A minimax search plan for constrained optimization problems

A minimax search strategy is described for locating the boundary point of a region on a line joining a feasible point to an infeasible point. Asymptotic strategies, useful when the number of experiments to be used in the search is not predetermined, are also given. These strategies are useful subroutines for many multidimensional optimization algorithms.The authors thank G. V. Reklaitis for initial discussions concerning this problem. John H. Beamer was an NSF Graduate Fellow at the time when this research was conducted.     

Structures and rheological properties of hen egg yolk low density lipoprotein layers spread at the air-water interface at pH 3 and 7

Low density lipoproteins (LDL) from egg yolk have a classical structure of lipoprotein with a core of neutral lipids surrounded by a monolayer of apoproteins and phospholipids. This structure collapses during adsorption and all constituents spread at the interface. To understand better the nature of the interactions between apoproteins and lipids at the interface, we have deposited LDL at an air-water interface and analysed the isotherms during their compression on a Langmuir trough. Then, these LDL films were studied by atomic force microscopy (AFM) imaging. To identify the protein and lipid structures, we imaged films before and after lipid solubilisation by butanol. To study the interactions in the LDL films, we have varied the pH, ionic strength and used simplified model systems. We also studied the correlation between observed structures and interfacial rheology of the film. The isotherms of interfacial LDL films were similar for pH 3 and 7, but their structures observed in AFM were different. At surface pressures below the transition corresponding to the demixion of apoprotein-neutral lipid complexes, the LDL film structure was not governed by electrostatic interactions. However, above this surface pressure transition (45mN/m), there was an effect of charge on this structure. Around the transition zone, the rheological properties of LDL films at pH 3 were different as a function of pH (viscous at pH 3 and visco-elastic at pH 7). So, the rheological properties of LDL films could be linked to the structures formed by apoproteins and observed in AFM.     

The Nature of One-sided Intergrowths on (001) of Triclinic Centrosymmetric K2Cr2O7 (II)

SHUBNIKOV first observed in 1912 that centrosymmetric K₂Cr₂O₇ crystals (P1 ) exhibit a growth anomaly in highly supersaturated solutions. The (001) faces of these crystals are always smooth, the parallel opposite faces are always rough. Electron micrographs show these rough surfaces to be crystallites that have grown in stacks. In Part I of this publication, the crystallite orientation was determined using electron-induced diffraction methods. As a rule, these crystallites are parallel intergrowths. Only a small number of crystals near the surface of the host crystal are twinned according to [010]. Part II sought to ascertain the cause of these one-sided intergrowths. To determine the most favourable energetic arrangement of two intergrown individuals, interactions across the intergrowth face as a function of shifts parallel to (001) and to (001 ) were calculated, 64 theoretically possible cases were considered. Only in the [010]-twin and the seldom-occurring [11 0]-twin is an approximation of the 2/m symmetry of the macroscopic twin arrangements also found in the intergrowth structure, and this is the case only when the (001 ) faces of the host and guest crystal are intergrown.     

Restoration of protein foam stability through electrostatic propylene glycol alginate-mediated protein–protein interactions

The action of propylene glycol alginate in the enhancement of foam stability of a destabilised Tween 20/bovine serum albumin mixed system was evaluated. A significant increase in the foam stability was observed in the presence of low concentrations of propylene glycol alginate. A pseudo-plateau level of foam stability was obtained in the presence of approximately 0.8 μg/ml propylene glycol alginate in the solution used to form the foam. Foam stability enhancement due to bulk viscosity changes and surface effects were elucidated. The increase in foam stability was investigated by reference to the properties of thin liquid films and the macroscopic interface of test solutions. Propylene glycol alginate was found to slow the rate of thin film drainage, increase the equilibrium thickness of the films, slow the lateral diffusion of a fluorescent probe molecule located in the adsorbed layer and increase the elasticity of the interface. Data are consistent with propylene glycol alginate-induced crosslinking of protein in the adsorbed layer. This polysaccharide presents a means for controlling protein foam stability.     

Effects of severe-strain-induced defects on the mechanical response of two kinds of high-angle grain boundaries

ABSTRACT

Grain boundaries of metallic materials subjected to severe plastic deformation exhibit significantly enhanced diffusivity and excess energy compared with their relaxed poly- or bi-crystalline counterparts even when the macroscopic degrees of freedom are the same in both types of grain boundaries. Boundaries of excess energy are/can be relaxed by annealing. As a first step in accounting for this experimentally observed high-energy state of general high-angle grain boundaries subjected to severe plastic deformation, a concept of localised basic shear units and the presence of localised extra free volume in these units situated in different locations in the grain boundaries, which was originally proposed to explain steady-state structural superplastic flow, is made use of. Using MD simulation, the mechanical response of these modified grain boundaries is compared with that of their relaxed state. The results are also compared with a case of a homogeneous distribution of extra free volume within the grain boundary. The localised shear units containing extra free volume introduced in the grain boundaries are found to alter their physical and mechanical features strongly, which, in turn, drastically affect, consistent with experimental results, the mechanical response of the heavily deformed material.     

The Real Part of the Character Table of a Finite Group

In the ordinary character table of a finite group G, the values of the real valued irreducible characters on the real conjugacy classes form a sub-table which is square by Brauer's permutation lemma. We call this table the real part of the character table of G. Unlike the ordinary character table, viewed as a square matrix the real part of the character table is often singular. We present some results linking nonsingularity of this table to other properties of G.     

A Note on Brauer's Induction Theorem in a Soluble Group

By Brauer's induction theorem, for any finite group G, each irreducible complex character of G is a sum of characters induced from linear characters of elementary subgroups of G. The purpose of this note is to show that for soluble G, such a sum always exists in which the subgroups have their indices in G divisible by the degree of the character.     

Efficient computation of generalized median estimators

The generalized median (GM) estimator is a family of robust estimators that balances the competing demands of statistical efficiency and robustness. By choosing a kernel that is efficient for the parameter, the GM estimator gains robustness by computing the median of the kernel evaluated at all possible subsets from the sample. The GM estimator is often computationally infeasible because the number of subsets can be large for even modest sample sizes. Writing the estimator in terms of the quantile function facilitates an approximation using a sample of all possible subsets. While both sampling with and without replacement are feasible, sampling without replacement is preferred because of the reduction in variance from the sampling fraction. The proposed algorithm uses sequential sampling to compute an approximation within a user-chosen margin of error.