Some results on B-matrices and doubly B-matrices

A real matrix with positive row sums and all its off-diagonal elements bounded above by their corresponding row means was called in [4] a B-matrix. In [5], the class of doubly B-matrices was introduced as a generalization of the previous class. We present several characterizations and properties of these matrices and for the class of B-matrices we consider corresponding questions for subdirect sums of two matrices (a general ‘sum’ of matrices introduced in [1] by S.M. Fallat and C.R. Johnson, of which the direct sum and ordinary sum are special cases), for the Hadamard product of two matrices and for the Kronecker product and sum of two matrices.Fundação para a Ciência e Tecnologia (FCT)Ministerio de Ciencia y Tecnología (Espanha

The completion problem for N-matrices

An $n\times m$ matrix is called an $N$-matrix if all principal minors are negative. In this paper, we are interested in $N$-matrix completion problems, that is, when a partial $N$-matrix has an $N$-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial $N$-matrix does not have an $N$-matrix completion. Here, we prove that a combinatorially symmetric partial $N$-matrix has an $N$-matrix completion if the graph of its specified entries is a 1-chordal graph. We also prove that there exists an $N$-matrix completion for a partial $N$-matrix whose associated graph is an undirected cycle.Fundação para a Ciência e a Tecnologia (FCT) – Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI) DGI - BFM2001-0081-C03-0

Application of magnetic cooling in electric vehicles

The features of an active magnetic regenerator refrigerator (AMRR) are determined for its application in mobile air-conditioning (MAC) systems. The thermal requirements of an electric vehicle have been firstly obtained and result in a cooling demand of 3.03 kW at a temperature span of 29.3 K. A comprehensive parametric study has been conducted in order to find the AMRR design and working parameters that fulfill the vehicle needs with a minimum electric consumption and device mass. Specifically, a permanent-magnet parallel-plate AMRR made of Gd-like materials is considered. According to the possibilities of current prototypes, in the study the cycle frequencies have been limited to 10 Hz and the applied magnetic fields, to 1.4 T. The results show that an AMRR made of plates between 30 and 40 µm thick and channels between 20 and 40 µm high could meet the vehicle demand with a COP between 2 and 4 and a total mass between 20 and 50 kg. Compared to vapor-compression devices for MAC systems (COP=2.5 and mass 12 to 15 kg), the AMRR works optimally with fluid flow rates at least 3 times larger. In order to integrate AMRRs into MAC systems, the hydraulic loops should be consequently redesigned.Barbara Torregrosa-Jaime acknowledges the Spanish Ministry of Education, Culture, and Sport (Ministerio de Educacion, Cultura y Deporte) for the Research Fellowship FPU ref. AP2010-2160.Torregrosa Jaime, B.; Payá Herrero, J.; Corberán Salvador, JM. (2016). Application of magnetic cooling in electric vehicles. Science and Technology for the Built Environment. 22(5):544-555. doi:10.1080/23744731.2016.1186459S54455522

N_0 completions on partial matrices

An $n\times n$ matrix is called an $N_0$-matrix if all its principal minors are nonpositive. In this paper, we are interested in $N_0$-matrix completion problems, that is, when a partial $N_0$-matrix has an $N_0$-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial $N_0$-matrix does not have an $N_0$-matrix completion. Here, we prove that a combinatorially symmetric partial $N_0$-matrix, with no null main diagonal entries, has an $N_0$-matrix completion if the graph of its specified entries is a 1-chordal graph or a cycle. We also analyze the mentioned problem when the partial matrix has some null main diagonal entries.Fundação para a Ciência e a Tecnologia(FCT) através do programa POCTISpanish DGI grant number MTM2007-6447

Design, Analysis, and Applications of Iterative Methods for Solving Nonlinear Systems

In this chapter, we present an overview of some multipoint iterative methods for solving nonlinear systems obtained by using different techniques such as composition of known methods, weight function procedure, and pseudo-composition, etc. The dynamical study of these iterative schemes provides us valuable information about their stability and reliability. A numerical test on a specific problem coming from chemistry is performed to compare the described methods with classical ones and to confirm the theoretical results

Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line

Altres ajuts: acords transformatius de la UABIn this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain again at least five limit cycles but now from infinity, which is of monodromic type, and with simpler computations. The proof uses a partial classification of the center problem when both systems are of center type

Orbitally symmetric systems with applications to planar centers

We present a generalization of the most usual symmetries in differential equations known as the time-reversibility and the equivariance ones. We check that the typical properties are also valid for the new definition that unifies both. With it, we are able to present new families of planar polynomial vector fields having equilibrium points of center type. Moreover, we provide the highest lower bound for the local cyclicity of an equilibrium point of polynomial vector fields of degree 6, M(6) ≥ 48

Dynamical analysis of an iterative method with memory on a family of third-degree polynomials

Qualitative analysis of iterative methods with memory has been carried out a few years ago. Most of the papers published in this context analyze the behaviour of schemes on quadratic polynomials. In this paper, we accomplish a complete dynamical study of an iterative method with memory, the Kurchatov scheme, applied on a family of cubic polynomials. To reach this goal we transform the iterative scheme with memory into a discrete dynamical system defined on R2. We obtain a complete description of the dynamical planes for every value of parameter of the family considered. We also analyze the bifurcations that occur related with the number of fixed points. Finally, the dynamical results are summarized in a parameter line. As a conclusion, we obtain that this scheme is completely stable for cubic polynomials since the only attractors that appear for any value of the parameter, are the roots of the polynomial.This paper is supported by the MCIU grant PGC2018-095896-B-C22. The first and the last authors are also supported by University Jaume I grant UJI-B2019-18. Moreover, the authors would like to thank the anonymous reviewers for their comments and suggestions