A planar chiral non-metallocenic analogue of the most popular N,N-dimethylbenzylaminate palladacycle

A racemic planar chiral tertiary amine pCp-CH₂NMe₂ (HL¹, pCp = [2.2]paracyclophane-4-yl) was prepared by aminomethylation of the bromide pCp-Br with Eschenmoser’s salt. Direct cyclopalladation of this new ligand with palladium(II) acetate results in the formation of the racemic CN-dimer rac-3 in a moderate yield of 64%. The enantiomerically pure dimer (S_pl, S_pl)-3 was obtained by the standard procedure of racemic palladacycle resolution using (S_C)-prolinate as a chiral derivatising agent. The ortho-palladated structure, absolute configuration of the chiral plane and stereochemical peculiarities of the new CN-palladacycle were established by means of NMR spectroscopy and an X-ray diffraction study of its (S_C)-prolinate derivative.     

Sn和Pb单掺杂Al4小团簇的理论研究

在CCSD(T)/aug-cc-pVTZ&;CEP-121G//B3LYP/6-311+G(d)&;LANL2DZ水平上, 研究了由更高周期的Sn和Pb单掺杂Al4团簇形成的五原子含铝体系XAl4(X=Sn, Pb), 确定了体系的低能异构体, 分析了关键异构体的结构和稳定性. 研究结果表明, 与SiAl4及GeAl4的基态平面四配位Si/Ge结构所不同, 等价电子的SnAl4和PbAl4体系的基态结构不是平面四配位Sn/Pb, 而是平面四配位Al, 其中杂原子Sn/Pb采取二配位方式, 此外, Sn/Pb采取三配位方式的非平面结构的稳定性也要优于平面四配位Sn/Pb结构.     

围长至少为4的平面图的邻点可区别边色数

图G的邻点可区别边染色是G的正常边染色,使得每一对相邻顶点有不同的颜色集合．G的邻点可区别边色数X＇a（G）是使得G有一个k-邻点可区别边染色的最小正整数七．本文证明了：若G是围长至少为4且最大度至少为6的平面图,则X＇a（G）≤△＋2．     

Effects of high order deformations on the strength of planar lattice materials

Lattice materials have been attractive over the last decade for use as load-carrying structures, energy absorbing elements and heat exchanging structures because of their excellent mechanical properties and multifunctional characters. However, the quantitative analysis accounting for high order deformations upon the collapse of lattice materials, which is important for their applications, has not been reported. An analytical investigation of yield surfaces with respect to the high order deformations was carried out for two typical planar lattice materials： triangular and Kagome lattices separately. The analytical results were validated by the finite element method （FEM） simulations. It was found that the effect of high order deformation on the yield strength increases with the relative density. The bending effect of the Kagome lattice is more obvious than that of the triangular one with the same relative density and stress state. The yield strength of the Kagome lattice calculated by neglecting the bending effect overestimates the result by more than 10% when the relative density is higher than about 11.1%, which may not be ignored in engineering applications. The yielding surfaces of the two lattice materials demonstrated in the paper also confirm the analytical results.     

Deflection criterion of a crack approaching a bi-material interface obliquely

Deflection criterion for oblique cracks terminating at a bi-material interface was established numerically based on a remote loading condition where the crack deflection event took place well within the K-dominant stress field. The criterion was described in terms of the ratio of the energy release rate of a deflected crack (G _d) to the maximum energy release rate of a penetrated crack (). The criterion was markedly more conservative than the existing solution based on wedge loading which did not converge with respect to limited number of a/L ratios in the literature (a is the size of the putative crack; L is the loading distance). Further, the criterion established herein for the cracks slightly oblique from the normal direction to the interface was more conservative than the crack normal to the interface.     

Simultaneous measurements of equivalence ratio and flame structure in multipoint injectors using PLIF

Simultaneous measurements of PLIF-kerosene and PLIF-OH have been successfully performed in a multipoint injection system for various overall equivalence ratio, air inlet temperature between 480 and 730 K and pressure up to 2.2 MPa. Single shot 2D-maps of the spatial distribution of kerosene vapour and OH radical in the combustor have been recorded with good signal-to-noise ratio. Results show that depending on the split between the pilot and the main injectors, the flame front exhibits a single or a double structure. Good spatial correlation between the repartition of the kerosene vapour and the position of the flame front was observed; in particular, no “dark zone” is observed between the fuel and the flame front. As temperature and pressure increase, fuel evaporation improves and the spatial distribution of OH radical becomes more homogeneous in the combustor, suggesting a partially-distributed combustion. To cite this article: M. Orain et al., C. R. Mecanique 337 (2009).     

Mixing Layers in Sink Flow: Effect of Length of Flight on Mixing in a Channel Downstream

We have experimentally and analytically studied transport of a passive scalar in the wake of a thin flat plate located at the centerline of a planar contraction with flat walls. The constant Launder parameter in the contraction, K = 6.25 ×10^− 6, was twice the value required for a turbulent boundary layer to relaminarize. In addition to the mixing analysis inside the contraction, layer mixing is also investigated downstream, where the flow continues inside a constant cross-section channel. In order to generate the passive scalar, the airflow above the plate was heated and the temperature stratification in the wake was traced by measuring the temperature field using constant current anemometry. Using different plate lengths, we found that the degree of mixing, obtained at a given position in the straight channel, is a function of the distance from the plate trailing edge to the contraction outlet. For a plate which does not protrude into the straight channel, we demonstrate the existence of an optimal trailing edge-contraction outlet distance that results in the lowest possible degree of mixing at a given downstream position in the straight channel. This finding is also supported by a semi-empirical relationship based on our developed self-similar solution for mixing layers in planar contractions.     

A Locking-Free Scheme of Nonconforming Rectangular Finite Element for the Planar Elasticity

In this paper, the authors present a locking-free scheme of the lowest order nonconforming rectangle finite element method for the planar elasticity with the pure displacement boundary condition. Optimal order error estimate, uniformly for the Laméconstant $\lambda\in(0,\infty)$ is obtained.     

ON THE LIMIT CYCLES OF PLANAR AUTONOMOUS SYSTEMS

91. IntroductionThe theory of ~ cycles is a very aCtive research field of qualitative theory of ordinary~nilal equationS. There have been many mathemsticians studying the nonetistence,~ence and piqueness of ~ cycles for plane systems, and most atteattiope were paidto some special formS (see [2-4, 610] and the references cited therein)' As we know, for thegeneral system on the Planei = p(z,g), b = Q(z,g), (1.1)where P, Q: RZ - R are continuouSly dmerentiable, there are some well-knoWn res…     

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics (MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Amp`ere law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.