Sistemas integrables discretos, polinomios matriciales ortogonales y problemas de Riemann-Hilbert

El propósito de esta tesis doctoral es el estudio de la conexión, mediante el problema de Riemann-Hilbert, entre sistemas discretos y la teoría de polinomios matriciales ortogonales. La investigación de los modelos integrables se originó en la Mecánica Clásica, en relación a la resolución de las ecuaciones de Newton [2]. Los trabajos de Liouville, Hamilton, Jacobi y otros sentaron las bases de los sistemas integrables como prototipos modelos resolubles por cuadraturas, v.g., por integración directa [7]. Hay una cantidad importante de investigación dedicada a los aspectos geométricos de los sistemas clásicos integrables y superintegrables [66], [82], especialmente en relación a la separación de variables de la ecuación de Hamilton-Jacobi [75]. Fue la aplicación, en la segunda mitad del siglo pasado, de la transformada espectral inversa para la resolución del problema de Cauchy de la ecuación de Korteweg-de Vries [42, 43] la que marcó el inicio de una nueva etapa en este campo, el del estudio de sistemas integrables con un número infinito de grados de libertad, que generalmente se expresan en términos de jerarquías de ecuaciones no lineales en derivadas parciales. Particularmente reseñable, por su aplicación en la hidrodinámica y en la óptica cuántica, es la aparición de las soluciones a un número de solitones arbitrario. En las últimas tres décadas ha habido un importante interés por el estudio de modelos discretos, v.g., sistemas dinámicos de nidos en un retículo de puntos, y expresados en términos de ecuaciones no lineales en diferencia parciales. Muchas de las técnicas encontradas en el mundo continuo se extendieron a este nuevo contexto discreto. Hay dos razones fundamentales para este interés...

A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

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.

Optimal investment under stochastic volatility and power type utility function

2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.

Involutivity of the Hamilton-Cartan equations of a second-order Lagrangian admitting a first-order Hamiltonian formalism

Involutivity of the Hamilton-Cartan equations of a second-order Lagrangian admitting a first-order Hamiltonian formalism

Extended Cahill-Glauber formalism for finite-dimensional spaces: I. Fundamentals

The Cahill-Glauber approach for quantum mechanics on phase space is extended to the finite-dimensional case through the use of discrete coherent states. All properties and features of the continuous formalism are appropriately generalized. The continuum results are promptly recovered as a limiting case. The Jacobi theta functions are shown to have a prominent role in the context.

Análise de parâmetros da função característica de Hamilton

A análise de velocidades é um processo fundamental na sísmica de reflexão, onde as velocidades de empilhamento bem como o tempo de trânsito de afastamento nulo (onde supõe-se que a fonte e o detetor ocupam a mesma posição) são parâmetros suficientes na determinação do modelo geológico para meios com camadas horizontais. Por outro lado quando expresso através do formalismo estabelecido por Hamilton, os mesmos parâmetros (velocidade e tempo de afastamento nulo) são suficientes para determinar a função característica para este mesmo tipo de meio. Para o caso de um modelo geológico heterogêneo com interfaces arbitrariamente curvas, a função característica de Hamilton é dada a partir da estimativa de nove parâmetros, onde os mesmos parâmetros são necessários na determinação do modelo geológico em 3D. Este trabalho tem por objetivo estimar os parâmetros que determinam a função característica de Hamilton para meios 3D e estudar a influência de cada parâmetro na função, através de cortes horizontais nas seções de tempos de trânsito (conhecidos como time slices), nas configurações de ponto médio comum e afastamento nulo. Dentro desta abordagem é dado um exemplo a partir de um modelo sintético onde, aqueles resultados obtidos com estudo da influência de cada parâmetro na função característica, são aplicados como um critério de ajuste entre a função característica calculada e a função de tempos de trânsito obtida no levantamento de dados.

