992 resultados para Continuously differentiable


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Mode of access: Internet.

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This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

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A review of published literature was made to establish the fundamental aspects of rolling and allow an experimental programme to be planned. Simulated hot rolling tests, using pure lead as a model material, were performed on a laboratory mill to obtain data on load and torque when rolling square section stock. Billet metallurgy and consolidation of representative defects was studied when modelling the rolling of continuously cast square stock with a view to determining optimal reduction schedules that would result in a product having properties to the high level found in fully wrought billets manufactured from large ingots. It is difficult to characterize sufficiently the complexity of the porous central region in a continuously cast billet for accurate modelling. However, holes drilled into a lead billet prior to rolling was found to be a good means of assessing central void consolidation in the laboratory. A rolling schedule of 30% (1.429:1) per pass to a total of 60% (2.5:1) will give a homogeneous, fully recrystallized product. To achieve central consolidation, a total reduction of approximately 70% (3.333:1) is necessary. At the reduction necessary to achieve consolidation, full recrystallization is assured. A theoretical analysis using a simplified variational principle with experimentally derived spread data has been developed for a homogeneous material. An upper bound analysis of a single, centrally situated void has been shown to give good predictions of void closure with reduction and the reduction required for void closure for initial void area fractions 0.45%. A limited number of tests in the works has indicated compliance with the results for void closure obtained in the laboratory.

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*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler.

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Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

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We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive condition. This last result slightly improves some earlier work by G. Barles and H. Ishii.

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We report on continuously measured 222Rn activity concentrations in near-surface air at Neumayer Station in the period 1995-2011. This 17-year record showed no long-term trend and has overall mean ± standard deviation of (0.019 ± 0.012) Bq/m**3. A distinct and persistent seasonality could be distinguished with maximum values of (0.028 ± 0.013) Bq/m**3 from January to March and minimum values of (0.015 ± 0.009) Bq/m**3 from May to October. Elevated 222Rn activity concentrations were typically associated with air mass transport from the Antarctic Plateau. Our results do not support a relation between enhanced 222Rn activity concentrations at Neumayer and cyclonic activity or long-range transport from South America. The impact of oceanic 222Rn emissions could not be properly assessed but we tentatively identified regional sea ice extent (SIE) variability as a significant driver of the annual 222Rn cycle.

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A recently developed novel biomass fuel pellet, the Q’ Pellet, offers significant improvements over conventional white pellets, with characteristics comparable to those of coal. The Q’ Pellet was initially created at bench scale using a proprietary die and punch design, in which the biomass was torrefied in-situ¬ and then compressed. To bring the benefits of the Q’ Pellet to a commercial level, it must be capable of being produced in a continuous process at a competitive cost. A prototype machine was previously constructed in a first effort to assess continuous processing of the Q’ Pellet. The prototype torrefied biomass in a separate, ex-situ reactor and transported it into a rotary compression stage. Upon evaluation, parts of the prototype were found to be unsuccessful and required a redesign of the material transport method as well as the compression mechanism. A process was developed in which material was torrefied ex-situ and extruded in a pre-compression stage. The extruded biomass overcame multiple handling issues that had been experienced with un-densified biomass, facilitating efficient material transport. Biomass was extruded directly into a novel re-designed pelletizing die, which incorporated a removable cap, ejection pin and a die spring to accommodate a repeatable continuous process. Although after several uses the die required manual intervention due to minor design and manufacturing quality limitations, the system clearly demonstrated the capability of producing the Q’ Pellet in a continuous process. Q’ Pellets produced by the pre-compression method and pelletized in the re-designed die had an average dry basis gross calorific value of 22.04 MJ/kg, pellet durability index of 99.86% and dried to 6.2% of its initial mass following 24 hours submerged in water. This compares well with literature results of 21.29 MJ/kg, 100% pellet durability index and <5% mass increase in a water submersion test. These results indicate that the methods developed herein are capable of producing Q’ Pellets in a continuous process with fuel properties competitive with coal.

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There is increasing interest in the use of continuous housing systems for dairy cows, with various reasons put forward to advocate such systems. However, the welfare of dairy cows is typically perceived to be better within pasture-based systems, although such judgements are often not scientifically based. The aim of this review was to interrogate the existing scientific literature to compare the welfare, including health, of dairy cows in continuously housed and pasture-based systems. While summarising existing work, knowledge gaps and directions for future research are also identified. The scope of the review is broad, examining relevant topics under three main headings; health, behaviour, and physiology. Regarding health, cows on pasture-based systems had lower levels of lameness, hoof pathologies, hock lesions, mastitis, uterine disease, and mortality compared to cows on continuously housed systems. Pasture access also had benefits for dairy cow behaviour, in terms of grazing, improved lying / resting times, and lower levels of aggression. Moreover, when given the choice between pasture and indoor housing, cows showed an overall preference for pasture, particularly at night. However, the review highlighted the need for a deeper understanding of cow preference and behaviour. Potential areas for concern within pasture-based systems included physiological indicators of more severe negative energy balance, and in some situations, the potential for compromised welfare with exposure to unpredictable weather conditions. In summary, the results from this review highlight that there remain considerable animal welfare benefits from incorporating pasture access into dairy production systems.

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Bioelectrochemical systems could have potential for bioremediation of contaminants either in situ or ex situ. The treatment of a mixture of phenanthrene and benzene using two different tubular microbial fuel cells (MFCs) designed for either in situ and ex situ applications in aqueous systems was investigated over long operational periods (up to 155 days). For in situ deployments, simultaneous removal of the petroleum hydrocarbons (>90% in term of degradation efficiency) and bromate, used as catholyte, (up to 79%) with concomitant biogenic electricity generation (peak power density up to 6.75 mWm−2) were obtained at a hydraulic retention time (HRT) of 10 days. The tubular MFC could be operated successfully at copiotrophic (100 ppm phenanthrene, 2000 ppm benzene at HRT 30 days) and oligotrophic (phenanthrene and benzene, 50 ppb each, HRT 10 days) substrate conditions suggesting its effectiveness and robustness at extreme substrate concentrations in anoxic environments. In the MFC designed for ex situ deployments, optimum MFC performance was obtained at HRT of 30 h giving COD removal and maximum power output of approximately 77% and 6.75 mWm−2 respectively. The MFC exhibited the ability to resist organic shock loadings and could maintain stable MFC performance. Results of this study suggest the potential use of MFC technology for possible in situ/ex situ hydrocarbon-contaminated groundwater treatment or refinery effluents clean-up, even at extreme contaminant level conditions.

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In this note we study the endomorphisms of certain Banach algebras of infinitely differentiable functions on compact plane sets, associated with weight sequences M. These algebras were originally studied by Dales, Davie and McClure. In a previous paper this problem was solved in the case of the unit interval for many weights M. Here we investigate the extent to which the methods used previously apply to general compact plane sets, and introduce some new methods. In particular, we obtain many results for the case of the closed unit disc. This research was supported by EPSRC grant GR/M31132