Domínios de potências fracionárias de operadores matriciais segundo Lasiecka-Triggiani

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

Multidimensional scaling analysis of fractional systems

This paper investigates the use of multidimensional scaling in the evaluation of fractional system. Several algorithms are analysed based on the time response of the closed loop system under the action of a reference step input signal. Two alternative performance indices, based on the time and frequency domains, are tested. The numerical experiments demonstrate the feasibility of the proposed visualization method.

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Domains of rural social work practice

Even though there is substantial agreement about the nature of rural contexts, practice principles, and factors influencing practice we still do not have a framework for organising this knowledge in a way that can directly inform the practitioner in their day-to-day work. In this paper, we introduce the concepts 'practice domains', 'domain location', and 'domain alignment' that, taken together, provide such a framework. We suggest that each practitioner works within a number of practice domains. A domain is a discourse about practice comprising narratives about how a social worker should practise and which factors they should take most account of in their practice decision making. Each practitioner, and each practice process, can be located somewhere within each domain (domain location) and also situated amongst domains according to their relative alignment with each of them (domain alignment). In this paper, we present this framework and show how it is useful for practitioners in understanding practice, identifying factors influencing it, and making practice decisions in immediate, concrete situations.

A general procedure for the derivation of principal domains of higher-order spectra

A general procedure to determine the principal domain (i.e., nonredundant region of computation) of any higher-order spectrum is presented, using the bispectrum as an example. The procedure is then applied to derive the principal domain of the trispectrum of a real-valued, stationary time series. These results are easily extended to compute the principal domains of other higher-order spectra

Numerical methods and analysis for a class of fractional advection-dispersion models

In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1 < γ < 2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.

Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

Dreams and nightmares of alternative powers' futures

This chapter argues the importance of the role and nature of other powers to world order. The author suggests that, if the US are not prepared to take a lead in creating a rules-based legal order, they should and can do so – and it is in their interests to do so. America should be a natural leader in this process, taking part in a global dialogue just as they did in the transatlantic dialogue during the late eighteenth century.

Arts practice and disconnected youth in Australia : impact and domains of change

Background: This paper describes research conducted with Big hART, Australia's most awarded participatory arts company. It considers three projects, LUCKY, GOLD and NGAPARTJI NGAPARTJI across separate sites in Tasmania, Western NSW and Northern Territory, respectively, in order to understand project impact from the perspective of project participants, Arts workers, community members and funders. Methods: Semi-structured interviews were conducted with 29 respondents. The data were coded thematically and analysed using the constant comparative method of qualitative data analysis. Results: Seven broad domains of change were identified: psychosocial health; community; agency and behavioural change; the Art; economic effect; learning and identity. Conclusions: Experiences of participatory arts are interrelated in an ecology of practice that is iterative, relational, developmental, temporal and contextually bound. This means that questions of impact are contingent, and there is no one path that participants travel or single measure that can adequately capture the richness and diversity of experience. Consequently, it is the productive tensions between the domains of change that are important and the way they are animated through Arts practice that provides sign posts towards the impact of Big hART projects.