Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.

Boundary-layer transition measurements in hypervelocity flows in a shock tunnel

Experiments to investigate the transition process in hypervelocity boundary layers were performed in the T4 free-piston shock tunnel. An array of thin-film heat-transfer gauges was used to detect the location and extent of the transitional region on a 1500 mm long x 120 turn wide flat plate, which formed one of the walls of a duct. The experiments were performed in a Mach 6 flow of air with 6- and 12-MJ/kg nozzle-supply enthalpies at unit Reynolds numbers ranging from 1.6 x 10(6) to 4.9 x 10(6) m(-1). The results show that the characteristics typical of transition taking place through the initiation, growth, and merger of turbulent spots are evident in the heat-transfer signals. A 2-mm-high excrescence located 440 turn from the leading edge was found to be capable of generating a turbulent wedge within an otherwise laminar boundary layer at a unit Reynolds number of 2.6 x 10(6) m(-1) at the 6-MJ/kg condition. A tripping strip, located 100 mm from the leading edge and consisting of a line 37 teeth of 2 rum height equally spaced and spanning the test surface, was also found to be capable of advancing the transition location at the same condition and at the higher enthalpy condition.

Multiple shoot formation in lentil (Lens culinaris) seeds

A protocol based on seed culture was developed for efficient in vitro propagation of lentil (Lens culinaris Medik). Benzyladenine (BA), thidiazuron (TDZ), and kinetin all induced multiple shoot formation. In terms of the number of long shoots (>2.0 cm) produced per seed, BA and TDZ at optimum concentrations (0.2-0.4 and 0.1 mg/litre, respectively) had similar efficiency, whereas kinetin produced less shoots. Murashige and Skoog (MS) salt composition was better than that of Gamborge (B5) for shoot induction. Increasing calcium (Ca) concentration was necessary to overcome shoot-tip necrosis. For shoot elongation, fresh medium of the same composition of shoot induction medium could be used for stumps from medium with low BA (

Analysis of the wind field and heat budget in an alpine lake basin during summertime fair weather conditions

Observational data collected in the Lake Tekapo hydro catchment of the Southern Alps in New Zealand are used to analyse the wind and temperature fields in the alpine lake basin during summertime fair weather conditions. Measurements from surface stations, pilot balloon and tethersonde soundings, Doppler sodar and an instrumented light aircraft provide evidence of multi-scale interacting wind systems, ranging from microscale slope winds to mesoscale coast-to-basin flows. Thermal forcing of the winds occurred due to differential heating as a consequence of orography and heterogeneous surface features, which is quantified by heat budget and pressure field analysis. The daytime vertical temperature structure was characterised by distinct layering. Features of particular interest are the formation of thermal internal boundary layers due to the lake-land discontinuity and the development of elevated mixed layers. The latter were generated by advective heating from the basin and valley sidewalls by slope winds and by a superimposed valley wind blowing from the basin over Lake Tekapo and up the tributary Godley Valley. Daytime heating in the basin and its tributary valleys caused the development of a strong horizontal temperature gradient between the basin atmosphere and that over the surrounding landscape, and hence the development of a mesoscale heat low over the basin. After noon, air from outside the basin started flowing over mountain saddles into the basin causing cooling in the lowest layers, whereas at ridge top height the horizontal air temperature gradient between inside and outside the basin continued to increase. In the early evening, a more massive intrusion of cold air caused rapid cooling and a transition to a rather uniform slightly stable stratification up to about 2000 m agl. The onset time of this rapid cooling varied about 1-2 h between observation sites and was probably triggered by the decay of up-slope winds inside the basin, which previously countered the intrusion of air over the surrounding ridges. The intrusion of air from outside the basin continued until about mid-night, when a northerly mountain wind from the Godley Valley became dominant. The results illustrate the extreme complexity that can be caused by the operation of thermal forcing processes at a wide range of spatial scales.

