Dinuclear gold (I)-di-N-heterocyclic carbene complexes: syntheses,structure, density functional theory calculation and photoluminescence study

The synthesis and characterizations for a series of dinuclear gold (I)-di-NHC complexes, 1–8 through the trans-metalation method of their respective silver (I)-di-NHC complexes, i–viii are reported (where NHC = N-heterocyclic carbene). The successful complexation of a series of unusual non-symmetrical and symmetrical di-NHC ligands, 3,3'-(ethane-1,2-diyl)-1-alkylbenzimidazolium-1'-butylbenzimidazolium (with alkyl = methyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, benzyl) with the gold (I) ions are suggested by elemental analysis, Fourier transform-infrared, ¹H- and ¹³C-NMR data. The ¹³C-NMR spectra of 1–8 show a singlet sharp peak in the range of 190.00–192.00 ppm, indicating the presence of a carbene carbon that bonded to the gold (I) ion. From single crystal X-ray diffraction data, the structure of complex 6 with the formula of [di-NHC-Au (I)]₂·2PF₆ is obtained [where NHC = 3,3'-(ethane-1,2-diyl)-1-hexylbenzimidazolium-1'-butylbenzimidazolium]. The photophysical study in solid state of 6 displays an intense photoluminescence with a strong emission maxima, λ_em = 480 nm, upon excitation at 340 nm at room temperature. Interestingly, the emission maximum at 77 K shows a structural character with a strong peak at 410 nm, a medium at 433 nm and a weak at 387 nm, accompanied by a tail band to about 500 nm.     

Harmonic 2-forms and positively curved 4-manifolds

Science China Mathematics - We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a strengthened Kato type inequality, then it is definite. We also discuss...     

On a class of new and practical performance indexes for approximation of fold bifurcations of nonlinear power flow equations

Efficient measurement of the performance index (the distance of a loading parameter from the voltage collapse point) is one of the key problems in power system operations and planning and such an index indicates the severity of a power system with regard to voltage collapse. There exist many interesting methods and ideas to compute this index. However, some successful methods are not yet mathematically justified while other mathematically sound methods are often proposed directly based on the bifurcation theory and they require the initial stationary state to be too close to the unknown turning point to make the underlying methods practical.This paper first gives a survey of several popular methods for estimating the fold bifurcation point including the continuation methods, bifurcation methods and the test function methods (Seydel's direct solution methods, the tangent vector methods and the reduced Jacobian method) and discuss their relative advantages and problems. Test functions are usually based on scaling of the determinant of the Jacobian matrix and it is generally not clear how to determine the behaviour of such functions. As the underlying nonlinear equations are of a particular type, this allows us to do a new analysis of the determinants of the Jacobian and its submatrices in this paper. Following the analysis, we demonstrate how to construct a class of test functions with a predictable analytical behaviour so that a suitable index can be produced. Finally, examples of two test functions from this class are proposed. For several standard IEEE test systems, promising numerical results have been achieved.     

双曲分布及其在VaR模型分析中的应用

传统的计算V aR的R iskM etrics方法不能对市场风险分布的“厚尾”现象给出较为满意的刻画和计算方法.本文引入双曲分布及其算法并将双曲分布应用到V aR模型的计算之中,事实上通过对股票市场的实证研究表明,股票市场数据呈厚尾现象,用双曲分布对数据的拟合要比R iskM etrics方法假定的正态分布更符合金融市场数据的实际情况,故本文的结论与方法对金融风险管理和其他金融建模是有价值的.     

Novel model of FM-noise conversion in a UMZI using RF external phase modulation of lasers: Theoretical and experimental results

In this paper, we propose and demonstrate a new and original model for theoretical calculation and experimental measurement of the noise power spectral density (NPSD) in phase-modulated optical links. The phase modulation is operated in the RF frequency range by an external phase modulator. The NPSD is derived for the first time in interferometric systems, by considering all effects such as the 1/f FM noise of the laser and white noise applied to light from a 1550 nm DFB laser, with phase modulation. The results show for the first time the influence of the phase modulation index, modulation frequency and interferometric delay in the phase-to-intensity noise conversion. The experimental and simulation results of conversion of FM-noise to intensity noise in an optical link by considering the external RF phase modulation are shown with good agreement.     

An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss

A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given.     

Synthesis of Highly Functionalized Isoxazolinediones from One-pot Reaction of Alkylidene Meldrum ’s Acid with Alkyl Isocyanides in the Presence of Arylhydroxylamines

Alkyl isocyanides undergo a smooth reaction with alkylidene Meldrum’s acids in the presence of arylhydroxylamines to produce N ¹-alkyl-2-(3,5-dioxo-2-aryltetrahydro-4-isoxazolyl)alkanamides in high yields.     

A novel synthesis of 5-perfluorophenyl 4,5-dihydro-1H-pyrazoles in THF or water

5-Perfluorophenyl 4,5-dihydro-1H-pyrazoles were synthesized from 1,3-dipolar cycloaddition reaction of perfluorobenyl 2,4,6-triisopropylbenzenesulfonylhydrazone and α,β-unsaturated carbonyl compounds or acrylonitrile in THF or water. It was worthy to note that better results were obtained when water was employed as the solvent, which was considered as an effective, economic and environmentally friendly method to synthesize these pyrazole derivatives.