of 1.60 and 0.11 ppm in their (1)H NMR resonances, respectively. Analogous reduction of the already "open" [5,6]methanofullerenes, [5,6]C(61)H(2) (2) and [5,6]C(71)H(2) (3 and 4), only slightly enhances the shielding of the hydrogen atoms over the homoconjugated 6-MRs (upfield shifts of 0.13, 0.68, and 0.14 ppm, respectively) but leads to exceptionally strong diamagnetic ring currents in the homoconjugated five- membered rings (5-MRs), as evidenced by dramatic shielding of the hydrogen atoms situated over them (upfield shift of 5.01, 6.78, and 1.63 ppm, respectively). The strongest shielding is seen for the hydrogen atom sitting over the 5-MR at the pole of C(71)H(2)(6)(-) (delta = -0.255 ppm) indicating that the excess charge density is concentrated at the poles.     

Toward separation of nuclear spin isomers with coherent light.

We propose an approach for separating nuclear spin isomers with coherent light and illustrate it by numerical calculations using fulvene as a model system. The scheme employs the equivalence of torsion and interchange of equivalent H-atoms in a class of molecules of which fulvene is a simple example. The exchange symmetry couples with the rotational symmetry to produce a spatial distinction between the two photo-excited nuclear spin isomers, and wavepacket interferometry is applied to separate the species.     

A recipe for evaluating and differentiating cos ϕ expressions

We present a simple recipe for calculating and differentiating cosine of bond angle and dihedral angle expressions. The resulting formulas can be incorporated in a straightforward manner into the bond angle and dihedral angle components of potential energy functions. These formulas rely only on expressions and derivatives of dot products, and, in particular, they avoid cross products as well as excessive Fortran function references. Consequently, the expressions derived in this article can be written compactly and evaluated rapidly.     

The Structure of Silylated Amides: N-Methyl-N-Trimethylsilyltrifluoroacetamide,a Reassignment of structure

The ²⁹Si and ¹⁴N nmr spectra of some bissilylamides and monosilylamides are reported. The results are compared with those for model silylesters, amines and imines. The compound of formula CF₃CONCH₃Si(CH₃)₃ (MSTFA) is shown to exist as a tautemeric mixture of a silylamide and a silylimidate. This assignment is confirmed by ¹³C nmr. A rationale is proposed for the structure directing effect of substituents on the amide carbon atom.     

Nonadiabatic alignment of asymmetric top molecules: rotational revivals

The rotational revival structure of asymmetric top molecules, following irradiation by an intense picosecond laser pulse, is explored theoretically and experimentally. Numerically we solve nonperturbatively for the rotational dynamics of a general asymmetric top subject to a linearly polarized intense pulse, and analyze the dependence of the dynamical alignment on the field and system parameters. Experimentally we use time-resolved photofragment imaging to measure the alignment of two molecules with different asymmetry, iodobenzene, and iodopentafluorobenzene. Our numerical results explain the experimental observations and generalize them to other molecules. The rotational revival structure of asymmetric tops differs qualitatively from the intensively studied linear top case. Potentially it provides valuable structural information about molecules.     

Photoionization dynamics of glycine adsorbed on a silicon cluster: "on-the-fly" simulations

Dynamics of glycine chemisorbed on the surface of a silicon cluster is studied for a process that involves single-photon ionization, followed by recombination with the electron after a selected time delay. The process is studied by "on-the-fly" molecular dynamics simulations, using the semiempirical parametric method number 3 (PM3) potential energy surface. The system is taken to be in the ground state prior to photoionization, and time delays from 5 to 50 fs before the recombination are considered. The time evolution is computed over 10 ps. The main findings are (1) the positive charge after ionization is initially mostly distributed on the silicon cluster. (2) After ionization the major structural changes are on the silicon cluster. These include Si-Si bond breaking and formation and hydrogen transfer between different silicon atoms. (3) The transient ionization event gives rise to dynamical behavior that depends sensitively on the ion state lifetime. Subsequent to 45 fs evolution in the charged state, the glycine molecule starts to rotate on the silicon cluster. Implications of the results to various processes that are induced by transient transition to a charged state are discussed. These include inelastic tunneling in molecular devices, photochemistry on conducting surfaces, and electron-molecule scattering.