Hepatic covalent adduct formation with zomepirac in the CD26-deficient mouse

Background and Aims: Zomepirac (ZP), a non-steroidal anti-inflammatory drug (NSAID), has been reported to cause immune-mediated liver injury. In vivo, ZP is metabolized to a chemically reactive acyl glucuronide conjugate (ZAG) which can undergo covalent adduct formation with proteins. Such acyl glucuronide-derived drug-protein adducts may be important in the development of immune and toxic responses caused by NSAID. We have shown using immunoabsorptions that the 110 kDa CD26 (dipeptidyl peptidase IV) is one of the hepatic target proteins for covalent modification by ZAG. In the present study, a CD26-deficient mouse strain was used to examine protein targets for covalent modification by ZP/metabolites in the liver. Methods and Results: The CD26-deficient phenotype was confirmed by immunohistochemistry, flow cytometry analysis, RT-PCR, enzyme assay and immunoblotting. Moreover, by using monoclonal antibody immunoblots, CD26 was not detected in the livers of ZP-treated CD26-deficient mice. Immunoblots using a polyclonal antiserum to ZP on liver from ZP-treated mice showed three major sizes of protein bands, in the 70, 110 and 140 kDa regions. Most, but not all, of the anti-ZP immunoreactivity in the 110 kDa region was absent from ZP-treated CD26-deficient mice. Conclusion: These data definitively showed that CD26 was a component of ZP-modified proteins in vivo. In addition, the data suggested that at least one other protein of approximately 110 kDa was modified by covalent adduct formation with ZAG. (C) 2002 Blackwell Science Asia Pty Ltd.

Modelling of microstructure formation and evolution during solidification

A comprehensive probabilistic model for simulating microstructure formation and evolution during solidification has been developed, based on coupling a Finite Differential Method (FDM) for macroscopic modelling of heat diffusion to a modified Cellular Automaton (mCA) for microscopic modelling of nucleation, growth of microstructures and solute diffusion. The mCA model is similar to Nastac's model for handling solute redistribution in the liquid and solid phases, curvature and growth anisotropy, but differs in the treatment of nucleation and growth. The aim is to improve understanding of the relationship between the solidification conditions and microstructure formation and evolution. A numerical algorithm used for FDM and mCA was developed. At each coarse scale, temperatures at FDM nodes were calculated while nucleation-growth simulation was done at a finer scale, with the temperature at the cell locations being interpolated from those at the coarser volumes. This model takes account of thermal, curvature and solute diffusion effects. Therefore, it can not only simulate microstructures of alloys both on the scale of grain size (macroscopic level) and the dendrite tip length (mesoscopic level), but also investigate nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies. The calculated results are compared with values of grain sizes and solidification morphologies of microstructures obtained from a set of casting experiments of Al-Si alloys in graphite crucibles.

New W-isotope evidence for rapid terrestrial accretion and very early core formation

The short-lived Hf-182-W-182-isotope system is an ideal clock to trace core formation and accretion processes of planets. Planetary accretion and metal/silicate fractionation chronologies are calculated relative to the chondritic Hf-182-W-182-isotope evolution. Here, we report new high-precision W-isotope data for the carbonaceous chondrite Allende that are much less radiogenic than previously reported and are in good agreement with published internal Hf-W chronometry of enstatite chondrites. If the W-isotope composition of terrestrial rocks, representing the bulk silicate Earth, is homogeneous and 2.24 epsilon(182W) units more radiogenic than that of the bulk Earth, metal/silicate differentiation of the Earth occurred very early. The new W-isotope data constrain the mean time of terrestrial core formation to 34 million years after the start of solar system accretion. Early terrestrial core formation implies rapid terrestrial accretion, thus permitting formation of the Moon by giant impact while Hf-182 was still alive. This could explain why lunar W-isotopes are more radiogenic than the terrestrial value. Copyright (C) 2002 Elsevier Science Ltd.

Instabilities and drop formation in cylindrical liquid jets in reduced gravity

The effects of convective and absolute instabilities on the formation of drops formed from cylindrical liquid jets of glycerol/water issuing into still air were investigated. Medium-duration reduced gravity tests were conducted aboard NASA's KC-135 and compared to similar tests performed under normal gravity conditions to aid in understanding the drop formation process. In reduced gravity, the Rayleigh-Chandrasekhar Equation was found to accurately predict the transition between a region of absolute and convective instability as defined by a critical Weber number. Observations of the physics of the jet, its breakup, and subsequent drop dynamics under both gravity conditions and the effects of the two instabilities on these processes are presented. All the normal gravity liquid jets investigated, in regions of convective or absolute instability, were subject to significant stretching effects, which affected the subsequent drop and associated geometry and dynamics. These effects were not displayed in reduced gravity and, therefore, the liquid jets would form drops which took longer to form (reduction in drop frequency), larger in size, and more spherical (surface tension effects). Most observed changes, in regions of either absolute or convective instabilities, were due to a reduction in the buoyancy force and an increased importance of the surface tension force acting on the liquid contained in the jet or formed drop. Reduced gravity environments allow better investigations to be performed into the physics of liquid jets, subsequently formed drops, and the effects of instabilities on these systems. In reduced gravity, drops form up to three times more slowly and as a consequence are up to three times larger in volume in the theoretical absolute instability region than in the theoretical convective instability region. This difference was not seen in the corresponding normal gravity tests due to the masking effects of gravity. A drop is shown to be able to form and detach in a region of absolute instability, and spanning the critical Weber number (from a region of convective to absolute instability) resulted in a marked change in dynamics and geometry of the liquid jet and detaching drops. (C) 2002 American Institute of Physics.

