Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

HPC management and engineering in the hybrid cloud

The evolution and maturation of Cloud Computing created an opportunity for the emergence of new Cloud applications. High-performance Computing, a complex problem solving class, arises as a new business consumer by taking advantage of the Cloud premises and leaving the expensive datacenter management and difficult grid development. Standing on an advanced maturing phase, today’s Cloud discarded many of its drawbacks, becoming more and more efficient and widespread. Performance enhancements, prices drops due to massification and customizable services on demand triggered an emphasized attention from other markets. HPC, regardless of being a very well established field, traditionally has a narrow frontier concerning its deployment and runs on dedicated datacenters or large grid computing. The problem with common placement is mainly the initial cost and the inability to fully use resources which not all research labs can afford. The main objective of this work was to investigate new technical solutions to allow the deployment of HPC applications on the Cloud, with particular emphasis on the private on-premise resources – the lower end of the chain which reduces costs. The work includes many experiments and analysis to identify obstacles and technology limitations. The feasibility of the objective was tested with new modeling, architecture and several applications migration. The final application integrates a simplified incorporation of both public and private Cloud resources, as well as HPC applications scheduling, deployment and management. It uses a well-defined user role strategy, based on federated authentication and a seamless procedure to daily usage with balanced low cost and performance.

Complex functions with Geogebra

Complex functions, generally feature some interesting peculiarities, seen as extensions real functions, complementing the study of real analysis. However, the visualization of some complex functions properties requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the study of the functions defined from ℂ to ℂ through traditional techniques and by the use of Domain Colouring. Here, we will show how we can use GeoGebra for the study of complex functions, using several representations and creating tools which complement the tools already provided by the software. Our proposals designed for students of the first year of engineering and science courses can and should be used as an educational tool in collaborative learning environments. The main advantage in its use in individual terms is the promotion of the deductive reasoning (conjecture / proof). In performed the literature review few references were found involving this educational topic and by the use of a single software.