关于6 Sigma与3 Sigma的比较

在企业推广6σ的过程中,经常有学员不明白为什么6σ比3σ好,甚至有人会说6σ的规格限比3σ的规格限宽,当然6σ的合格率比3σ的合格率高。本文认为文献[1]、[2]关于6σ与3σ的比较图是引起这种误会的根源。为此本文给出另外的比较和解释。     

σ-满正规空间的逆极限

本文证明:设X是逆系统(X_απ_β~α,A}的逆极限,|A|=λ,假设每个投射π_α:X→X_α是开且到上的。X是λ-仿紧和λ-可遮的,如果每个X_α是σ-满正规的(可遮的,σ-集体正规的),则X是σ-满正规的(可造的,σ-集体正规的)。作为这一结果的推论,我们还将证明正规σ-满正规性满足如文[1]中的通常形式的逆极限定理及遗传σ-满正规性的类似结果。     

Bonding Situation of σ-E−H Complexes in Transition Metal and Main Group Compounds

The ambiguous bonding situation of σ-E−H (E=Si, B) complexes in transition metal compounds has been rationalized by means of Density Functional Theory calculations. To this end, the combination of the Energy Decomposition Analysis (EDA) method and its Natural Orbital for Chemical Valance (NOCV) extension has been applied to representative complexes described in the literature where the possible η¹ versus η² coordination mode is not unambiguously defined. Our quantitative analyses, which complement previous data based on the application of the Quantum Theory of Atoms in Molecules (QTAIM) approach, indicate that there exists a continuum between genuine η¹ and η² modes depending mainly on the strength of the backdonation. Finally, we also applied this EDA-NOCV approach to related main-group species where the backdonation is minimal.     

Ambident electrophilicity of 4-nitrobenzochalcogenadiazoles: Kinetic studies and structure-reactivity relationships

The kinetics of the reactions of 4-nitrobenzofurazane 1a , 4-nitrobenzothiadiazole 1b , and 4-nitrobenzoselenadiazole 1c with a series of 4-Y-substituted phenoxide anions 2a-e (Y = OMe, Me, H, Cl, and CN) in aqueous solution at 20°C were investigated photometrically. The derived second-order rate constants (k₂) have been combined with the nucleophilicity parameters values of these series of anions 2a-e to determine the electrophilicity parameters E of electrophiles 1a-c according to the linear free-energy relationship (log k₂)/s versus N. General reactivity of these electrophiles 1a-c is found to be fairly similar with E values ranging in −10.77 ± 0.61 < E < −7.53 ± 0.29. The comparison with structurally related neutral electron-deficient heteroaromatic and aromatic compounds revealed that 1a - c are more reactive than 1,3,5-trinitrobenzene, as benchmark aromatic electrophile used in nucleophilic addition or substitution processes. The rate constants for the reactions of 4-nitrobenzochalcogenadiazoles 1a-c with some other nucleophiles were measured and found to agree with those calculated from Mayr's equation. Finally, analysis of the rate data in terms of the Brønsted approach reveals that 1a-c exhibits especially low intrinsic reactivity in σ-adducts 3 forming reactions.     

Porosity of perturbed optimization problems in Banach spaces

Let X be a Banach space and Z a nonempty closed subset of X. Let be a lower semicontinuous function bounded from below. This paper is concerned with the perturbed optimization problem infz∈Z{J(z)+‖x−z‖}, denoted by (x,J)-inf for x∈X. In the case when X is compactly fully 2-convex, it is proved in the present paper that the set of all points x in X for which there does not exist z₀∈Z such that J(z₀)+‖x−z₀‖=infz∈Z{J(z)+‖x−z‖} is a σ-porous set in X. Furthermore, if X is assumed additionally to be compactly locally uniformly convex, we verify that the set of all points x∈X?Z⁰ such that the problem (x,J)-inf fails to be approximately compact, is a σ-porous set in X?Z⁰, where Z⁰ denotes the set of all z∈Z such that z∈PZ(z). Moreover, a counterexample to which some results of Ni [R.X. Ni, Generic solutions for some perturbed optimization problem in nonreflexive Banach space, J. Math. Anal. Appl. 302 (2005) 417-424] fail is provided.     

Derivations and local derivations on Freudenthal almost f-algebras

Let A be an Archimedean f  -algebra and let N(A)$N(A)$ be the set of all nilpotent elements of A. Colville et al. [4] proved that a positive linear map d:A→A$d:A\to A$ is a derivation if and only if d(A)⊂N(A)$d(A)\subset N(A)$ and d(A²)={0}$d(A^2)=\{0\}$, where A²$A^2$ is the set of all products ab in A.