Studies in mass spectrometry. IV—Fragmentation of aryltriflates. Substituent effects on [ArO]+ ion abundances: Looking for a best suited electron energy in the steady state approach. Experimental evidence for the ‘through bond’ stabilization of aryl cations by meta electron donor Substituents

The fragmentation patterns of 24 substituted phenyltrifluoromethanesulfonates has been determined by exact mass and metastable transition measurements. The influence of the ring substituent(s) on the abundance of the [ArO]+ ions has been investigated at low energies and a new standard parameter for plotting against Hammett's ó constants is proposed. The direct loss of CF₃SO₃ from the molecular ion of 3,5-(diisopropyl)-phenyl-, 3,5-(dicyclopropyl)phenyl- and 3,5-di(α-methylcyclopropyl)-phenyl-methanesulfonate, and further observations on the fragmentation processes of these compounds are consistent with M.O. calculations on the ‘through bond’ stabilization of the [Ar]+ σ state by meta electron donor substituents.     

Approximation to a set-valued mapping,I: A proposal

Given a multivalued mappingF, we address the problem of finding another multivalued mappingS that agrees locally withF. We limit ourselves to the case whenF(x) is convex compact for eachx. We propose anS obtained by linearizing the support function ofF(x) and give conditions under which thisS approximatesF in the sense of Hausdorff distance. We show equality betweenS and other proposals obtained from tangent cones to the graph ofF. Finally, we apply these results to the approximate subdifferential of a convex function.     

Colloidal Analysis of Particles Extracted from Microalloyed Steels

Different colloidal particle characterization methods are examined for their suitability to determine the particle size distribution of particles extracted from steels. Microalloyed steels are dissolved to extract niobium and titanium carbonitride particles that are important for the mechanical properties of these steels. Such particles have sizes ranging from several nanometers to hundreds of nanometers depending on the precipitation stage during the thermomechanically controlled rolling process. The size distribution of the particles is analyzed by dynamic light scattering (DLS), analytical ultracentrifugation (AUC), and hollow fiber flow field-flow fractionation (HF5) and compared to data obtained for reference particles as well as data from electron microscopy, the standard sizing technique used in metallurgy today. AUC and HF5 provide high-quality size distributions, average over large particle numbers that enables statistical analysis, and yield useful insights for alloy design; however, DLS fails due to a lack of resolution. Important aspects in the conversion and comparison of size distributions obtained for broadly distributed particle systems with different measurement principles and the role of surfactants used in sample preparation are discussed.     

Directional derivatives in nonsmooth optimization

In this note, we consider two notions of second-order directional derivatives and discuss their use in the characterization of minimal points for nonsmooth functions.This research was supported by NSF Grant No. ECS-8214081, by the Fund for Promotion of Research at the Technion, and by Deutsche Forschungsgemeinschaft.     

Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems

The purpose of this paper is to derive, in a unified way, second order necessary and sufficient optimality criteria, for four types of nonsmooth minimization problems: thediscrete minimax problem, thediscrete l ₁-approximation, the minimization of theexact penalty function and the minimization of theclassical exterior penalty function. Our results correct and supplement conditions obtained by various authors in recent papers.     

A remark on a regularity assumption for the mathematical programming problem in Banach spaces

This paper deals with a recently proposed Slater-like regularity condition for the mathematical programming problem in infinite-dimensional vector spaces (Ref. 1). The attractive feature of this constraint qualification is the fact that it can be considered as a condition only on theactive part of the constraint. We prove that the studied regularity condition is equivalent to the regularity assumption normally used in the study of the mathematical programming problem in infinite-dimensional vector spaces.     

Host–guest interactions between niobocene dichloride and α-, β-, and γ-cyclodextrins: preparation and characterization

The possible inclusion complexes of Cp₂NbCl₂ into α-, β-, and γ-CD hosts have been investigated. The existence of a true inclusion complex in the solid state was confirmed by a combination of thermogravimetric analysis, FTIR, PXRD, and ¹³C CP-MAS NMR spectroscopies. The solid-state results demonstrated that α-cyclodextrin does not form inclusion complexes with Cp₂NbCl₂ whereas β- and γ-cyclodextrins do form such complexes. PXRD, NMR, and thermal analysis showed that the organometallic molecules of Cp₂NbCl₂OH are included in the cavities of β- and γ-cyclodextrins, possibly adopting a symmetrical conformation in the complex, with each glucose unit in a similar environment. In solution, ¹H NMR experiments suggest that niobocene has a shallow penetration on the β-CD leading to upfield shift on H-3 signal with a minor perturbation on the H-5 proton while for γ-CD, both H-3 and H-5 are shifted upfield substantially. This suggests that niobocene penetrates deeper into the γ-CD cavity than in the β-CD cavity, as a result of the cavity size. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.