Structural changes in mixed Langmuir-Blodgett films upon nanoparticle formation

The formation of CdS nanoparticles by reacting mixed Langmuir-Blodgett films of arachidic acid and either octadecylamine or dimethyldioctadecylammonium nitrate on a cadmium-containing subphase with hydrogen sulfide gas has resulted in the identification of a number of structural changes, observed using grazing incidence X-ray diffraction. In the case of octadecylamine, the structure after reaction is a hexagonal close-packed array of surfactant-stabilized nanoclusters, with a lattice constant of a = 17.65 Angstrom. In both octadecylamine and dimethyldioctadecylammonium nitrate films, the presence of a unit cell tilted at 38degrees to the plane of the substrate was found. Despite these changes, the average nanoparticle size was unaffected by the addition of either second component to the film.

Influence of synthesis parameters on the formation of mesoporous SAPOs

The synthesis and characterization of high-quality mesoporous silicoaluminophosphates (SAPOs) with a hexagonally arranged pore structure and a good thermal stability are described. The influence of some important synthesis parameters including temperature, time, and Si content in the synthesis gel was examined. The local environments of Al, P, and Si were investigated using MAS NMR spectroscopy. The acidity of the mesoporous SAPOs was studied and compared with those of aluminosilicate MCM-41 and SAPO-5. Results show that both the synthesis temperature and time have a significant impact on the formation of mesoporous SAPOs, whereas the presence of Si in the synthesis gel has a direct influence on the structure type and the quality of the resulting mesoporous SAPO materials. High-quality mesoporous SAPOs can be synthesized from the synthesis gels with Si/Al ratio smaller than 0.5 in the presence of cationic surfactants in a weakly basic aqueous solution. The mesoporous SAPO materials show interesting acidity properties, possessing both strong and mild sites. (C) 2002 Elsevier Science Inc. All rights reserved.

Metabolism of tamoxifen by recombinant human cytochrome P450 enzymes: Formation of the 4-hydroxy, 4′-hydroxy andN-desmethyl metabolites and isomerization oftrans-4-hydroxytamoxifen

The cytochrome P450 (P450)-mediated biotransformation of tamoxifen is important in determining both the clearance of the drug and its conversion to the active metabolite, trans-4-hydroxytamoxifen. Biotransformation by P450 forms expressed extrahepatically, such as in the breast and endometrium, may be particularly important in determining tissue-specific effects of tamoxifen. Moreover, tamoxifen may serve as a useful probe drug to examine the regioselectivity of different forms. Tamoxifen metabolism was investigated in vitro using recombinant human P450s. Forms CYP1A1, 1A2, 1B1, 2A6, 2B6, 2C9, 2C19, 2D6, 2E1, 3A4, 3A5, and 3A7 were coexpressed in Escherichia coli with recombinant human NADPH-cytochrome P450 reductase. Bacterial membranes were harvested and incubated with tamoxifen or trans-4-hydroxytamoxifen under conditions supporting P450-mediated catalysis. CYP2D6 was the major catalyst of 4-hydroxylation at low tamoxifen concentrations (170 +/- 20 pmol/40 min/0.2 nmol P450 using 18 muM tamoxifen), but CYP2B6 showed significant activity at high substrate concentrations (28.1 +/- 0.8 and 3.1 +/- 0.5 nmol/120 min/0.2 nmol P450 for CYP2D6 and CYP2B6, respectively, using 250 muM tamoxifen). These two forms also catalyzed 4'-hydroxylation (13.0 +/- 1.9 and 1.4 +/- 0.1 nmol/120 min/0.2 nmol P450, respectively, for CYP2B6 and CYP2D6 at 250 muM tamoxifen; 0.51 +/- 0.08 pmol/40 min/0.2 nmol P450 for CYP2B6 at 18 muM tamoxifen). Tamoxifen N-demethylation was mediated by CYP2D6, 1A1, 1A2, and 3A4, at low substrate concentrations, with contributions by CYP1B1, 2C9, 2C19 and 3A5 at high concentrations. CYP1B1 was the principal catalyst of 4-hydroxytamoxifen trans-cis isomerization but CYP2B6 and CYP2C19 also contributed.