Approximate solution of u'=-A2u using a relation between exp(-tA2) and exp(itA)

Let A be a positive definite operator in a Hilbert space and consider the initial value problem for u(t) = -A(2)u. Using a representation of the semigroup exp(-A(2)t) in terms of the group exp(iAt) we express u in terms of the solution of the standard heat equation w(t) = W-yy, with initial values v solving the initial value problem for v(y) = iAv. This representation is used to construct a method for approximating u in terms of approximations of v. In the case that A is a 2(nd) order elliptic operator the method is combined with finite elements in the spatial variable and then reduces the solution of the 4(th) order equation for u to that of the 2(nd) order equation for v, followed by the solution of the heat equation in one space variable.

Impact of Grazing, Fire and Extraction on the Bamboo (Dendrocalamus-Strictus and Bambusa-Arundinacea) Populations of Karnataka

Dendrocalamus strictus and Bambusa arundinacea are monocarpic, gregariously flowering species of bamboo, common in the deciduous forests of the State of Karnataka in India. Their populations have significantly declined, especially since the last flowering. This decline parelleis increasing incidence of grazing, fire and extraction in recent decades. Results of an experiment in which the intensities of grazing and fire were varied, indicate that while grazing significantly depresses the survival of seedlings and the recruitment of new eulms of bamboo clumps, fire appeared to enhance seedling survival, presumably by reducing competition of lass fire-resistant species. New shoots of bamboo are destroyed by insects and a variety of herbivorous mammals. In areas of intense herbivore pressure, a bamboo clump initiates the production of a much larger number of new culrm, but results in many fewer and shorter intact culms. Extraction renders the new shoots more susceptible to herbivore pressure by removal of the protective covering of branches at the base of a bamboo clump. Hence, regular and extensive extraction by the paper mills in conjuction with intense grazing pressure strongly depresses the addition of new culms to bamboo clumps. Regulation of grazing in the forest by domestic livestock along with maintenance of the cover at the base of the clumps by extracting the culms at a higher level should reduce the rate of decline of the bamboo stocks.

Approximate potential-distance relationship for clays

The conventional procedure of determining the surface potential of clay platelet and the variation of potential with distance is lengthy and time consuming. Simplified graphical procedures using Gouy theory have been developed and presented. The new procedures are simple, accurate and very much less time consuming.

Analysis of word embeddings and sequence features for clinical information extraction

This study investigates the use of unsupervised features derived from word embedding approaches and novel sequence representation approaches for improving clinical information extraction systems. Our results corroborate previous findings that indicate that the use of word embeddings significantly improve the effectiveness of concept extraction models; however, we further determine the influence that the corpora used to generate such features have. We also demonstrate the promise of sequence-based unsupervised features for further improving concept extraction.

Ion extraction from a plasma through a conical orifice

A method of ion extraction from plasmas is reported in which the interference of field lines due to the extraction system in the plasma region is avoided by proper shaping of the extractor electrode and is supported by field plots.

Purification of pharmaceuticals and nutraceutical compounds by sub- and supercritical extraction and chromatography

This thesis discusses the use of sub- and supercritical fluids as the medium in extraction and chromatography. Super- and subcritical extraction was used to separate essential oils from herbal plant Angelica archangelica. The effect of extraction parameters was studied and sensory analyses of the extracts were done by an expert panel. The results of the sensory analyses were compared to the analytically determined contents of the extracts. Sub- and supercritical fluid chromatography (SFC) was used to separate and purify high-value pharmaceuticals. Chiral SFC was used to separate the enantiomers of racemic mixtures of pharmaceutical compounds. Very low (cryogenic) temperatures were applied to substantially enhance the separation efficiency of chiral SFC. The thermodynamic aspects affecting the resolving ability of chiral stationary phases are briefly reviewed. The process production rate which is a key factor in industrial chromatography was optimized by empirical multivariate methods. General linear model was used to optimize the separation of omega-3 fatty acid ethyl esters from esterized fish oil by using reversed-phase SFC. Chiral separation of racemic mixtures of guaifenesin and ferulic acid dimer ethyl ester was optimized by using response surface method with three variables per time. It was found that by optimizing four variables (temperature, load, flowate and modifier content) the production rate of the chiral resolution of racemic guaifenesin by cryogenic SFC could be increased severalfold compared to published results of similar application. A novel pressure-compensated design of industrial high pressure chromatographic column was introduced, using the technology developed in building the deep-sea submersibles (Mir 1 and 2). A demonstration SFC plant was built and the immunosuppressant drug cyclosporine A was purified to meet the requirements of US Pharmacopoeia. A smaller semi-pilot size column with similar design was used for cryogenic chiral separation of aromatase inhibitor Finrozole for use in its development phase 2.

