Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. (c) 2009 Elsevier Inc. All rights reserved.

A H-1-NMR STUDY OF BILIRUBIN IX-ALPHA SOLUBILIZATION BY CHOLATE MICELLES - APPLICATION OF NUCLEAR OVERHAUSER EFFECTS

The solubilization of bilirubin IX-Alpha in aqueous solution by sodium cholate micelles has been examined by 270 MHz 1H-NMR spectroscopy. Incorporation of bilirubin into the micelles is accompanied by specific shifts of bilirubin vinyl and bridgehead protons and the C18 and C19 methyl groups of the steroid. The observed chemical shifts show a monotonic concentration dependence suggesting that changes in aggregation size are continuous. Nuclear Overhauser effects (NOE) have been shown to be a useful probe or micellization. A 4:1 cholate/bilirubin mixture has been investigated by difference NOE spectroscopy. The observation of intermolecular nuclear Overhauser effects between peripheral protons of bilirubin and cholate are diagnostic of spatially proximate groups. Inter-cholate nuclear Overhauser effects increase in magnitude upon bilirubin incorporation suggesting closer packing of steroid molecules on solubilization of the pigment. Intramolecular nuclear Overhauser effects observed for solubilized bilirubin are consistent with a compact intramolecularly hydrogen-bonded conformation resembling that determined for bilirubin in the solid state.

Characterization of dry sliding wear of Al---Si alloys

Controversy exists in the published literature as to the effect of silicon content and pressure on the dry sliding wear of Al---Si alloys. The present paper attempts to clarify the question by reporting a statistical analysis of data obtained from factorially designed experiments conducted on a pinon-disc machine in the pressure range 0.105–1.733 MPa and speed range 0.19–0.94 m s−1. Under these conditions it was found that, in the range 4–24 wt.% Si, wear of binary unmodified alloys does not significantly differ between the alloys. However, it is significantly less than that corresponding to an alloy containing no silicon. The effect of pressure on wear rate was found to be linear and monotonie and, over the narrow range of speeds used, the wear rate was found to be unaffected by speed. The coefficient of friction was found to be insensitive to variations in silicon content, pressure and speed.

Asymptotic behavior of a hierarchical system of learning automata

Learning automata arranged in a two-level hierarchy are considered. The automata operate in a stationary random environment and update their action probabilities according to the linear-reward- -penalty algorithm at each level. Unlike some hierarchical systems previously proposed, no information transfer exists from one level to another, and yet the hierarchy possesses good convergence properties. Using weak-convergence concepts it is shown that for large time and small values of parameters in the algorithm, the evolution of the optimal path probability can be represented by a diffusion whose parameters can be computed explicitly.

On vibration of eccentrically stiffened plates with varying stiffener length

Results of a study of the variation of natural frequencies with respect to the length of the stiffener of a square panel clamped all along its boundary and stiffened in the middle by a concentric stiffener were recently reported [ 11. Significant increases in certain frequencies, namely those with modes symmetric about both the medians of the plate, were observed when small gaps were not left between the plate boundary and the stiffener end. As an extension to that work, results of a study of the effect of the eccentricity of the stiffener on the frequency variation with the length of the stiffener are reported here.

Two-dimensional solidification in a cylindrical mold with imperfect mold contact

A two-dimensional axisymmetric problem of solidification of a superheated liquid in a long cylindrical mold has been studied in this paper by employing a new embedding technique. The mold and the melt has an imperfect contact and the heat transfer coefficient has been taken as a function of space and time. Short-time exact analytical solutions for the moving boundary and temperature distributions in the liquid, solid and mold have been obtained. The numerical results indicate that with the present solution, for some parameter values, substantial solidified thickness can be obtained. The method of solution is simple and straightforward, and consists of assuming fictitious initial temperatures for some suitable fictitious extensions of the actual regions. Sufficient conditions for the commencement of the solidification have been discussed.

Monoblock cylinder internally pressurised under asymmetric end constraints Some aspects of design

The finite element method is used to analyse stresses and displacements in a monoblock cylinder open at one end only. The cylinder is internally pressurised. The analysis shows that the minimum pressure required to cause yield in the cylinder decreases rapidly with increasing cylinder height until the height is about the same as the outer radius of the cylinder, beyond which the decrease is marginal. Introduction of a fillet at the internal corner enhances the design pressure substantially while a fillet at the outer corner affects this pressure only marginally.

Tissue culture of forest trees: Clonal multiplication of Eucalyptus grandis L

Axillary shoot proliferation was obtained using explants of Eucalyptus grandis L. juvenile and mature stages on a defined medium. Murashige and Skoog medium (MS) supplemented with benzyladenine (BA), naphthalene acetic acid (NAA) and additional thiamine. Excised shoots were induced to root on a sequence of three media: (1) White's medium containing indoleacetic acid (IAA), NAA and indole butyric acid; (IBA), (2) half-strength MS medium with charcoal and (3) half-strength MS liquid medium. The two types of explants differed in rooting response, with juvenile-derived shoots giving 60% rooting and adult-derived ones only 35%. Thus, the factors limiting cloning of selected trees in vitro are determined to be those controlling rooting of shoots in E. grandis.

Photoelastic parametric studies of mode I stress intensity factors

Results of photoelastic investigations on single edge-notch tension specimens of varying notch angle and crack length are reported. The experimental results of Mode I stress intensity factors are compared with analytical results.