On the generalized canonical equations of Hamilton for a time-dependent mass particle

Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii (see historical review in Mikhailov (Mech. Solids 10(5):32-40, 1975), efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the so-called 'generalized canonical equations of Hamilton' for a variable mass particle. The applied technique consists in the consideration of the mass variation process as a dissipative phenomenon. Kozlov's (Stek. Inst. Math 223:178-184, 1998) method, originally devoted to the derivation of the generalized canonical equations of Hamilton for dissipative systems, is accordingly extended to the scenario of variable mass systems. This is done by conveniently writing the flux of kinetic energy from or into the variable mass particle as a 'Rayleigh-like dissipation function'. Cayley (Proc. R Soc. Lond. 8:506-511, 1857) was the first scholar to propose such an analogy. A deeper discussion on this particular subject will be left for a future paper.

Jacobi quartic curves revisited

This paper provides new results about efficient arithmetic on Jacobi quartic form elliptic curves, y 2 = d x 4 + 2 a x 2 + 1. With recent bandwidth-efficient proposals, the arithmetic on Jacobi quartic curves became solidly faster than that of Weierstrass curves. These proposals use up to 7 coordinates to represent a single point. However, fast scalar multiplication algorithms based on windowing techniques, precompute and store several points which require more space than what it takes with 3 coordinates. Also note that some of these proposals require d = 1 for full speed. Unfortunately, elliptic curves having 2-times-a-prime number of points, cannot be written in Jacobi quartic form if d = 1. Even worse the contemporary formulae may fail to output correct coordinates for some inputs. This paper provides improved speeds using fewer coordinates without causing the above mentioned problems. For instance, our proposed point doubling algorithm takes only 2 multiplications, 5 squarings, and no multiplication with curve constants when d is arbitrary and a = ±1/2.

Rejoinder to James Hamilton

Hamilton (2001) makes a number of comments on our paper (Harding and Pagan, 2002b). The objectives of this rejoinder are, firstly, to note the areas in which we agree; secondly, to define with greater clarity the areas in which we disagree; and, thirdly, to point to other papers, including a longer version of this response, where we have dealt with some of the issues that he raises. The core of our debate with him is whether one should use an algorithm with a specified set of rules for determining the turning points in economic activity or whether one should use a parametric model that features latent states. Hamilton begins his criticism by stating that there is a philosophical distinction between the two methods for dating cycles and concludes that the method we use “leaves vague and intuitive exactly what this algorithm is intended to measure”. Nothing is further from the truth. When seeking ways to decide on whether a turning point has occurred it is always useful to ask the question, what is a recession? Common usage suggests that it is a decline in the level of economic activity that lasts for some time. For this reason it has become standard to describe a recession as a decline in GDP that lasts for more than two quarters. Finding periods in which quarterly GDP declined for two periods is exactly what our approach does. What is vague about this?

An interview with sound artist Guy Webster by Jillian Hamilton and Jeremy Yuille

Guy Webster is a sound artist who has been featured in numerous festivals, galleries, conferences and theatres in Australia, Japan, UK and Europe. As part of the Transmute Collective he developed the immersive soundscape of Intimate Transactions. On 2nd November, 2005 Jilliann Hamilton and Jeremy Yuille met with Guy Webster to discuss his approach to immersion in soundsapes.

