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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. 相似文献
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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. 相似文献
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Andreas Hegetschweiler Aljosha-Rakim Jochem Anna Zimmermann Johannes Walter Thorsten Staudt Tobias Kraus 《Particle & Particle Systems Characterization》2021,38(7):2000236
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. 相似文献
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Directional derivatives in nonsmooth optimization 总被引:2,自引:0,他引:2
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. 相似文献
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Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems 总被引:4,自引:0,他引:4
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. 相似文献
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A remark on a regularity assumption for the mathematical programming problem in Banach spaces 总被引:3,自引:0,他引:3
J. Zowe 《Journal of Optimization Theory and Applications》1978,25(3):375-381
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. 相似文献