Adsorption isitherms for neutral organic compounds-A hierarchy in modelling: Part IV. Charge of maximum adsorption-Statistical mechanical basis

The charge at which adsorption of orgamc compounds attains a maximum ( \sigma MAX M) at an electrochenucal interface is analysed using several multi-state models in a hierarchical manner The analysis is based on statistical mechamcal results for the following models (A) two-state site parity, (B) two-state muhl-slte, and (C) three-state site parity The coulombic interactions due to permanent and reduced dipole effects (using mean field approximation), electrostatic field effects and specific substrate interactions have been taken into account. The simplest model in the hierarchy (two-state site parity) yields the exphcit dependence of ( \sigma MAX M) on the permanent dipole moment, polarizability of the solvent and the adsorbate, lattice spacing, effective coordination number, etc Other models in the baerarchy bring to hght the influence of the solvent structure and the role of substrate interactions, etc As a result of this approach, the "composition" of oM.x m terms of the fundamental molecular constants becomes clear. With a view to use these molecular results to maxamum advantage, the derived results for ( \sigma MAX M) have been converted into those involving experimentally observable parameters lake Co, C 1, E N, etc Wherever possible, some of the earlier phenomenologlcal relations reported for ( \sigma MAX M), notably by Parsons, Damaskm and Frumkln, and Trasattl, are shown to have a certain molecular basis, vlz a simple two-state sate panty model.As a corollary to the hxerarcbacal modelling, \sigma MAX M and the potential corresponding to at (Emax) are shown to be constants independent of 0max or Corg for all models The lmphcatlon of our analysis f o r OmMa x with respect to that predicted by the generalized surface layer equation (which postulates Om~ and Ema x varlaUon with 0) is discussed in detail Finally we discuss an passing o M. and the electrosorptlon valency an this context.

A study of placement algorithms through trial interchange of logic modules

Based on trial interchanges, this paper develops three algorithms for the solution of the placement problem of logic modules in a circuit. A significant decrease in the computation time of such placement algorithms can be achieved by restricting the trial interchanges to only a subset of all the modules in a circuit. The three algorithms are simulated on a DEC 1090 system in Pascal and the performance of these algorithms in terms of total wirelength and computation time is compared with the results obtained by Steinberg, for the 34-module backboard wiring problem. Performance analysis of the first two algorithms reveals that algorithms based on pairwise trial interchanges (2 interchanges) achieve a desired placement faster than the algorithms based on trial N interchanges. The first two algorithms do not perform better than Steinberg's algorithm1, whereas the third algorithm based on trial pairwise interchange among unconnected pairs of modules (UPM) and connected pairs of modules (CPM) performs better than Steinberg's algorithm, both in terms of total wirelength (TWL) and computation time.

Induced Resistance: Potential for Control of Postharvest Diseases of Horticultural Crops

Fortunately, plants have developed highly effective mechanisms with which to defend themselves when attacked by potentially disease-causing microorganisms. If not, then they would succumb to the many pathogenic fungi, bacteria, viruses, nematodes and insect pests, and disease would prevail. These natural defence systems of plants can be deliberately activated to provide some protection against the major pathogens responsible for causing severe yield losses in agricultural and horticultural crops. This is the basis of what is known as ‘induced’ or ‘acquired’ disease resistance in plants. Although the phenomenon of induced resistance has been known amongst plant pathologists for over 100 years, its inclusion into pest and disease management programmes has been a relatively recent development, ie. within the last 5 years. This review will discuss very briefly some of the characteristics of the induced resistance phenomenon, outline some of the advantages and limitations to its implementation and provide some examples within a postharvest pathology context. Finally some approaches being investigated by the fruit pathology team at DPI Indooroopilly and collaborators will be outlined.

Elastic analysis of pin joints in plates under some combined pin and plate loads

Joints are primary sources of weakness in structures. Pin joints are very common and are used where periodic disassembly of components is needed. A circular pin in a circular hole in an infinitely large plate is an abstraction of such a pin joint. A two-dimensional plane-stress analysis of such a configuration is carried out, here, subjected to pin-bearing and/or biaxial-plate loading. The pin is assumed to be rigid compared to the plate material. For pin load the reactive stresses at the edges of the infinite plate tend to zero though their integral over the external boundary equals to the pin load. The pin-hole interface is unbonded and so beyond some load levels the plate separates from the pin and the extent of separation is a non-linear function of load level. The problem is solved by inverse technique where the extent of contact is specified and the causative loads are evaluated directly. In the situations where combined load is acting the separation-contact zone specification generally needs two parameters (angles) to be specified. The present report deals with analysing such a situation in metallic (or isotropic) plates. Numerical results are provided for parametric representation and the methodology is demonstrated.

Base-base interactions in nucleic acids containing A-T base pairs: Structure of poly[d(A-T)]

The Watson-Crick type of base pairing is considered to be mandatory for the formation of duplex DNA. However, conformational calculations carried out in our laboratory, have shown that some combinations of backbone torsion angles and sugar pucker lead to duplexes with Hoogsteen type of base pairing also. Here we present the results of energy calculations performed on A-T containing doublet sequences in the D-form with both Hoogsteen and Watson-Crick type of base pairing and the 3 viable models for the A-T containing polynucleotide duplex poly[d(A-T)].

Anisotropic gaussian beams

Anisotropic gaussian beams are obtained as exact solutions to the parabolic wave equation. These beams have a quadratic phase front whose principal radii of curvature are non-degenerate everywhere. It is shown that, for the lowest order beams, there exists a plane normal to the beam axis where the intensity distribution is rotationally symmetric about the beam axis. A possible application of these beams as normal modes of laser cavities with astigmatic mirrors is noted.