On finite groups with generalized σ-subnormal Schmidt subgroups

Let G be a finite group and σ?=?{σ_i|i∈I} some partition of the set of all primes. A subgroup A of G is said to be generalized σ-subnormal in G if A?=??L,T?, where L is a modular subgroup and T is a σ-subnormal subgroup of G. In this paper, we prove that if every Schmidt subgroup of G is generalized σ-subnormal in G, then the commutator subgroup G^′ of G is σ-nilpotent.     

Classification of So-Called Non-Covalent Interactions Based on VSEPR Model

The variety of interactions have been analyzed in numerous studies. They are often compared with the hydrogen bond that is crucial in numerous chemical and biological processes. One can mention such interactions as the halogen bond, pnicogen bond, and others that may be classified as σ-hole bonds. However, not only σ-holes may act as Lewis acid centers. Numerous species are characterized by the occurrence of π-holes, which also may play a role of the electron acceptor. The situation is complicated since numerous interactions, such as the pnicogen bond or the chalcogen bond, for example, may be classified as a σ-hole bond or π-hole bond; it ultimately depends on the configuration at the Lewis acid centre. The disadvantage of classifications of interactions is also connected with their names, derived from the names of groups such as halogen and tetrel bonds or from single elements such as hydrogen and carbon bonds. The chaos is aggravated by the properties of elements. For example, a hydrogen atom can act as the Lewis acid or as the Lewis base site if it is positively or negatively charged, respectively. Hence names of the corresponding interactions occur in literature, namely hydrogen bonds and hydride bonds. There are other numerous disadvantages connected with classifications and names of interactions; these are discussed in this study. Several studies show that the majority of interactions are ruled by the same mechanisms related to the electron charge shifts, and that the occurrence of numerous interactions leads to specific changes in geometries of interacting species. These changes follow the rules of the valence-shell electron-pair repulsion model (VSEPR). That is why the simple classification of interactions based on VSEPR is proposed here. This classification is still open since numerous processes and interactions not discussed in this study may be included within it.     

现代质量管理与6σ流程控制

本文以作者在GE和MOTOROLA服务的体会简要介绍近年来6σ质量管理在全球的应用发展情况。随后对Kσ原则下的过程能力指数及不合格品率作了计算和比较,并对有漂移情况下6σ流程控制作了讨论和评价。     

Cooperativity between the hydrogen bonding and halogen bonding in F3CX ··· NCH(CNH) ··· NCH(CNH) complexes (X=Cl,Br)

MP2 calculations with the cc-pVTZ basis set were used to analyse the intermolecular interactions in F₃CX?···?NCH(CNH)?···?NCH(CNH) triads (X=Cl, Br), which are connected via hydrogen and halogen bonds. Molecular geometries, binding energies, and infrared spectra of the dyads and triads were investigated at the MP2/cc-pVTZ computational level. Particular attention was given to parameters such as the cooperative energies, cooperative dipole moments, and many-body interaction energies. All studied complexes, with the simultaneous presence of a halogen bond and a hydrogen bond, show cooperativity with energy values ranging between ?1.32 and ?2.88?kJ?mol^?1. The electronic properties of the complexes were analysed using the Molecular Electrostatic Potential (MEP), electron density shift maps and the parameters derived from the Atoms in Molecules (AIM) methodology.     

Computational study of non-covalent interactions in oxirane…XF complexes (X = H,F, Cl,Br, Li) and their F-/Li-substituted analogues

A computational study found oxirane^…XF (X = H, Cl, Br, F, Li) dimers to be energetically stable, with their interaction energies increasing with the magnitude of the XF dipole moment in the order XF = LiF > BrF ～ HF > ClF > F₂. Their relative stabilities roughly correlate with the amount of charge transferred from the lone pairs on the O atom of oxirane to the antibonding σ* orbital of XF. However, the most strongly bound dimer, oxirane^…LiF, is stabilised by the largest dipole but involves the smallest charge transfer. The variation in the strength of the oxirane^…XF interaction was subsequently investigated by the sequential substitution of the protons on oxirane by either electron-donating Li or electron-withdrawing F atoms.     

(m,n)-树的一个充分必要条件

通过引进(m,n)-洞的概念,推广了已有的结论,得到了(m,n)-树的一个新的充分必要条件.     

Existence and porosity for a class of perturbed optimization problems in Banach spaces

Let X be a Banach space and Z a nonempty closed subset of X. Let be an upper semicontinuous function bounded from above. This paper is concerned with the perturbed optimization problem supz∈Z{J(z)+‖x−z‖}, which is denoted by (x,J)-sup. We shall prove in the present paper that if Z is a closed boundedly relatively weakly compact nonempty subset, then the set of all x∈X for which the problem (x,J)-sup has a solution is a dense Gδ-subset of X. In the case when X is uniformly convex and J is bounded, we will show that the set of all points x in X for which there does not exist z₀∈Z such that J(z₀)+‖x−z₀‖=supz∈Z{J(z)+‖x−z‖} is a σ-porous subset of X and the set of all points x∈X?Z⁰ such that there exists a maximizing sequence of the problem (x,J)-sup which has no convergent subsequence is a σ-porous subset of X?Z⁰, where Z⁰ denotes the set of all z∈Z such that z is in the solution set of (z,J)-sup.     

Double σ-multiplicative matrices

The class of σ-regular matrices was defined and characterized by Schaefer [P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972) 104-110] and further studied by Mursaleen [Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford 34 (1983) 77-86], Ahmad and Mursaleen [Z.U. Ahmad, Mursaleen, An application of Banach limits, Proc. Amer. Math. Soc. 103 (1988) 244-246]. In this paper we characterize four-dimensional σ-multiplicative matrices, and establish a core theorem.     

制造业全要素生产率的地区差异及收敛性研究——基于企业微观数据的实证

本文构建了技术进步内生的生产函数,并根据企业微观面板数据,采用OP模型和收敛模型测算了中国制造业全国层面及区域层面的全要素生产率,并分析了制造业全要素生产率的地区差异和收敛性。结果显示:2002~2011年中国制造业全国层面全要素生产率年均增长2.36%,受金融危机的影响,2008~2011年仅为-2.14%;在地区差异上,东部地区制造业全要素生产率要低于中西部地区;收敛分析显示,全域的全要素生产率既不存在β收敛也不存在σ收敛,但却存在“俱乐部”收敛,即中西部地区和东部地区内部各自收敛;同时,本文的分析还显示,资本增长率和研发投入都对全要素生产率的增长有显著正影响。