939 resultados para Second Order Parabolic Heat Equation


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Primary olfactory neurons are located in the olfactory neuroepithelium lining the nasal cavity. Their axons converge and form glomeruli with the dendrites of second-order neurons in the olfactory bulb. The molecular basis of primary olfactory axon guidance, targeting and subsequent arborisation is largely unknown. In this study we examined the spatio-temporal expression of the Eph receptor EphB2 and its ligands, ephrin-B1 and ephrin-B2, during development of the rat primary olfactory system. Unlike in other regions of the nervous system where receptor and ligand expression patterns are usually non-overlapping, EphB2, ephrin-B1 and ephrin-B2 were all expressed by primary and second-order olfactory neurons. In the embryonic animal we found that these three proteins had distinct and different expression patterns. EphB2 was first expressed at E18.5 by the perikarya of primary olfactory neurons. In contrast, ephrin-B1 was expressed from E13.5 and was localised to the axons of these cells up to E18.5 but was then restricted to the perikarya. Ephrin-B2, however, was expressed by olfactory ensheathing cells. EphB2, ephrin-B1 and ephrin-B2 were also expressed in the prenatal olfactory bulb and were restricted to the perikarya of mitral cells. In the post-natal olfactory bulb there was a shift in the localisation of both EphB2 and ephrin-B1 to the dendritic arborisations of mitral cells. The dynamic and tightly regulated spatio-temporal expression patterns of EphB2, ephrin-B1 and ephrin-B2 by specific olfactory cell populations suggest that these molecules have the potential to regulate important developmental events in the olfactory system. (C) 2001 Elsevier Science B.V. All rights reserved.

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The batch removal of hexavalent chromium (Cr(Vl)) from wastewater under different experimental conditions using economic adsorbents was investigated in this study. These adsorbents were produced from the pyrolysis and activation of the waste tyres (TAC) and from the pyrolysis of sawdust (SPC). The performance of these adsorbents against commercial activated carbon F400 (CAC) has also been carried out. The removal was favoured at low pH, with maximum removal at pH = 2 for all types of carbon. The effects of concentration, temperature and particle size have been reported. All sorbents were found to efficiently remove Cr(VI) from solution. The batch sorption kinetics have been tested for a first-order reversible reaction, a first-order and second-order reaction. The rate constants of adsorption for all these kinetic models have been calculated. The applicability of the Langmuir isotherm for the present system has been tested at different temperatures. The thermodynamic parameters (AGO, K,) obtained indicate the endothermic nature of Cr(Vl) adsorption on TAC, SPC and CAC. (C) 2001 Elsevier Science B.V. All rights reserved.

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The veg1 (vegetative) mutant in pea (Pisum sativum L.) does not flower under any circumstances and gi (gigas) mutants remain vegetative under certain conditions. gi plants are deficient in production of floral stimulus, whereas veg1 plants lack a response to floral stimulus. During long days in particular, these non-flowering mutant plants eventually enter a stable compact phase characterised by a large reduction in internode length, small leaves and growth of lateral shoots from the upper-stem (aerial) nodes. The first-order laterals in turn produce second-order laterals and so on in a reiterative pattern. The apical bud is reduced in size but continues active growth. Endogenous hormone measurements and gibberellin application studies with gi-1, gi-2 and veg1 plants indicate that a reduction in gibberellin and perhaps indole-3-acetic acid level may account, at least partially, for the compact aerial shoot phenotype. In the gi-1 mutant, the compact phenotype is rescued by transfer from a 24- to an 8-h photoperiod. We propose that in plants where flowering is prevented by a lack of floral stimulus or an inability to respond, the large reduction in photoperiod gene activity during long days may lead to a reduction in apical sink strength that is manifest in an altered hormone profile and weak apical dominance.

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Service quality is assessed by customers along the dimensions of staff conduct, credibility, communication, and access to teller services. Credibility and staff conduct emerge as the highest loading first-order factors. This highlights the significance of rectifying mistakes while keeping customers informed, and employing branch staff that are responsive and civilized in their conduct. Discovery of a valid second-order factor, namely, overall customer service quality, underscores the importance of providing quality service across all its dimensions. For example, if the bank fails to rectify mistakes and keep customers informed but excels in all other dimensions, its overall customer service quality can still be rated poorly.

