A Germylene Supported by Two 2-Pyrrolylphosphane Groups as Precursor to PGeP Pincer Square-Planar Group 10 Metal(II) and T-Shaped Gold(I) Complexes

An efficient synthesis of 2-di-tert-butylphosphanylmethylpyrrole (HpyrmPtBu₂), by treating 2-dimethylaminomethylpyrrole (HpyrmNMe₂) with tBu₂PH at 135 °C in the absence of any solvent, has allowed the preparation of the new PGeP germylene Ge(pyrmPtBu₂)₂ ( 1 ), by treating [GeCl₂(dioxane)] with LipyrmPtBu₂, in which the Ge atom is stabilized by intramolecular interactions with one (solid state) or both (solution) of its phosphane groups. Reactions of germylene 1 with Group 10 metal dichlorido complexes containing easily displaceable ligands have led to [MCl{κ³P,Ge,P-GeCl(pyrmPtBu₂)₂}] [M=Ni ( 2 ), Pd ( 3 ), Pt ( 4 )], which have an unflawed square-planar metal environment. Treatment of germylene 1 with [AuCl(tht)] (tht=tetrahydrothiophene) rendered [Au{κ³P,Ge,P-GeCl(pyrmPtBu₂)₂}] ( 5 ), which is a rare case of a T-shaped gold(I) complex. The hydrolysis of 5 gave the linear gold(I) derivative [Au(κP-HpyrmPtBu₂)₂]Cl ( 6 ). Complexes 2 – 5 contain a PGeP pincer chloridogermyl ligand that arises from the insertion of the Ge atom of germylene 1 into a M−Cl bond of the corresponding metal reagent. The bonding in these molecules has been studied by DFT/NBO/QTAIM calculations. These results demonstrate that the great flexibility of germylene 1 makes it a better precursor to PGeP pincer complexes than the previously known germylenes of this type.     

Bent Phosphaallenes With “Hidden” Lone Pairs as Ligands

Phosphaheteroallenes R−P=C=L, with L = N-heterocyclic carbenes (NHCs), can be viewed to a certain extent as phosphaisonitriles stabilized with NHCs, R−P=C:←L. The suitability of these molecules as ligands for coinage-metal ions was investigated and coordination through the central carbon center was observed in most cases. A combination of experiments, spectroscopic methods, and DFT calculations indicates the presence of a hidden electron pair at the carbon center of R−P=C:←L. Remarkably, this lone pair also inserts intramolecularly in C−H bonds showing the carbene-type reactivity which is expected for phosphaisonitriles.     

Statistical Fluctuation of Linear-System Driven by Colored Noise

The Brownian motion driven by colored noise in the harmonic oscillator potential is studied, and the "best Fokker-Planck equationn" is proposed. The analytical formulse of the second moments of coordinate and velocity are obtained. The fluctuation behavior of a system under influence of the correlation time of colored noise is discussed.     

On the sum of the Laplacian eigenvalues of a tree

Given an n-vertex graph G=(V,E), the Laplacian spectrum of G is the set of eigenvalues of the Laplacian matrix L=D-A, where D and A denote the diagonal matrix of vertex-degrees and the adjacency matrix of G, respectively. In this paper, we study the Laplacian spectrum of trees. More precisely, we find a new upper bound on the sum of the k largest Laplacian eigenvalues of every n-vertex tree, where k∈{1,…,n}. This result is used to establish that the n-vertex star has the highest Laplacian energy over all n-vertex trees, which answers affirmatively to a question raised by Radenkovi? and Gutman [10].     

Boundaries of Coxeter Matroids

The purpose of this paper is to introduce, for a finite Coxeter groupW, the mod 2 boundary operator on the space of all Coxeter matroids (also known asWP-matroids) forWandP, wherePvaries through all the proper standard parabolic subgroups ofW(Theorem 3 of the paper). A remarkably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter groupW(Theorem 1) yields a natural definition of the boundary of a Coxeter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroupsQ_iofP(Theorem 2). These results have very natural interpretations in the case of ordinary matroids and flag-matroids (Section 3).     

An analysis of seismic attenuation in random porous media

The attenuation of seismic wave in rocks has been one of the interesting research topics, but till now no poroelasticity models can thoroughly explain the strong attenuation of wave in rocks. In this paper, a random porous medium model is designed to study the law of wave propagation in complex rocks based on the theory of Biot poroelasticity and the general theory of stochastic process. This model sets the density of grain, porosity, permeability and modulus of frame as random parameters in space, and only one fluid infiltrates in rocks for the sake of better simulation effect in line with real rocks in earth strata. Numerical simulations are implemented. Two different inverse quality factors of fast P-wave are obtained by different methods to assess attenuation through records of virtual detectors in wave field (One is amplitude decay method in time domain and the other is spectral ratio method in frequency domain). Comparing the attenuation results of random porous medium with those of homogeneous porous medium, we conclude that the attenuation of seismic wave of homogeneous porous medium is far weaker than that of random porous medium. In random porous media, the higher heterogeneous level is, the stronger the attenuation becomes, and when heterogeneity σ = 0.15 in simulation, the attenuation result is consistent with that by actual observation. Since the central frequency (50 Hz) of source in numerical simulation is in earthquake band, the numerical results prove that heterogeneous porous structure is one of the important factors causing strong attenuation in real stratum at intermediate and low frequency.     

一维新型阶梯函数光子晶体透射特性

研究了阶梯型折射率n22、n11(阶梯分布高度)的大小、对应的分布厚度、不同入射角以及缺陷模对阶梯函数型光子晶体透射特性的影响.由费马原理给出光在函数光子晶体中的运动方程,再由电磁传播理论给出函数光子晶体的传输矩阵,进一步推导出函数光子晶体的透射率以及电场分布的表达式.研究表明,1)随n22,n11大小或者厚度改变,其禁带变宽;2)随光的入射角增加,其禁带变窄;3)当加入缺陷层时,随着缺陷层介质折射率增加,缺陷模强度减小且位置发生红移;4)在函数光子晶体中,缺陷层前电场分布保持不变,而在缺陷层处以及之后的电场强度都明显增强,这不同于常规光子晶体的电场分布仅在缺陷层处局域增强.     

天目铁木愈伤组织和芽苗诱导技术

以天目铁木嫩茎尖为外植体,应用均匀设计法筛选其基部愈伤组织诱导和愈伤组织再分化芽苗的最适合培养基.结果表明,最适合的嫩茎尖基部愈伤组织诱导培养基为1/2DR+TDZ 2.30 mg·L^-1+2,4-D 0.55 mg·L^-1,诱导率为93.5%;愈伤组织芽苗再分化培养基为1/2DR+TDZ 3.30 mg·L^-1+KT 0.70 mg·L^-1,分化率达99.8%以上. 成功建立了天目铁木嫩茎尖离体诱导愈伤组织和芽苗再分化体系,且再生芽苗与野生植株染色体数目相同.     

Palladium‐Catalyzed Intramolecular Carbene Insertion into C(sp3)−H Bonds

A palladium‐catalyzed carbene insertion into C(sp³)?H bonds leading to pyrrolidines was developed. The coupling reaction can be catalyzed by both Pd⁰ and Pd^II, is regioselective, and shows a broad functional group tolerance. This reaction is the first example of palladium‐catalyzed C(sp³)?C(sp³) bond assembly starting from diazocarbonyl compounds. DFT calculations revealed that this direct C(sp³)?H bond functionalization reaction involves an unprecedented concerted metalation–deprotonation step.