Theory of differential inequalities with appliciations to singular perturbiation problems and method of lines

During recent years, the theory of differential inequalities has been extensively used to discuss singular perturbation problems and method of lines to partial differential equations. The present thesis deals with some differential inequality theorems and their applications to singularly perturbed initial value problems, boundary value problems for ordinary differential equations in Banach space and initial boundary value problems for parabolic differential equations. The method of lines to parabolic and elliptic differential equations are also dealt The thesis is organised into nine chapters

Lipase from marine Aspergillus awamori BTMFW032: Production, partial purification and application in oil effluent treatment

Marine fungus BTMFW032, isolated from seawater and identified as Aspergillus awamori, was observed to produce an extracellular lipase, which could reduce 92% fat and oil content in the effluent laden with oil. In this study, medium for lipase production under submerged fermentation was optimized statistically employing response surface method toward maximal enzyme production. Medium with soyabean meal- 0.77% (w/v); (NH4)2SO4-0.1 M; KH2PO4-0.05 M; rice bran oil-2% (v/v); CaCl2-0.05 M; PEG 6000-0.05% (w/v); NaCl-1% (w/v); inoculum-1% (v/v); pH 3.0; incubation temperature 35 8C and incubation period-five days were identified as optimal conditions for maximal lipase production. The time course experiment under optimized condition, after statistical modeling, indicated that enzyme production commenced after 36 hours of incubation and reached a maximum after 96 hours (495.0 U/ml), whereas maximal specific activity of enzyme was recorded at 108 hours (1164.63 U/mg protein). After optimization an overall 4.6- fold increase in lipase production was achieved. Partial purification by (NH4)2SO4 precipitation and ion exchange chromatography resulted in 33.7% final yield. The lipase was noted to have a molecular mass of 90 kDa and optimal activity at pH 7 and 40 8C. Results indicated the scope for potential application of this marine fungal lipase in bioremediation.

A new inexpensive method for the preparation of acicular precursors for magnetic recording media

Magnetic materials meant for audio/video recording applications necessitate that polycrystalline materials be in acicular shape. So preparation of acicular precursors for magnetic storage materials assumes significance. The employment of aqueous solutions do not produce needle shape crystallites. Glycerol is one of the complexing media used for the precipitation of ferrous oxalate dihydrate. An inexpensive method using starch for preparation of acicular particles is described. The influence of an additive namely Gd on acicularity is also investigated

Approximate Approximations and a Boundary Point Method for the Linearized Stokes System

The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded convex domain G subset R^2, where the second part consists of three steps: In a first step the unknown potential density is replaced by a linear combination of exponentially decreasing basis functions concentrated near the boundary points. In a second step, integration over the boundary partial G is replaced by integration over the tangents at the boundary points such that even analytical expressions for the potential approximations can be obtained. In a third step, finally, the linear algebraic system is solved to determine an approximate density function and the resulting solution of the Stokes boundary value problem. Even not convergent the method leads to an efficient approximation of the form O(h^2) + epsilon, where epsilon can be chosen arbitrarily small.

Evaluating partial root-zone irrigation and mulching in okra (Abelmoschus esculentus L.) under a sub-humid tropical climate

The field experiments were conducted to compare the alternate partial root-zone irrigation (APRI) with and without black plastic mulch (BPM) with full root-zone irrigation (FRI) in furrow-irrigated okra (Abelmoschus esculentus L. Moench) at Bhubaneswar, India. APRI means that one of the two neighbouring furrows was alternately irrigated during consecutive watering. FRI was the conventional method where every furrow was irrigated during each watering. The used irrigation levels were 25% available soil moisture depletion (ASMD), 50% ASMD, and 75% ASMD. The plant growth and yield parameters were observed to be significantly (p < 0.05) higher with frequent irrigation (at 25% ASMD) under all irrigation strategies. However, APRI + BPM produced the maximum plant growth and yield using 22% and 56% less water over APRI without BPM and FRI, respectively. The highest pod yield (10025 kg ha^-1) was produced under APRI at 25% ASMD + BPM, which was statistically at par with the pod yield under APRI at 50% ASMD + BPM. Irrigation water use efficiency (IWUE), which indicates the pod yield per unit quantity of irrigation water, was estimated to be highest (12.3 kg m^-3) under APRI at 50% ASMD + BPM, followed by APRI at 25% ASMD + BPM. Moreover, the treatment APRI at 50% ASMD + BPM was found economically superior to other treatments, generating more net return (US $ 952 ha^-1) with higher benefit–cost ratio (1.70).

An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

Hydraulic modeling of runoff over a rough surface under partial inundation

This study presents a numerical method to derive the Darcy- Weisbach friction coefficient for overland flow under partial inundation of surface roughness. To better account for the variable influence of roughness with varying levels of emergence, we model the flow over a network which evolves as the free surface rises. This network is constructed using a height numerical map, based on surface roughness data, and a discrete geometry skeletonization algorithm. By applying a hydraulic model to the flows through this network, local heads, velocities, and Froude and Reynolds numbers over the surface can be estimated. These quantities enable us to analyze the flow and ultimately to derive a bulk friction factor for flow over the entire surface which takes into account local variations in flow quantities. Results demonstrate that although the flow is laminar, head losses are chiefly inertial because of local flow disturbances. The results also emphasize that for conditions of partial inundation, flow resistance varies nonmonotonically but does generally increase with progressive roughness inundation.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Inclusion of nonlinear demand-supply relationships within large-scale partial equilibrium linear programming models

This paper presents a new method for the inclusion of nonlinear demand and supply relationships within a linear programming model. An existing method for this purpose is described first and its shortcomings are pointed out before showing how the new approach overcomes those difficulties and how it provides a more accurate and 'smooth' (rather than a kinked) approximation of the nonlinear functions as well as dealing with equilibrium under perfect competition instead of handling just the monopolistic situation. The workings of the proposed method are illustrated by extending a previously available sectoral model for the UK agriculture.

