A one-dimensional prescribed curvature equation modeling the corneal shape

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

A one-dimensional prescribed curvature equation modeling the corneal shape.

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

Trace elements quantification in Portuguese red wines

Dissertation for the Degree of Master in Technology and Food Safety – Food Quality

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Nonlinear Dynamics for Local Fractional Burgers Equation Arising in Fractal Flow

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.

BIWiki - Using a Business Intelligence Wiki to Form a Virtual Community of Practice for Portuguese Master's Students

Web 2.0 software in general and wikis in particular have been receiving growing attention as they constitute new and powerful tools, capable of supporting information sharing, creation of knowledge and a wide range of collaborative processes and learning activities. This paper introduces briefly some of the new opportunities made possible by Web 2.0 or the social Internet, focusing on those offered by the use of wikis as learning spaces. A wiki allows documents to be created, edited and shared on a group basis; it has a very easy and efficient markup language, using a simple Web browser. One of the most important characteristics of wiki technology is the ease with which pages are created and edited. The facility for wiki content to be edited by its users means that its pages and structure form a dynamic entity, in permanent evolution, where users can insert new ideas, supplement previously existing information and correct errors and typos in a document at any time, up to the agreed final version. This paper explores wikis as a collaborative learning and knowledge-building space and its potential for supporting Virtual Communities of Practice (VCoPs). In the academic years (2007/8 and 2008/9), students of the Business Intelligence module at the Master's programme of studies on Knowledge Management and Business Intelligence at Instituto Superior de Estatistica e Gestao de Informacao of the Universidade Nova de Lisboa, Portugal, have been actively involved in the creation of BIWiki - a wiki for Business Intelligence in the Portuguese language. Based on usage patterns and feedback from students participating in this experience, some conclusions are drawn regarding the potential of this technology to support the emergence of VCoPs; some provisional suggestions will be made regarding the use of wikis to support information sharing, knowledge creation and transfer and collaborative learning in Higher Education.

Master's in Autonomous Systems: An Overview of the Robotics Curriculum and Outcomes at ISEP, Portugal

Robotics research in Portugal is increasing every year, but few students embrace it as one of their first choices for study. Until recently, job offers for engineers were plentiful, and those looking for a degree in science and technology would avoid areas considered to be demanding, like robotics. At the undergraduate level, robotics programs are still competing for a place in the classical engineering graduate curricula. Innovative and dynamic Master's programs may offer the solution to this gap. The Master's degree in autonomous systems at the Instituto Superior de Engenharia do Porto (ISEP), Porto, Portugal, was designed to provide a solid training in robotics and has been showing interesting results, mainly due to differences in course structure and the context in which students are welcomed to study and work.

Hydrologic modeling and uncertainty analysis of an ungauged watershed using mapwindow-swat

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies

On the pricing of bivariate options in the presence of a discrete dividend payment

A Work Project, presented as part of the requirements for the Award of a Master's Double Degree in Finance from the NOVA School of Business and Economics / Masters Degree in Economics from Insper

Students' choice of a master in management in Portugal: A means-end chain approach

In the increasingly competitive market of higher education introduced by the Bologna Declaration, understanding the decision-making of master in management students is at the center of institutional management and marketing efforts on its mission to attract prospective students in a less costly, more efficient manner. The means-end chain approach, applied to the choice of a Portuguese institution in which to pursue a master in management, points to the position in rankings and to the non-specificity of the program as the most important attributes. Additionally, results show that students with distinct demographic, household, or background characteristics choose in significantly different manners.

Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations