On the evaluation of powers /

Bibliography: leaf 6.

On the nonlinear Neumann problem involving the critical Sobolev exponent on the boundary

in this paper we investigate the solvability of the Neumann problem (1.1) involving the critical Sobolev exponents on the right-hand side of the equation and in the boundary condition. It is assumed that the coefficients Q and P are smooth. We examine the common effect of the mean curvature of the boundary a deltaOhm and the shape of the graph of the coefficients Q and P on the existence of solutions of problem (1.1). (C) 2003 Published by Elsevier Inc.

Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

Critical behavior of one-particle spectral weights in the transverse Ising model

We investigate the critical behavior of the spectral weight of a single quasiparticle, one of the key observables in experiment, for the particular case of the transverse Ising model. Series expansions are calculated for the linear chain and the square and simple cubic lattices. For the chain model, a conjectured exact result is discovered. For the square and simple cubic lattices, series analyses are used to estimate the critical exponents. The results agree with the general predictions of Sachdev [Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999)].

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

TEOLOGIA DA PROSPERIDADE: ADAPTAÇÃO DA RELIGIÃO À LÓGICA DA SOCIEDADE DE CONSUMO.

Esta dissertação analisa a Teologia da Prosperidade, especialmente seu poder de adaptar a religião à lógica da sociedade de consumo. Essa teologia surge nos Estados Unidos na década de 1940, consolidando-se rapidamente no meio evangélico, chegou a influenciar inclusive as igrejas denominadas tradicionais. Sua ênfase está na promessa da prosperidade para seus fiéis. A pesquisa pretende descrever as raízes e o contexto do surgimento desta teologia, sua chegada e propagação no Brasil, seus principais expoentes e sua apropriação pelas igrejas neopentecostais. A suspeita que orienta a pesquisa é a de que o êxito da Teologia da Prosperidade se deve à sua capacidade de adaptar a religião à lógica da sociedade de consumo.

A IMPORTÂNCIA DA MÚSICA NA FORMAÇÃO DO INDIVÍDUO: UMA REFLEXÃO SOBRE OS OBSTÁCULOS DA DIFUSÃO DA EDUCAÇÃO MUSICAL NO ESPAÇO ESCOLAR

Este trabalho investigou as interações a entre Música e Matemática, considerando experiências e reflexões de expoentes das ciências exatas, que com seus conceitos de intervalo musical, razões e proporções, consonância, harmonia, temperamento, série harmônica, contribuíram para a estruturação arte da música como ciência. Sob a luz dessa ciência da música, mediante análise descritiva de partitura, contou a história de um país que, segundo o P.I.S.A., se manteve no ranking da educação de 2000 a 2012, revelando interdisciplinaridade das ciências e interações dos conceitos de pensamento analógico, preconizados por Levy e Machado e da teoria das inteligências múltiplas de Gardner. E por fim, se propôs a refletir sobre a importância da educação musical na formação do indivíduo e sobre os obstáculos de sua difusão no espaço escolar.

Good practice guide in learning and teaching

This is the second edition of our Aston Business School (ABS) Good Practice Guide and the enthusiasm of the contributors appears undiminished. I am again reminded that I work with a group of very committed, dedicated and professional colleagues. Once again this publication is produced to celebrate and promote good teaching across the School and to offer encouragement to those imaginative and innovative staff who continue to wish to challenge students to learn to maximum effect. It is hoped that others will pick up some good ideas from the articles contained in this volume. Contributors to this Guide were not chosen because they are the best teachers in the School, although they are undoubtedly all amongst my colleagues who are exponents of enthusiastic and inspiring approaches to learning. The Quality Unit approached these individuals because they declared on their Annual Module Reflection Forms that they were doing something interesting and worthwhile which they thought others might find useful. Amongst those reading the Guide I am sure that there are many other individuals who are trying to operate similar examples of good practice in their teaching, learning and assessment methods. I hope that this publication will provoke these people into providing comments and articles of their own and that these will form the basis of next year’s Guide. It may also provoke some people to try these methods in their own teaching. The themes of the articles this year can be divided into two groups. The first theme is the quest to help students to help themselves to learn via student-run tutorials, surprise tests and mock examinations linked with individual tutorials. The second theme is making learning come to life in exciting practical ways by, for example, hands-on workshops and simulations, story telling, rhetorical questioning and discussion groups. A common theme is one of enthusiasm, reflection and commitment on behalf of the lecturers concerned. None of the approaches discussed in this publication are low effort activities on the part of the facilitator, but this effort is regarded as worthwhile as a means of creating greater student engagement. As Biggs (2003)[1] says, in his similarly inspiring way, students learn more the less passive they are in their learning. (Ref). The articles in this publication bear witness of this and much more. Since last year Aston Business School has launched its Research Centre in Higher Education Learning and Management (HELM) which is another initiative to promote excellent learning and teaching. Even before this institution has become fully operational, at least one of the articles in this publication has seen the light of day in the research arena and at least two others are ripe for dissemination to a wider audience via journal publication. More news of our successes in this activity will appear in next year’s edition. May I thank the contributors for taking time out of their busy schedules to write the articles this summer, and to Julie Green who runs the ABS Quality Unit, for putting our diverse approaches into a coherent and publishable form and for chasing us when we have needed it! I would also like to thank Ann Morton and her colleagues in the Centre for Staff Development who have supported this publication. During the last year the Centre has further stimulated the learning and teaching life of the School (and the wider University) via their Learning and Teaching Week and sponsorship of Teaching Quality Enhancement Fund (TQEF) projects. Pedagogic excellence is in better health at Aston than ever before – long may this be because this is what life in HE should be about.