Evaluation of the Hamilton Youth Court Pilot 2003-2005

Pilot Youth Courts were introduced at Hamilton Sheriff Court in June 2003 and at Airdrie Sheriff Court in June 2004. Although introduced as one of a number of measures aimed at responding more effectively to youth crime (including young people dealt with through the Children’s Hearings System), the Youth Courts were intended for young people who would otherwise have been dealt with in the adult Sheriff Summary Court. The objectives of the pilot Youth Courts were to: • reduce the frequency and seriousness of re-offending by 16 and 17 year old offenders, particularly persistent offenders (and some 15 year olds who are referred to the court); • promote the social inclusion, citizenship and personal responsibility of these young offenders while maximising their potential; • establish fast track procedures for those young persons appearing before the Youth Court; • enhance community safety, by reducing the harm caused to individual victims of crime and providing respite to those communities which are experiencing high levels of crime; and • test the viability and usefulness of a Youth Court using existing legislation and to demonstrate whether legislative and practical improvements might be appropriate. Evaluation of the Hamilton and Airdrie Sheriff Youth Court pilots suggested that they had been successful in meeting the objectives set for them by the Youth Court Feasibility Group. Both were tightly run courts that dealt with a heavy volume of business. The particular strengths of the Youth Court model over previous arrangements included the fast-tracking of young people to and through the court, the reduction in trials, the availability of a wider range of resources and services for young people and ongoing judicial review. The successful operation of the pilot Youth Courts was dependent upon effective teamwork among the relevant agencies and professionals concerned. Good information sharing, liaison and communication appeared to exist across agencies and the procedures that were in place to facilitate the sharing of information seemed to be working well. This was also facilitated by the presence of dedicated staff within agencies, resulting in clear channels of communication, and in the opportunity provided by the multi-agency Implementation Groups to identify and address operational issues on an ongoing basis. However, whether Youth Courts are required in Scotland or whether procedural improvement were possible in the absence of dedicated resources and personnel was more difficult to assess. Two issues in particular required further attention. First, consideration needed to be given to whether the Youth Courts should be more explicitly youth focused and what this might entail. Second, greater clarity was required regarding for whom the Youth Courts were intended. This suggested the need for further discussion of Youth Court targeting and its potential consequences among the various agencies concerned.

Review: "Transfigured Stages : Major Practitioners and Theatre Aesthetics in Australia" by Margaret Hamilton

In Transfigured Stages: Major Practitioners and Theatre Aesthetics in Australia, Margaret Hamilton traces the emergence of a postdramatic performance aesthetic in Australian theatre in the 1980s, 1990s and early 2000s through what she characterizes as an ‘analysis’ (p. 15) or ‘critique’ (p. 16)of a series of pivotal productions. For Hamilton, the transfigured aesthetic in the spotlight here is one typified by a focus on memory, imagination, desire, fear or disgust as facets of the human condition; by a visual, televisual or interactive dramaturgy; and, most critically, by a metatheatrical tendency to make tensions in the theatre-making process part and parcel of the tensions in the performance itself (pp.18–20)...

Eruption centres of the Hamilton area of the Newer Volcanics Province, Victoria, Australia: Pinpointing volcanoes from a multifaceted approach to landform mapping

Volcanic eruption centres of the mostly 4.5 Ma-5000 BP Newer Volcanics Province in the Hamilton area of southeastern Australia were examined in detail using a multifaceted approach, including ground truthing and analysis of ArcGIS Total Magnetic Intensity and seamless geology data, NASA Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) digital elevation models and Google Earth satellite image interpretation. Sixteen eruption centres were recognised in the Hamilton area, including three previously unrecorded volcanoes-one of which, the Cas Maar, constitutes the northernmost maar-cone volcanic complex in the Western Plains subprovince. Seven previously allocated eruption centres were placed into question based on field and laboratory observations. Three phases of volcanic activity have been suggested by other authors and are interpreted to correlate with ages of >4 Ma, ca 2 Ma and <0.5 Ma, which may be further subdivided based on preservation of outcrop. Geochemical compositions of the dominantly basaltic products become increasingly alkaline and enriched in incompatible elements from Phases 1 to 2, with Phase 3 eruptions both covering the entire geochemical range and extending into increasingly enriched compositions. This research highlights the importance of a multifaceted approach to landform mapping and demonstrates that additional volcanic centres may yet be discovered in the Newer Volcanics Province

A creature of statute: Copyright law and legal formalism

This article argues that copyright law is not just a creature of statute, but it is also a social and imaginative contruct. It evaluates a number of critiques of legal formalism. Part 1 examines whether the positive rules and principles of copyright law are the product of historical contingency and political expediency. Part 2 considers the social operation of copyright law in terms of its material effects and cultural significance. Part 3 investigates the future of copyright law, in light of the politics of globalisation and the impact of new information technologies.