941 resultados para Characteristic Initial Value Problem
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Bibliography: leaf 33.
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"Supported in part by the Department of Energy under contract ENERGY/EY-76-S-02-2383, and submitted in partial fulfillment of the requirements of the Graduate College for the degree of doctor of philosophy."
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Bibliography: p. 32.
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The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, epsilon(N) = alphaepsilon cot beta (in which beta is the beach slope, alpha is the amplitude parameter and epsilon is the shallow water parameter) and are limited to tan(-1) (alphaepsilon) much less than beta less than or equal to pi/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as 6 and a increase, and reaches 7% of the linear solution. (C) 2003 Elsevier Ltd. All rights reserved.
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Despite the evidence of greater fatigability of the cervical flexor muscles in neck pain patients, the effect of unilaterality of neck pain on muscle fatigue has not been investigated. This study compared myoelectric manifestations of sternocleidomastoid (SCM) and anterior scalene (AS) muscle fatigue between the painful and non-painful sides in patients with chronic unilateral neck pain. Myoelectric signals were recorded from the sternal head of SCM and the AS muscles bilaterally during sub-maximal isometric cervical flexion contractions at 25% and 50% of the maximum voluntary contraction (MVC). The time course of the mean power frequency, average rectified value and conduction velocity of the electromyographic signals were calculated to quantify myoelectric manifestations of muscle fatigue. Results revealed greater estimates of the initial value and slope of the mean frequency for both the SCM and AS muscles on the side of the patient's neck pain at 25% and 50% of MVC. These results indicate greater myoelectric manifestations of muscle fatigue of the superficial cervical flexor muscles ipsilateral to the side of pain. This suggests a specificity of the effect of pain on muscle function and hence the need for specificity of therapeutic exercise in the management of neck pain patients. (C) 2003 European Federation of Chapters of the International Association for the Study of Pain. Published by Elsevier Ltd. All rights reserved.
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Objective: The purpose of this study was to investigate whether an endurance-strength training program is effective in reducing myoelectric manifestations of sternocleidomastoid (SCM) and anterior scalene (AS) muscle fatigue which have been found to be greater in people with chronic neck pain. Methods: Fifty-eight female patients with chronic non-severe neck pain were randomized into one of two 6-week exercise intervention groups: an endurance-strength training regime for the cervical flexor muscles or a referent exercise intervention involving low load retraining of the cranio-cervical flexor muscles. The primary outcomes were a change in maximum voluntary contraction (MVC) force and change of the initial value and rate of change of the mean frequency, average rectified value and conduction velocity detected from the SCM and AS muscles during sub-maximal isometric cervical flexion contractions at 50, 25 and 10% MVC. Results: At the 7th week follow-up assessment, the endurance-strength training group revealed a significant increase in MVC force and a reduction in the estimates of the initial value and rate of change of the mean frequency for both the SCM and AS muscles (P < 0.05). Both exercise groups reported a reduced average intensity of neck pain and reduced neck disability index score (P < 0.05). Conclusions: An endurance-strength exercise regime for the cervical flexor muscles is effective in reducing myoelectric manifestations of superficial cervical flexor muscle fatigue as well as increasing cervical flexion strength in a group of patients with chronic non-severe neck pain. Significance: Provision of load to challenge the neck flexor muscles is required to reduce the fatigability of the SCM and AS muscles in people with neck pain. Improvements in cervical muscle strength and reduced fatigability may be responsible for the reported efficacy with this type of exercise program. (c) 2006 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All fights reserved.
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We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by Edalat and Pattinson [1]. Compared to Edalat and Pattinson's implementation, our algorithm uses a more efficient arithmetic based on an arbitrary precision floating-point library. Despite the additional overestimations due to floating-point rounding, we obtain a similar bound on the convergence rate of the produced approximations. Moreover, our convergence analysis is detailed enough to allow a static optimisation in the growth of the precision used in successive Picard iterations. Such optimisation greatly improves the efficiency of the solving process. Although a similar optimisation could be performed dynamically without our analysis, a static one gives us a significant advantage: we are able to predict the time it will take the solver to obtain an approximation of a certain (arbitrarily high) quality.
