Soledad Moreno-Pulido

• PhD Mathematics
• PhD teacher at Universidad de Cádiz

Multi-fractal detrended fluctuation analysis (MF-DFA) describes long-range correlations across scales in time series in terms of the linear fittings of the fluctuation functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upg...

Minimum norm problems consist of finding the distance of a closed subset of a normed space to the origin. Usually, the given closed subset is also asked to be convex, thus resulting in a convex minimum norm problem. There are plenty of techniques and algorithms to compute the distance of a closed convex set to the origin, which mostly exist in the...

Background: Opioid drug prescription (ODP) and opioid-related mortality (ORM) have increased in Spain. However, their relationship is complex, as ORM is registered without considering the type of opioid (legal or illegal). Objective: This ecological study aimed to examine the correlation between ODP and ORM in Spain and discuss their usefulness...

The study of multifractal properties is one of the current scopes in the analysis of complex networks. Last decade, several multifractal algorithms have been proposed, both adding new approaches and improving their accuracy or time consumption. One of the methods that provide more advantages is the sandbox method, which does not require to solve th...

The design of optimal Magnetic Resonance Imaging (MRI) coils is modeled as a minimum-norm problem (MNP), that is, as an optimization problem of the form $\min_{x\in\mathcal{R}}\|x\|$ min x ∈ R ∥ x ∥ , where $\mathcal{R}$ R is a closed and convex subset of a normed space X . This manuscript is aimed at revisiting MNPs from the perspective of Functio...

There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where the nonlinear terms are “small” compared to the linear ones): the Method of Strained Parameters, the Naive Singular Perturbation Method, the Method of Multiple Scales, the Method of Harmonic Balance and the Method of Averaging. The St...

A supporting vector of a matrix A for a certain norm \(\Vert \cdot \Vert \) on \(\mathbb {R}^n\) is a vector x such that \(\Vert x\Vert =1\) and \(\Vert Ax\Vert =\Vert A\Vert =\displaystyle \max _{\Vert y\Vert =1}\Vert Ay\Vert \). In this manuscript, we characterize the existence of supporting vectors in the infinite-dimensional case for both the \...

Inner structure appeared in the literature of topological vector spaces as a tool to characterize the extremal structure of convex sets. For instance, in recent years, inner structure has been used to provide a solution to The Faceless Problem and to characterize the finest locally convex vector topology on a real vector space. This manuscript goes...

Temporal evolution of the (multi-)fractality in the Madrid Metro subway (Spain) is explored by using it as a study case of a public transport network (PTN). By considering this subway as a graph network, a box-covering method for multifractal analysis of complex networks is employed for assessing the evolution of multifractal parameters along time...

In this manuscript we characterize the completeness of a normed space through the strong lacunary ( N θ ) and lacunary statistical convergence ( S θ ) of series. A new characterization of weakly unconditionally Cauchy series through N θ and S θ is obtained. We also relate the summability spaces associated with these summabilities with the strong p-...

In this manuscript we provide an exact solution to the maxmin problem max ∥ A x ∥ subject to ∥ B x ∥ ≤ 1 , where A and B are real matrices. This problem comes from a remodeling of max ∥ A x ∥ subject to min ∥ B x ∥ , because the latter problem has no solution. Our mathematical method comes from the Abstract Operator Theory, whose strong machinery a...

Complex networks have been studied in recent years due to their relevance in biological, social and technical real systems, such as the world wide web, social networks and biochemical interactions. One of the most current features of complex networks is the presence of (multi-)fractal properties. In spite of the amount of contributions that have be...

Objective. To investigate the evolution of opioid-related mortality and potential years of life lost in Spanish general population from 2008 to 2017. To evaluate the differences between Spain and US. Methods. A descriptive study using retrospective annual data from 2008 to 2017 in Spanish and US general population. Information on the population and...

The supporting vectors of a matrix A are the solutions of max∥x∥2=1∥Ax∥22. The generalized supporting vectors of matrices A1,⋯,Ak are the solutions of max∥x∥2=1∥A1x∥22+⋯+∥Akx∥22. Notice that the previous optimization problem is also a boundary element problem since the maximum is attained on the unit sphere. Many problems in Physics, Statistics and...

In this manuscript we provide an exact solution to the maxmin problem max Ax min Bx where A and B are real matrices. Our method comes from the Abstract Operator Theory, whose strong machinery allows us to reduce the previous problem to max Cx x ≤ 1 which can be solved exactly by relying on supporting vectors. Finally, as an appendix, we provide an...

We study measures defined on effect algebras. We characterize real-valued measures on effect algebras and find a class of effect algebras, that include the natural effect algebras of sets, on which σ -additive measures with values in a finite dimensional Banach space are always bounded. We also prove that in effect algebras the Nikodym and the Grot...

We obtain a new version of the Orlicz-Pettis theorem within the frame of the strong p-Cesàro convergence.

In this manuscript, we compute the Bishop-Phelps-Bollobás modulus for functionals in classical Banach spaces, such as Hilbert spaces, spaces of continuous functions c0 and ℓ1.

In this paper we will characterize the completeness and barrelledness of a normed space through the strong p-Ces?ro summability of series. A new characterization of weakly unconditionally Cauchy series and unconditionally convergent series through the strong p-Ces?ro summability is obtained.

The set of supporting vectors of a continuous linear operator, that is, the normalized vectors at which the operator attains its norm, is decomposed into its convex components. In the complex case, the set of supporting vectors of a nonzero functional is proved to be path-connected. We also introduce the concept of generalized supporting vectors fo...

We introduce two Bishop-Phelps-Bollobas moduli of a Banach space which measure, for a given Banach space, what is the best possible Bishop-Phelps-Bollobas theorem in this space. We show that there is a common upper bound for these moduli for all Banach spaces and we present an example showing that this bound is sharp. We prove the continuity of the...

We prove the classical Phillips Lemma in the setting of measures defined on effect algebras of sets. This leads to several Vitali-Hahn-Saks-type results for these measures.