On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Control of chaotic instability in a dual-spin spacecraft with dissipation using energy methods

Control of chaotic instability in a rotating multibody system in the form of a dual-spin spacecraft with an axial nutational damper is achieved using an algorithm derived using energy methods. The control method is implemented on two realistic spacecraft parameter configurations which have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude and consequently impair pointing accuracy. The control method is formulated from nutational stability results derived using an energy sink approximation for a dual-spin spacecraft with an asymmetric platform and axisymmetric rotor. The effectiveness of the control method is shown numerically and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents and Bifurcation diagrams.

Vibration instability in rolling mills: Modeling and experimental results

Models for the occurrence of the vibrational instability during rolling known as third octave chatter are presented and discussed. An analysis of rolling mill chatter was performed for the purpose of identifying characteristics of the vibrations and to determine any dependency on the rolling schedule. In particular, a stability criterion for the critical rolling speed is used to predict the maximum rolling speed without chatter instability on schedules from a 5 stand tandem mill rolling thin steel product. The results correlate well with measurements of critical speed occurring on the mill using a vibration monitor: This research provides significant insights into the chatter phenomena and has been used to investigate control methods for suppression of the instability.

Improvements to peroxide oxidation methods for analysing sulfur in acid sulfate soils

Improvements to peroxide oxidation methods for analysing acid sulfate soils (ASS) are introduced. The soil solution ratio has been increased to 1 : 40, titrations are performed in suspension, and the duration of the peroxide digest stage is substantially shortened. For 9 acid sulfate soils, the peroxide oxidisable sulfur value obtained using the improved method was compared with the reduced inorganic sulfur result obtained using the chromium reducible sulfur method. Their regression was highly significant, the slope of the regression line was not significantly different (P = 0.05) from unity, and the intercept not significantly different from zero. A complete sulfur budget for the improved method showed there was no loss of sulfur as has been reported for earlier peroxide oxidation techniques. When soils were very finely ground, efficient oxidation of sulfides was achieved, despite the milder digestion conditions. Highly sulfidic and organic soils were shown to be the most difficult to analyse using either the improved method or the chromium method. No single analytical method can be universally applied to all ASS, rather a suite of methods is necessary for a thorough understanding of many ASS. The improved peroxide method, in combination with the chromium method and the 4 M HCl extraction, form a sound platform for informed decision making on the management of acid sulfate soils.

Ab initio modelling of basal plane oxidation of graphenes and implications for modelling char combustion

Ab initio calculations have been performed to determine the energetics of oxygen atoms adsorbed onto graphene planes and the possible reaction path extracting carbon atorns in the form of carbon monoxide. Front the energetics it is confirmed that this reaction path will not significantly contribute to the gasification of well ordered carbonaceous chars. Modelling results which explore this limit Lire presented. (C) 2002 Elsevier Science Ltd, All rights reserved.

The impact of genotyping error on haplotype reconstruction and frequency estimation

The choice of genotyping families vs unrelated individuals is a critical factor in any large-scale linkage disequilibrium (LD) study. The use of unrelated individuals for such studies is promising, but in contrast to family designs, unrelated samples do not facilitate detection of genotyping errors, which have been shown to be of great importance for LD and linkage studies and may be even more important in genotyping collaborations across laboratories. Here we employ some of the most commonly-used analysis methods to examine the relative accuracy of haplotype estimation using families vs unrelateds in the presence of genotyping error. The results suggest that even slight amounts of genotyping error can significantly decrease haplotype frequency and reconstruction accuracy, that the ability to detect such errors in large families is essential when the number/complexity of haplotypes is high (low LD/common alleles). In contrast, in situations of low haplotype complexity (high LD and/or many rare alleles) unrelated individuals offer such a high degree of accuracy that there is little reason for less efficient family designs. Moreover, parent-child trios, which comprise the most popular family design and the most efficient in terms of the number of founder chromosomes per genotype but which contain little information for error detection, offer little or no gain over unrelated samples in nearly all cases, and thus do not seem a useful sampling compromise between unrelated individuals and large families. The implications of these results are discussed in the context of large-scale LD mapping projects such as the proposed genome-wide haplotype map.

Catalytically active Dengue virus NS3 protease forms aggregates that are separable by size exclusion chromatography

An active form of the Dengue virus protease NS3 (CF40.Gly.NS3pro) was expressed in Escherichia coli. This construct consists of a critical 40 amino acid cofactor domain from NS2B fused to the N-terminal 184 amino acid protease domain of NS3 via a flexible, covalent linker (Gly(4)SerGly(4)). The recombinantly produced protein is soluble and has a hexa-histidine tag engineered at the N-terminus for ease of purification using metal affinity chromatography. However, the presence of lower molecular weight impurities after affinity chromatography indicated the need for additional purification steps. The consistent appearance of these impurities suggested that they may be the products of proteolysis and/or auto-proteolysis. The latter possibility was subsequently excluded by the observation of the same impurities in a purified, catalytically inactive form of the recombinant protease (CF40.Gly.NS3pro.SA). Further analysis indicated that these impurities may represent premature translation termination products. Regardless of their origin, they were shown to form various sized aggregates with full-length CF40.Gly.NS3pro that can be separated by size exclusion chromatography, yielding fractions of active protease of sufficient purity for crystallisation trials. The ultimate goal of these studies is to obtain a crystal structure of a catalytically active form of the Dengue virus NS3 protease for structure-based drug design. (C) 2002 Elsevier Science (USA). All rights reserved.

Crystallization of PNMT, the adrenaline-synthesizing enzyme, is critically dependent on a high protein concentration

Phenylethanolamine N-methyltransferase, PNMT, utilizes the methylating cofactor S-adenosyl-L-methionine to catalyse the synthesis of adrenaline. Human PNMT has been crystallized in complex with an inhibitor and the cofactor product S-adenosyl-L-homocysteine using the hanging-drop technique with PEG 6000 and lithium chloride as precipitant. A critical requirement for crystallization was a high enzyme concentration (>90 mg ml(-1)) and cryocrystallography was used for high-quality data measurement. Diffraction data measured from a cryocooled crystal extend to a resolution of 2.3 Angstrom. Cryocooled crystals belong to space group P4(3)2(1)2 and have unit-cell parameters a = b = 94.3, c = 187.7 Angstrom.