The maximal angle between 5×5 positive semidefinite and 5×5 nonnegative matrices

The paper is devoted to the study of the maximal angle between the $5\times 5$ semidefinite matrix cone and $5\times 5$ nonnegative matrix cone. A signomial geometric programming problem is formulated in the process to find the maximal angle. Instead of using an optimization problem solver to solve the problem numerically, the method of Lagrange Multipliers is used to solve the signomial geometric program, and therefore, to find the maximal angle between these two cones.

Sparse FIR Filter Design Based on Signomial Programming

The goal of sparse FIR filter design is to minimize the number of nonzero filter coefficients, while keeping its frequency response within specified boundaries. Such a design can be formally expressed via minimization of l0-norm of filter’s impulse response. Unfortunately, the corresponding minimization problem has combinatorial complexity. Therefore, many design methods are developed, which solve the problem approximately, or which solve the approximate problem exactly. In this paper, we propose an approach, which is based on the approximation of the l0-norm by an lp-norm with 0 < p < 1. We minimize the lp-norm using recently developed method for signomial programming (SGP). Our design starts with forming a SGP problem that describes filter specifications. The optimum solution of the problem is then found by using iterative procedure, which solves a geometric program in each iteration. The filters whose magnitude responses are constrained in minimax sense are considered. The design examples are provided illustrating that the proposed method, in most cases, results in filters with higher sparsity than those of the filters obtained by recently published methods.

It is worth turning on GeoGebra 3D

I am a PhD student at the Doctoral School of Mathematics and Computer Science at University of Debrecen in the topic of Mathematical Competence Development with ICT. In this article, I present some examples, where the 3D version of GeoGebra can be applied successfully not only in research but also in everyday work. I have picked examples that require spatial representation but where it is much more complicated and less effective to achieve through concrete manipulatives than through any 3-dimensional dynamic geometric program. However, the two-dimensional version of any dynamic geometry program could be used to construct a figure, but besides easy constructing, formatting the figures is easier in the 3D version. Classification: D40, N80, U70. Keywords: development of spatial view, spatial experience, GeoGebra 3D worksheet.

Digital by Nature: The Cephalopods and the Algorithms

This Abstract presents the realisation of the experimental wooden structure, known as “Ammoniterasz” - (Ammonites+Terrace). During the making of this structure, the authors tried to analyse the practical usage of algorithmic design and the generative method. In the generative design, the 3D shape of the real structure is made using an algorithm with predefined editing rules. With an algorithm, it is possible to carry out a real-time structural analysis, together with different kinds of optimisation calculations and production methods. The compilation of the algorithm is created either with scripts or with a 3D graphic surface, which results in a flow chart, by another name, a visual script. Unlike the traditional shaping methods, with generative design, the result is not a static one, but a process which can offer countless options for the pre-defined design (geometric) program. To use a biological analogy: in this way, the designer is creating the rules of a growing process.