Assays for enhanced activity of low efficacy partial agonists at the D-2 dopamine receptor

Background and purpose: Low efficacy partial agonists at the D-2 dopamine receptor may be useful for treating schizophrenia. In this report we describe a method for assessing the efficacy of these compounds based on stimulation of [S-35]GTP gamma S binding. Experimental approach: Agonist efficacy was assessed from [S-35]GTP gamma S binding to membranes of CHO cells expressing D2 dopamine receptors in buffers with and without Na+. Effects of Na+ on receptor/G protein coupling were assessed using agonist/[H-3] spiperone competition binding assays. Key results: When [S-35]GTP gamma S binding assays were performed in buffers containing Na+, some agonists (aripiprazole, AJ-76, UH-232) exhibited very low efficacy whereas other agonists exhibited measurable efficacy. When Na+ was substituted by N-methyl D-glucamine, the efficacy of all agonists increased (relative to that of dopamine) but particularly for aripiprazole, aplindore, AJ-76, (-)-3-PPP and UH-232. In ligand binding assays, substitution of Na+ by N-methyl D-glucamine increased receptor/G protein coupling for some agonists -. aplindore, dopamine and (-)-3-PPP-but for aripiprazole, AJ-76 and UH-232 there was little effect on receptor/G protein coupling. Conclusions and implications: Substitution of Na+ by NMDG increases sensitivity in [S-35] GTPgS binding assays so that very low efficacy agonists were detected clearly. For some agonists the effect seems to be mediated via enhanced receptor/G protein coupling whereas for others the effect is mediated at another point in the G protein activation cycle. AJ-76, aripiprazole and UH-232 seem particularly sensitive to this change in assay conditions. This work provides a new method to discover these very low efficacy agonists.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

GSHMC: an efficient method for molecular simulation

The hybrid Monte Carlo (HMC) method is a popular and rigorous method for sampling from a canonical ensemble. The HMC method is based on classical molecular dynamics simulations combined with a Metropolis acceptance criterion and a momentum resampling step. While the HMC method completely resamples the momentum after each Monte Carlo step, the generalized hybrid Monte Carlo (GHMC) method can be implemented with a partial momentum refreshment step. This property seems desirable for keeping some of the dynamic information throughout the sampling process similar to stochastic Langevin and Brownian dynamics simulations. It is, however, ultimate to the success of the GHMC method that the rejection rate in the molecular dynamics part is kept at a minimum. Otherwise an undesirable Zitterbewegung in the Monte Carlo samples is observed. In this paper, we describe a method to achieve very low rejection rates by using a modified energy, which is preserved to high-order along molecular dynamics trajectories. The modified energy is based on backward error results for symplectic time-stepping methods. The proposed generalized shadow hybrid Monte Carlo (GSHMC) method is applicable to NVT as well as NPT ensemble simulations.

A modified PNN algorithm with optimal PD modeling using the orthogonal least squares method

In this paper a modified algorithm is suggested for developing polynomial neural network (PNN) models. Optimal partial description (PD) modeling is introduced at each layer of the PNN expansion, a task accomplished using the orthogonal least squares (OLS) method. Based on the initial PD models determined by the polynomial order and the number of PD inputs, OLS selects the most significant regressor terms reducing the output error variance. The method produces PNN models exhibiting a high level of accuracy and superior generalization capabilities. Additionally, parsimonious models are obtained comprising a considerably smaller number of parameters compared to the ones generated by means of the conventional PNN algorithm. Three benchmark examples are elaborated, including modeling of the gas furnace process as well as the iris and wine classification problems. Extensive simulation results and comparison with other methods in the literature, demonstrate the effectiveness of the suggested modeling approach.

Identification of partial resetting using De as a function of illumination time

Modern age samples from various depositional environments were examined for signal resetting. For 19 modern aeolian/beach samples all De values obtained were View the MathML source, with ∼70% having View the MathML source. For 21 fluvial/colluvial samples, all De values were View the MathML source with ∼80% being View the MathML source. De as a function of illumination (OSL measurement) time (De(t)) plots were examined for all samples. Based on previous laboratory experiments, increases in De(t) were expected for partially reset samples, and constant De(t) for fully reset samples. All aeolian samples, both modern age and additional ‘young’ samples (<1000 years), showed constant (flat) De(t) while all modern, non-zero De, fluvial/colluvial samples showed increasing De(t). ‘Replacement plots’, where a regenerated signal is substituted for the natural, yielded constant (flat) De(t). These findings support strongly the use of De(t) as a method of identifying incomplete resetting in fluvial samples. Potential complicating factors, such as illumination (bleaching) spectrum, thermal instability and component composition are discussed and a series of internal checks on the applicability of the De(t) for each individual aliquot/grain level are outlined.