Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Contribution towards a reflection about methodological strategies in design education and the function of drawing in design

This work presents a reflection on Design education and specifically on the role of Drawing in this area. As a subject, Design has expanded its field of action expanding into new areas such as Experience Design or Service Design. It became necessary for the designer to have more than an education based on technological knowledge or know-how. Many authors like Meredith Davis, Don Norman or Jamie Hobson point out the urgency to review the curricula of Design courses because nowadays “… design is more than appearance, design is about interaction, about strategy and about services. Designers change social behavior” (Norman 2011). When shifting from a product-centered design to a person-centered design (in a structure, a service or in a relationship) what should the function of drawing in a design course be? What should its curriculum be? Our work methodology will be to confront today’s perspectives on design theory and practice in an attempt to add to the discussion on the methodological strategies in design teaching in the contemporary context.

Contribution towards a reflection about methodological strategies in Design Education and the function of Drawing in Design

This work presents a reflection on Design education and specifically on the role of Drawing in this area. As a subject, Design has expanded its field of action expanding into new areas such as Experience Design or Service Design. It became necessary for the designer to have more than an education based on technological knowledge or know-how. Many authors like Meredith Davis, Don Norman or Jamie Hobson point out the urgency to review the curricula of Design courses because nowadays “ … design is more than appearance, design is about interaction, about strategy and about services. Designers change social behavior” (Norman, 2011) When shifting from a product-centered design to a person-centered design (in a structure, a service or in a relationship) what should the function of drawing in a design course be? What should its curriculum be? Our work methodology will be to confront today’s perspectives on design theory and practice in an attempt to add to the discussion on the methodological strategies in design teaching in the contemporary context.

Thermal degradation of Pb(Zr0.53Ti0.47)O3/poly(vinylidene fluoride) composites as a function of ceramic grain size and concentration

Poly(vinylidene fluoride)/Pb(Zr0.53Ti0.47)O3,([PVDF]1−x/[PZT]x) composites of volume fractions x and (0–3) type connectivity were prepared in the form of thin films. PZT powders with average grain sizes of 0.2, 0.84, and 2.35 μm in different volume fraction of PZT up to 40 % were mixed with the polymeric matrix. The influence of the inorganic particle size and its content on the thermal degradation properties of the composites was then investigated by means of thermo-gravimetric analysis. It is observed that filler size affects more than filler concentration the degradation temperature and activation energy of the polymer. In the same way and due to their larger specific area, smaller particles leave larger solid residuals after the polymer degradation. The polymer degradation mechanism is not significantly modified by the presence of the inorganic fillers. On the other hand, an inhibition effect occurs due to the presence of the fillers, affecting particularly the activation energy of the process.