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 precision apparatus, with solid phase micro-extraction monitoring capability, for incorporation studies of gaseous precursors into insect-derived metabolites

An apparatus is described that facilitates the determination of incorporation levels of isotope labelled, gaseous precursors into volatile insect-derived metabolites. Atmospheres of varying gas compositions can be generated by evacuation of a working chamber followed by admission of the required levels of component gases, using a precision, digitised pressure read-out system. Insects such as fruit-flies are located initially in a small introduction chamber, from which migration can occur downwards into the working chamber. The level of incorporation of labelled precursors is continuously assayed by the Solid Phase Micro Extraction (SPME) technique and GC-MS analyses. Experiments with both Bactrocera species (fruit-flies) and a parasitoid wasp, Megarhyssa nortoni nortoni (Cresson) and oxygen-18 labelled dioxygen illustrate the utility of this system. The isotope effects of oxygen-18 on the carbon-13 NMR spectra of 1,7- dioxaspiro[5,5]undecane are also described.

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.

Oxidative extraction and ion-exchange of lithium in Li2MoO3: synthesis of Li2âxMoO3 and H2MoO3

It is shown that lithium can be oxidatively extracted from Li2MoO3 at room temperature using Br2 in CHCl3. The delithiated oxides, Li2â��xMoO3 (0 < x â�¤ 1.5) retain the parent ordered rocksalt structure. Complete removal of lithium from Li2MoO3 using Br2 in CH3CN results in a poorly crystalline MoO3 that transforms to the stable structure at 280�°C. Li2MoO3 undergoes topotactic ion-exchange in aqueous H2SO4 to yield a new protonated oxide, H2MoO3.

High subsoil chloride concentrations reduce soil water extraction and crop yield on Vertosols in north-eastern Australia

Salinity, sodicity, acidity, and phytotoxic levels of chloride (Cl) in subsoils are major constraints to crop production in many soils of north-eastern Australia because they reduce the ability of crop roots to extract water and nutrients from the soil. The complex interactions and correlations among soil properties result in multi-colinearity between soil properties and crop yield that makes it difficult to determine which constraint is the major limitation. We used ridge-regression analysis to overcome colinearity to evaluate the contribution of soil factors and water supply to the variation in the yields of 5 winter crops on soils with various levels and combinations of subsoil constraints in the region. Subsoil constraints measured were soil Cl, electrical conductivity of the saturation extract (ECse), and exchangeable sodium percentage (ESP). The ridge regression procedure selected several of the variables used in a descriptive model, which included in-crop rainfall, plant-available soil water at sowing in the 0.90-1.10 m soil layer, and soil Cl in the 0.90-1.10 m soil layer, and accounted for 77-85% of the variation in the grain yields of the 5 winter crops. Inclusion of ESP of the top soil (0.0-0.10 m soil layer) marginally increased the descriptive capability of the models for bread wheat, barley and durum wheat. Subsoil Cl concentration was found to be an effective substitute for subsoil water extraction. The estimates of the critical levels of subsoil Cl for a 10% reduction in the grain yield were 492 mg cl/kg for chickpea, 662 mg Cl/kg for durum wheat, 854 mg Cl/kg for bread wheat, 980 mg Cl/kg for canola, and 1012 mg Cl/kg for barley, thus suggesting that chickpea and durum wheat were more sensitive to subsoil Cl than bread wheat, barley, and canola.

Effect of DNA extraction on ageing success in coral trout (Plectropomus leopardus) otoliths

To maximize the information commonly collected from otoliths, the effect of DNA extraction on the estimation of age with otoliths was evaluated by comparing sagittal otolith samples from common coral trout (Plectropomus leopardus) for clarity and ageing discrepancies in DNA-extracted and untreated control otoliths. The DNA extraction process had no significant effect, indicating that archived otoliths can be used as a source of DNA while retaining their utility for age estimation.

Kinetics of Extraction of Iron(II1) by Bis(2-ethylhexyl Phosphate in a Laminar Liquid-Liquid Jet Reactor

The kinetics of iron(II1) extraction by bis(Zethylhexy1) phosphate (HDEHP, HA) in kerosene from sulfuric acid solutions has been studied in a liquid-liquid laminar jet reactor. The contact time of the interface in this reacting device is of the same order of magnitude as the surface renewal time in dispersion mixing and much less than that obtained in the relatively quiescent condition of the Lewis cell. Yet the analysis of the data in this study suggested a rate-controlling step involving surface saturation quite in conformity with that obtained in the Lewis cell and not with that in dispersion mixing as reported in the literature. Further, the mechanism suggested a weaker dependence of the rate on hydrogen ion concentration which was reported by other workers.