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We discuss the connection between quantum interference effects in optical beams and radiation fields emitted from atomic systems. We illustrate this connection by a study of the first- and second-order correlation functions of optical fields and atomic dipole moments. We explore the role of correlations between the emitting systems and present examples of practical methods to implement two systems with non-orthogonal dipole moments. We also derive general conditions for quantum interference in a two-atom system and for a control of spontaneous emission. The relation between population trapping and dark states is also discussed. Moreover, we present quantum dressed-atom models of cancellation of spontaneous emission, amplification on dark transitions, fluorescence quenching and coherent population trapping.

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The neurexins are a large family of neuronal cell-surface proteins believed to be involved in intercellular signalling and the formation of intercellular junctions. To begin to assess the role of these proteins in the olfactory bulb, we describe here the expression patterns of their transmembrane and secreted ligands, the neuroligins and neurexophilins, during both embryonic and postnatal development. In situ hybridisation showed that neuroligin 1 and 2 were expressed by second order mitral cells during early postnatal development but not in adults. The secreted ligand for a-neurexin, neurexophilin 1, was also expressed in the postnatal olfactory bulb. Neurexophilin 1 was detected in only periglomerular cells during the early postnatal period of glomerular formation but later was also expressed in mitral cells. These results suggest that neurexin-ligand interactions may be important for development and/or maturation of synaptic connections in the primary olfactory pathway.

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High index Differential Algebraic Equations (DAEs) force standard numerical methods to lower order. Implicit Runge-Kutta methods such as RADAU5 handle high index problems but their fully implicit structure creates significant overhead costs for large problems. Singly Diagonally Implicit Runge-Kutta (SDIRK) methods offer lower costs for integration. This paper derives a four-stage, index 2 Explicit Singly Diagonally Implicit Runge-Kutta (ESDIRK) method. By introducing an explicit first stage, the method achieves second order stage calculations. After deriving and solving appropriate order conditions., numerical examples are used to test the proposed method using fixed and variable step size implementations. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.

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The long short-term memory (LSTM) is not the only neural network which learns a context sensitive language. Second-order sequential cascaded networks (SCNs) are able to induce means from a finite fragment of a context-sensitive language for processing strings outside the training set. The dynamical behavior of the SCN is qualitatively distinct from that observed in LSTM networks. Differences in performance and dynamics are discussed.

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Cell surface glycoconjugates have been implicated in the growth and guidance of subpopulations of primary olfactory axons. While subpopulations of primary olfactory neurons have been identified by differential expression of carbohydrates in the rat there are few reports of similar subpopulations in the mouse. We have examined the spatiotemporal expression pattern of glycoconjugates recognized by the lectin from Wisteria floribunda (WFA) in the mouse olfactory system. In the developing olfactory neuroepithelium lining the nasal cavity, WFA stained a subpopulation of primary olfactory neurons and the fascicles of axons projecting to the target tissue, the olfactory bulb. Within the developing olfactory bulb, WFA stained the synaptic neuropil of the glomerular and external plexiform layers. In adults, strong expression of WFA ligands was observed in second-order olfactory neurons as well as in neurons in several higher order olfactory processing centres in the brain. Similar, although distinct, staining of neurons in the olfactory pathway was detected with Dolichos biflorus agglutinin. These results demonstrate that unique subpopulations of olfactory neurons are chemically coded by the expression of glycoconjugates. The conserved expression of these carbohydrates across species suggests they play an important role in the functional organization of this region of the nervous system.

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We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

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Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

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The standard mathematical models in population ecology assume that a population's growth rate is a function of its environment. In this paper we investigate an alternative proposal according to which the rate of change of the growth rate is a function of the environment and of environmental change. We focus on the philosophical issues involved in such a fundamental shift in theoretical assumptions, as well as on the explanations the two theories offer for some of the key data such as cyclic populations. We also discuss the relationship between this move in population ecology and a similar move from first-order to second-order differential equations championed by Galileo and Newton in celestial mechanics.

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Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

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This paper describes the buckling phenomenon of a tubular truss with unsupported length through a full-scale test and presents a practical computational method for the design of the trusses allowing for the contribution of torsional stiffness against buckling, of which the effect has never been considered previously by others. The current practice for the design of a planar truss has largely been based on the linear elastic approach which cannot allow for the contribution of torsional stiffness and tension members in a structural system against buckling. The over-simplified analytical technique is unable to provide a realistic and an economical design to a structure. In this paper the stability theory is applied to the second-order analysis and design of the structural form, with detailed allowance for the instability and second-order effects in compliance with design code requirements. Finally, the paper demonstrates the application of the proposed method to the stability design of a commonly adopted truss system used in support of glass panels in which lateral bracing members are highly undesirable for economical and aesthetic reasons.

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Mestrado em Engenharia Química