几乎无爪图的叶子数较少的生成树

A spanning tree with no more than 3 leaves is called a spanning 3-ended tree.In this paper, we prove that if G is a k-connected(k ≥ 2) almost claw-free graph of order n and σ_(k+3)(G) ≥ n + k + 2, then G contains a spanning 3-ended tree, where σk(G) =min{∑_(v∈S)deg(v) : S is an independent set of G with |S| = k}.     

随机变量和模型及其实证研究

对于敏感性问题,无法采用直接问答的方式进行调查。本文研究了随机变量和模型,并将该模型应用到药店利润率调查中;在具体操作上,为节约经费与提高精度,对每个个体采集两次数据;为进一步满足被调查者对药店利润率的保密心理,对由指数分布生成的随机数,统一加上一个较大的数,以使被调查者看到的随机数远大于药店的毛利百分数。最后根据调查数据,利用随机和模型给出了药店毛利百分数的均值、方差以及分位点。     

Insights into bishemicyanines with long emission wavelengths and high sensitivity in viscous environments

A systematic spectral analysis was presented for bishemicyanine dyes(Hsd and D2) and monohemicyanine dyes(Hs and DSMI).The bishemicyanine dyes displayed long emission wavelengths,large Stokes shifts,low background quantum yields in aqueous solutions and high sensitivity in viscous environments.Better understanding of the structure-property relationships could benefit the design of improved dyes.Computational studies on these dyes revealed the three conjugated forms of bishemicyanines are in equilibrium due to two positive charges and a branched bulk substituent.Bishemicyanines possessed obviously lower rotating energy barrier of C-C bond rotation compared to the monohemicyanine dyes.Moreover,the synergetic effects of the rotation about the φ_4 bond,φ_5 bond and φ_7 bond of the bishemicyanines(Hsd and D2) lead to lower fluorescence quantum yields in a free state and larger fluorescence quantum yield enhancements in viscous environment compared to that of monohemicyanine dyes(Hs and DSMI).The results demonstrate a foundation for interpretation of the behavior of the dyes,thus providing guidelines for future of new bishemicyanine fluorophores with specific applications.     

Explicit ultimate bound sets of a new hyperchaotic system and its application in estimating the Hausdorff dimension

The robust adaptive fuzzy control problem is investigated for a single machine bus system with static var compensator (SVC). This design does not require that speed of the generator rotor and susceptance of the overall system are measured, and also does not require that the parameters of controlled system are known accurately. The fuzzy logic systems are used to approximate the nonlinear functions of the system, and a fuzzy state observer is designed to estimate the speed of the generator rotor and susceptance. By utilizing the fuzzy state observer, and combining the adaptive backstepping technique with adaptive fuzzy control design, an observer-based adaptive fuzzy output-feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and the angle of the generator rotor follows a desired value. Simulation results are presented to show the effectiveness of the approach.     

High yield preparation of a novel tetrakis[ruthenium tris(bipyridine)]calix[6]arene derivative with good diastereomeric purity

In order to develop methodology for the selective preparation of complex molecular structures with potential photochemical or electron transfer functions, the diastereoselective synthesis of multiple ruthenium tris(bipyridine) complexes tethered to a central calix[6]arene core was investigated. Applying recently developed methodology, the resolved precursor cis-Δ-[Ru(bpy)₂(DMSO)Cl]PF₆ (98.6% ee) was efficiently reacted with a novel calix[6]arene derivative, to give the tetrakis[Ru(bpy)₂(bpy′)]calix[6]arene derivative (9) with almost complete retention of absolute stereochemistry at each of the four metal centres, as seen by the unusually strong molar circular dichroism (CD) spectrum. The synthesis of racemic 9 was also carried out, and demonstrated to have an inactive CD spectrum.     

Time-dependent perturbation: a recursive generation of the transition amplitudes between bound states

We present a new expansion of the solution to the time-dependent Schrödinger equation it ∂U/∂t = {H₀ + V(t)}U. A complete set of eigenvectors of H₀ spanning the Hilbert space in which H₀ and V operate is partitioned in two subsets. Transition amplitudes from the first subspace to the second one are calculated by building an adequate series of intermediate representations with respect to the couplings which produce the transition from the model space into its orthogonal complement. These expansions yield a coupling matrix series V⁽ⁿ⁾ for which an iterative solution V⁽ⁿ⁾ → V⁽ⁿ⁺¹⁾ is derived. This solution leads to a recursive numerical treatment of the calculation of transition amplitudes. A simple example, concerning a harmonic oscillator under an intense laser field, is considered using a Fourier analysis of the perturbation.     

Liquid-liquid-vapor phase equilibria behavior of certain binary carbon dioxide + n-alkylbenzene mixtures

The liquid-liquid-vapor loci for the binary mixtures CO₂ + n-hexylbenzene, n-heptylbenzene, and n-octylbenzene were experimentally studied. The compositions and molar volumes of the liquid phases are reported along with the pressure and temperature. For these three alkylbenzenes, the nature of the liquid-liquid-vapor loci experiences a transition, with the CO₂ + n-heptylbenzene mixture exhibiting two separate liquid-liquid-vapor branches.     

Diastereoselective synthesis of β- and γ2-muurolene: a carbocationic pathway from mono- to sesquiterpenes

The Lewis acid catalysed addition of the piperityl chlorides6 to isoprene yields adduct7, which undergoes a cis-stereoselective cyclisation to give the diastereoisomeric muurolene monohydrochlorides8. Treatment with potassium tert-butoxide affords β- and γ₂- muurolene 2.     

A New polyamine synthesis.

A new flexible method for the step by step construction of polyamines based on the reaction of dichloroboranes with azides is reported.