Synthesis of Long‐Sought C66 with Exohedral Stabilization

Previously reported fused‐pentagon fullerenes stabilized by exohedral derivatization do not share the same cage with those stabilized by endohedral encapsulation. Herein we report the crystallographic identification of ^#4348C₆₆Cl₁₀, which has the same cage as that of previously reported Sc₂@C₆₆. According to the geometrical data of ^#4348C₆₆Cl₁₀, both strain relief (at the fused pentagons) and local aromaticity (on the remaining sp²‐hybrided carbon framework) contribute to the exohedral stabilization of this long‐sought 66 carbon atom cage.     

Natural Products with Anti‐Bredt and Bridgehead Double Bonds

Well over a hundred years ago, Professor Julius Bredt embarked on a career pursuing and critiquing bridged bicyclic systems that contained ring strain induced by the presence of a bridgehead olefin. These endeavors founded what we now know as Bredt’s rule (Bredtsche Regel). Physical, theoretical, and synthetic organic chemists have intensely studied this premise, pushing the boundaries of such systems to arrive at a better understood physical phenomenon. Mother nature has also seen fit to construct molecules containing bridgehead double bonds that encompass Bredt’s rule. For the first time, this topic is reviewed in a natural product context.     

Filling a Gap: The Coordinatively Saturated Group 4 Carbonyl Complexes TM(CO)8 (TM=Zr,Hf) and Ti(CO)7

Homoleptic Group 4 metal carbonyl cation and neutral complexes were prepared in the gas phase and/or in solid neon matrix. Infrared spectroscopy studies reveal that both zirconium and hafnium form eight-coordinate carbonyl neutral and cation complexes. In contrast, titanium forms only the six-coordinate Ti(CO)₆⁺ and seven-coordinate Ti(CO)₇. Titanium octacarbonyl Ti(CO)₈ is unstable as a result of steric repulsion between the CO ligands. The 20-electron Zr(CO)₈ and Hf(CO)₈ complexes represent the first experimentally observed homoleptic octacarbonyl neutral complexes of transition metals. The molecules still fulfill the 18-electron rule, because one doubly occupied valence orbital does not mix with any of the metal valence atomic orbitals. Zr(CO)₈ and Hf(CO)₈ are stable against the loss of one CO because the CO ligands encounter less steric repulsion than Zr(CO)₇ and Hf(CO)₇. The heptacarbonyl complexes have shorter metal−CO bonds than that of the octacarbonyl complexes due to stronger electrostatic and covalent bonding, but the significantly smaller repulsive Pauli term makes the octacarbonyl complexes stable.     

两类简单多数原则的完全特征

易建新(2005)引入了两类多数投票的社会福利函数,本文用无关备选对象的独立性、匿名性、中立性等公理给出了它们的完全特征.     

液-固色谱流动相体积分数层次结构模型与保留值的关系

用液-固色谱流动相"假定"的体积分数层次结构模型,可得到质点团溶解溶质时的体积分数,进而得到共溶剂中溶质的溶解度、固定相上的溶质吸附量,从而推导出多元流动相组成与溶质保留值的关系.如三元流动相与溶质保留值的关联式为:lnk'=φB3lnk'B3 φB2lnk'B2 φB1lnk'B1 φB1(φB20.5 φB30.5)ln(q)(外Ⅱ) φB30.5φB21.0φB11.5ln(q)(外Ⅰ),经实验数据拟合,本式较其他关联式略胜一筹.     

Structural,electronic, magnetic properties and critical behavior of the equiatomic quaternary Heusler alloy CoFeTiSn

In this article, we study the exchange coupling interactions of the equiatomic quaternary Heusler alloy CoFeTiSn, using the two methods: Monte Carlo simulations and the ab-initio method. In a first step, we use the ab-initio calculations to investigate the structural, the electronic and the magnetic properties of this alloy under the GGA method. The analysis of the energy dependence on the lattice parameter a (Å) of the equiatomic quaternary Heusler alloy CoFeTiSn, is discussed for different atomic configurations. The ferromagnetic configuration is found to be the more stable one, with an optimal lattice parameter value 6.00 Å. On the other hand, the electronic structure results show that the compound CoFeTiSn exhibits a half-metallic character and a spin polarization of 100% at the Fermi-level. The total magnetic moment of this alloy is found to be equal to 2.00 μ_B which follows the Slater Pauling rule. Our results support the half-metallic behavior of the studied material. In order to complete this study, we reported the dependence of the critical transition temperature as a function of the parameter α of the equiatomic quaternary Heusler alloy CoFeTiSn. We showed that the critical temperature increases almost linearly with an increase of the values of the parameter α.     

Quantum fractionalism: The Born rule as a consequence of the complex Pythagorean theorem

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in orthogonal projections from the complex line of a quantum state to eigenspaces of an observable. Unit total probability corresponds to a complex Pythagorean theorem: the measure of a subset of the complex line is the sum of the measures of its projections on all eigenspaces.Postulating the existence of a continuum infinity of identical quantum universes, all with the same quasi-classical worlds, we show that projection factors give relative amounts of worlds. These appear as relative frequencies of results in quantum experiments, and play the role of probabilities in decisions and inference. This solves the probability problem of Everett's theory, allowing its preferred basis problem to be solved as well, and may help settle questions about the nature of probability.     

复杂势场量子弹球中疤痕态的量子化条件

量子疤痕是波函数在经典不稳定周期轨道周围反常凝聚的一种量子或波动现象.人们对疤痕态的量子化条件进行了大量研究,对深入理解半经典量子化起到了一定的促进作用.之前大部分研究工作主要集中在硬墙量子弹球上,即给定边界形状的无穷深量子势阱系统.本文研究具有光滑复杂势场的二维量子弹球系统,考察疤痕态的量子化条件及其重复出现的规律,得到了与硬墙弹球不一样的结果,对理解这类现象是一个有益的补充.这些结果将有助于理解具有无规长程杂质分布的二维电子系统的态密度谱和输运行为.     

Applications of Markov spectra for the weighted partition network by the substitution rule

The weighted self-similar network is introduced in an iterative way. In order to understand the topological properties of the self-similar network, we have done a lot of research in this field.Firstly, according to the symmetry feature of the self-similar network, we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then, we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally, we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.     

Study of semileptonic decay of ${\bar{B}}_{s}^{0} \rightarrow \phi {l}^{+}{l}^{-}$ in QCD sum rule

In this work we study the semileptonic decay of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) with the QCD sum rule method. We calculate the ${\bar{B}}_{s}^{0}\to \phi $ translation form factors relevant to this semileptonic decay, then the branching ratios of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) decays are calculated with the form factors obtained here. Our result for the branching ratio of ${\bar{B}}_{s}^{0}\to \phi {\mu }^{+}{\mu }^{-}$ agree very well with the recent experimental data. For the unmeasured decay modes such as ${\bar{B}}_{s}^{0}\to \phi {e}^{+}{e}^{-}$ and ${\bar{B}}_{s}^{0}\to \phi {\tau }^{+}{\tau }^{-}$, we give theoretical predictions.