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The aim of this study was to use the transformation of anionic to metathesis polymerization to produce block co-polymers of styrene-b-pentenylene using WC16 /PStLi and WC16/PStLi/ AlEtC12 catalyst systems. Analysis of the products using SEC and 1H and 13C NMR spectroscopy enabled mechanisms for metathesis initiation reactions to be proposed. The initial work involved preparation of the constituent homo-polymers. Solutions of polystyryllithium in cyclohexane were prepared and diluted so that the [PStLi]o<2x10-3M. The dilution produced initial rapid decay of the active species, followed by slower spontaneous decay within a period of days. This was investigated using UV / visible spectrophotometry and the wavelength of maximum absorbance of the PStLi was found to change with the decay from an initial value of 328mn. to λmax of approximately 340nm. after 4-7 days. SEC analysis of solutions of polystyrene, using RI and UV / visible (set at 254nm.) detectors; showed the UV:RI peak area was constant for a range of polystyrene samples of different moleculor weight. Samples of polypentenylene were prepared and analysed using SEC. Unexpectedly the solutions showed an absorbance at 254nm. which had to be considered when this technique was used subsequently to analyse polymer samples to determine their styrene/ pentenylene co-polymer composition. Cyclohexane was found to be a poor solvent for these ring-opening metathesis polymerizations of cyclopentene. Attempts to produce styrene-b-pentenylene block co-polymers, using a range of co-catalyst systems, were generally unsuccessful as the products were shown to be mainly homopolymers. The character of the polymers did suggest that several catalytic species are present in these systems and mechanisms have been suggested for the formation of initiating carbenes. Evidence of some low molecular weight product with co-polymer character has been obtained. Further investigation indicated that this is most likely to be ABA block copolymer, which led to a mechanism being proposed for the termination of the polymerization.
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In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.
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Purpose: The purpose of this study was to determine whether stereoacuity can be used as an indicator of prism adaptation. In particular, we wanted to know whether the time required for stereoacuity to return to the initial level after viewing through a prism can be used to determine the degree of adaptation. Materials and Methods: Eighteen subjects participated in this study. Stereoacuity and dissociated phoria were determined using the TNO stereotest and the Maddox rod, respectively. Prism vergences were measured using a prism bar. For each participant, prism power equivalent to the blur point of base-in (BI) and base-out (BO) fusional vergence at 40 cm was divided and placed in front of both eyes. At 0, 3, 6, 9 and 12 min after prism introduction, the stereoacuity was measured, and at 0 and 12 min, the heterophoria was measured. Results: The repeated measures ANOVA showed a significant difference between the mean stereoacuity for BI and BO prisms at the different measurement times (p < 0.05). For BO prism, the initial value was different between 0 and 3 min after the prism introduction, whereas for BI prism, a difference in stereoacuity was found between the pre-prism value and the value at 0, 3 and 6 min. The size of the heterophoria with BO and BI prisms was different from 0 to 12 min (p < 0.05). Conclusion: The time required for stereoacuity to return to baseline level was more than 3 min for BO, and more than 6 min for BI prism. In addition, the time required to return to baseline values was not similar for the stereoacuity and heterophoria. The recovery of stereoacuity is slower when adapting to divergence, as when looking from near to far. This implies that stereopsis responds faster to near targets than to distant one, and may precede complete phoria adaptation. © 2014 Informa Healthcare USA, Inc. All rights reserved: reproduction in whole or part not permitted.
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AOSD'03 Practitioner Report Performance analysis is motivated as an ideal domain for benefiting from the application of Aspect Oriented (AO) technology. The experience of a ten week project to apply AO to the performance analysis domain is described. We show how all phases of a performance analysts’ activities – initial profiling, problem identification, problem analysis and solution exploration – were candidates for AO technology assistance – some being addressed with more success than others. A Profiling Workbench is described that leverages the capabilities of AspectJ, and delivers unique capabilities into the hands of developers exploring caching opportunities.
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Arenesulfonic-acid functionalized SBA-15 materials have been used in the production of biodiesel from low grade oleaginous feedstock. These materials display an outstanding catalytic activity, being able to promote the transformation of crude palm oil with methanol into fatty acid methyl esters with high yield (85%) under mild reaction conditions. However, high sensitivity of the catalyst against poisoning by different substances has also been detected. Thus, alkaline metal cations, such as sodium or potassium exert a negative influence on the catalytic activity of these materials, being necessary amounts around 500 ppm of sodium in the reaction media to decrease the catalytic activity of these materials to a half of its initial value in just two reaction runs. The deactivation of arenesulfonic acid functionalized SBA-15 materials seems to occur in this case by ion exchange of the acid protons at the sulfonic groups. Organic unsaponifiable compounds like lecithin or retinol also induce a negative influence in the catalytic activity of these sulfonic acid-based materials, though not so intense as in the case of alkaline metals. The deactivating mechanism associated to the influence of the organic compounds seems to be linked to the adsorption of such substances onto the catalytic acid sites as well as on the silica surface. The accumulation of lecithin in the surface of catalyst, observed by means of thermogravimetric analysis, suggest the creation of a strong interaction, probably by ion pair, between this compound and the sulfonic acid group.
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An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application of approximation enables us to relate these problems to a problem of optimal program control, described by a system of ordinary differential equations, with a scalar pay-off function. It is found that the result of this problem is not changed, if the players use positional or program strategies. For the considered differential game, it is interesting that the ε-Slater saddle points are not equivalent and there exist two ε-Slater saddle points for which the values of all components of the vector pay-off function at one of them are greater than the respective components of the other ε-saddle point.
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Mathematics Subject Classification: 26A33, 31B10
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This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.