Statistical mechanics of low-density parity-check codes

We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multispin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.

The creep behaviour of pressure diecast zinc-aluminium based alloys

The creep behaviour of three pressure diecast commercial zinc-aluminium based alloys: Mazak 3, corresponding to BS 1004A, and the new alloys ZA.8 and ZA.27 with a series of alloys with compositions ranging from 0% to 30% aluminium was investigated. The total creep elongation of commercial alloys was shown to be well correlated using an empirical equation. Based on this a parametrical relationship was derived which allowed the total creep extension to be related to the applied stress, the temperature and the time of test, so that a quantitative assessment of creep of the alloys could be made under different conditions. Deviation from the normal creep kinetics occurred in alloys ZA.8 and ZA.27 at very low stresses, 150°C, due to structural coarsening combined with partial transformation of ε -phase into T' phase. The extent of primary creep was found to increase with aluminium content, but secondary creep rates decreased in the order Mazak 3, ZA.8 and ZA.27. Thus, based on the above equation, ZA.8 was found to have a substantially better total creep resistance than ZA.27, which in turn was marginally better than Mazak 3 for strains higher than 0.5%, but inferior for smaller strains, due to its higher primary creep extension. The superior creep resistance of ZA.8 was found to be due to the presence of strictly-orientated, thin plate-like precipitates of ε(CuZn4) phase in the zinc matrix of the eutectic and the lamellarly decomposed β phase, in which the precipitation morphology and orientation of ε in the zinc matrix was determined. Over broad ranges of temperature and stresses, the stress exponents and activation energies for creep were found to be consistent with some proposed creep rate mechanisms; i.e. viscous glide for Mazak 3, dislocation climb over second phase particles for ZA.8 and dislocation climb for ZA.27, controlled by diffusion in the zinc-rich phase. The morphology of aluminium and copper-rich precipitates formed from the solid solution of zinc was clearly revealed. The former were found to further increase the creep rate of inherently low creep resistant zinc, but the latter contributed significantly to the creep resistance. Excess copper in the composition, however, was not beneficial in improving the creep resistance. Decomposition of β in copper-containing alloys was found to be through a metastable Zn-Al phase which is strongly stabilised by copper, and the final products of the decomposition had a profound effect on the creep strength of the alloys. The poor creep resistance of alloy ZA.27 was due to the presence of particulate products derived from decomposed β-phase and a large volume of fine, equiaxed products of continuously decomposed α-dendrites.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

The creep properties of a series of zinc-rich zinc-aluminium alloys

The compressive creep behaviour of six sand cast zinc-rich alloys: No3 and No5, corresponding to BS 1004A and BS 1004B, respectively, alloy No2, ILZRO,.16 and two newer alloys ACuZinc5 and ACuZinc10 was investigated. The total creep contraction of the alloys was found to be well correlated using an empirical equation. On the basis of this equation, a parametrical relationship was derived which allowed the total creep contraction to be related to the applied stress, the temperature and the time of test, so that a quantitative assessment of compressive creep of the alloys could be made under different testing conditions. The primary creep and secondary creep rates were found for the alloys at different temperatures and stresses. Generally, the primary creep contraction was found to increase with copper content, whereas secondary creep rates decreased in the order No3, ACuZinc10, ACuZinc5 and No2. ILZRO.16 was tested only at the highest stress and two higher temperatures. The results showed that ILZRO.16 had higher creep resistance than all the other alloys. Thus, based on the above empirical equation, alloy No2 was found to have a substantially better total creep resistance than alloys No3 and No5, and slightly better than ACuZinc5 and ACuZinc10 for strains up to 1%. Both ACuZinc alloys had higher creep strength than commercial alloys No3 and No5. Alloy No5 had much higher creep resistance than alloy No3 under all conditions. The superior creep resistance of alloy No2 was considered to be due to the presence of small precipitates of -phase in the zinc matrix and a regular eutectic morphology. The stress exponents and activation energies for creep under different testing conditions were found to be consistent with some established creep-controlling mechanisms; i.e. dislocation climb for alloy No3, dislocation climb over second phase particles for alloys No5, No2, ACuZinc10, controlled by lattice diffusion in the zinc-rich phase. The lower creep resistance of alloy No3 was mainly due to the lower creep strength of copper-free primary particles having greater volume than eutectic in the microstructure. Alloys No5, ACuZinc5 and ACuZinc10 showed much better creep resistance than alloy No3, based on the precipitation-hardening due to the presence of small -phase precipitates. The primary dendrites in both ACuZinc alloys however were not of much benefit in improving the creep resistance of the alloys.