Chapter 7 DEA multiplier analytic center sensitivity with an illustrative application to independent oil companies

The setE of extreme points which are also efficient are of basic importance in defining the efficiency frontier, from which the observations for all other DMUs are evaluated in DEA. A significant question which we address is “What variations in the data can be tolerated before the membership inE is changed?” This topic is explored using (1) a simple illustrative example, and (2) production data for 30 independent oil companies during the period 1983–1985. Data were allowed to vary simultaneously for all observations and in different subsets determined by random drawings of data for points both inE and not inE. The results were found to be robust in this study, thereby lending further support to earlier studies which also found these classifications into efficient and inefficient performers to be robust in DEA. Technical developments for these new methods of sensitivity analysis are supplied. These developments feature an application of analytic center (interior point) algorithms which ensure that the Strong Complementary Slackness Condition (SCSC) is fulfilled. The solutions satisfy a mathematical condition called “centrality”. Generally, the solutions are at interior points calledanalytic centers. At these interior points, continuity of the input-output ratios ensures that DMUs inE remain inE for at least small relative variations in the data, while empirically these properties have been found to extend to much larger variations in the data sets.     

CHEMICAL MODIFICATION AND CHARACTERIZATION OF THE ALPHA CYSTEINE 106 AT THE Vibrio harveyi LUCIFERASE ACTIVE CENTER

Vibrio harveyi luciferase, an alpha beta dimer, was effectively inactivated by treatment with the methylation agent methyl p-nitrobenzene sulfonate. However, inactivation of luciferase in the presence of excess amounts of this reagent did not follow pseudo-first-order kinetics. After taking the autodecay of this reagent into consideration in kinetic analysis, the pseudo-first-order constants and subsequently the second-order rate constant (83 min-1 M-1 at pH 7 and 23 degrees C) were determined. The inactivation rate can be retarded by the addition of the decanal or the reduced FMN substrate but not by the reaction product FMN. The binding of decanal specifically protected one target residue against modification with a concomitant protection of luciferase against inactivation. A pentapeptide containing this specific target residue was isolated and identified to be Phe-Gly-Ile-X-Arg with X corresponding to the S-methylated form of the cysteinyl residue at position 106 of the luciferase alpha subunit. It is concluded that this reactive alpha Cys-106 is at the aldehyde site and is also near the reduced flavin site of luciferase. The modified enzyme exhibited no gross conformational changes detectable by protein fluorescence measurements, which may be due to the small size change of the target cysteinyl residue after methylation. The methylated enzyme still retained the ability to bind one decanal and one reduced FMN without any substantial changes in binding affinities. The cause of luciferase inactivation by the methylation of alpha Cys-106 has been shown to be the impaired ability to form the 4a-hydroperoxy-flavin intermediate from the bound flavin substrate or to stabilize this intermediate.     

A previously unrecognised hydronium di-cation in the crystal structure of a cucurbituril derivative

Examination of the crystal structure of the adduct of hydronium tetrachloroferrate dichloride with cucurbituril resulted in the discovery that the hydronium cation present therein is not the well known H7O3+ species; rather, it is an unprecedented cyclic species of composition (H14O6)2+, templated by the formation of five hydrogen bonds to cucurbituril.     

The composition, charge and architecture of hydronium ions as observed in the crystalline state

The structures of hydronium ions present in single crystals have, by and large, been thought as being relatively simple and characterized by the classical formulae H₃O⁺, , and . All of them are thought to be quasi-planar, acyclic entities of charge +1, exclusively. In this review, we show that such is not the case in view of the fact that there exist documented examples of cyclic hydronium ions, that their charge can be larger than +1 and that they exist in aggregates containing more than four oxygens. Moreover, it is documented that hydronium ions exist in the form of geometrical isomers or conformers. To cite this article: I. Bernal, C. R. Chimie 9 (2006).     

Simple braids for surface homeomorphisms

Let S be a compact, oriented surface with negative Euler characteristic and let be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector , then there exists a simple braid with the same rotation vector.     

Application of low energy ion blocking for adsorption site determination of Na Atoms on a Cu(111) surface

Ion blocking in the low keV energy range is demonstrated to be a sensitive method for probing surface adsorption sites by means of the technique of time-of-flight scattering and recoiling spectroscopy (TOF-SARS). Adsorbed atoms can block the nearly isotropic backscattering of primary ions from surface atoms in the outmost layers of a crystal. The relative adsorption site position can be derived unambiguously by simple geometrical constructs between the adsorbed atom site and the surface atom sites. Classical ion trajectory simulations using the scattering and recoiling imaging code (SARIC) and molecular dynamics (MD) simulations provide the detailed ion trajectories. Herein we present a quantitative analysis of the blocking effects produced by sub-monolayer Na adsorbed on a Cu(111) surface at room temperature. The results show that the Na adsorption site preferences are different at different Na coverages. At a coverage θ = 0.25 monolayer, Na atoms preferentially populate the fcc threefold surface sites with a height of 2.7 ± 0.1 Å above the 1st layer Cu atoms. At a lower coverage of θ = 0.10 monolayer, there is no adsorption site preference for the Na atoms on the Cu(111) surface.     

Involutive operator algebras

Positivity - Examples of operator algebras with involution include the operator $$*$$-algebras occurring in noncommutative differential geometry studied recently by Mesland, Kaad, Lesch, and...     

Model problem for the motion of a compressible, viscous flow with the no-slip boundary condition

We consider the Navier–Stokes equations for the motion of a compressible, viscous, pressureless fluid in the domain ${\Omega = \mathbb{R}^3_+}$ with the no-slip boundary conditions. We construct a global in time, regular weak solution, provided that initial density ρ ₀ is bounded and the magnitude of the initial velocity u ₀ is suitably restricted in the norm ${\|\sqrt{\rho_0(\cdot)}{\bf u}_0(\cdot)\|_{L^2(\Omega)} + \|\nabla{\bf u}_0(\cdot)\|_{L^2(\Omega)}}$ .