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Pedro Patricio

Publications and source records attributed to Pedro Patricio.

10 recordsLinked to original sources
arXiv2019

Representations and properties of the W-weighted core-EP inverse

In this paper, we investigate the weighted core-EP inverse introduced by Ferreyra, Levis and Thome. Several computational representations of the weighted core-EP inverse are obtained in terms of singular-value decomposition, full-rank decomposition and QR decomposition. These representations are expressed in terms of various matrix powers as well as matrix product involving the core-EP inverse, Moore-Penrose inverse and usual matrix inverse. Finally, those representations involving only Moore-Penrose inverse are compared and analyzed via computational complexity and numerical examples.

math.RA↗
arXiv2018

Continuity of the core-EP inverse and its applications

In this paper, firstly we study the continuity of the core-EP inverse without explicit error bounds by virtue of two methods. One is the rank equality, followed from the classical generalized inverse. The other one is matrix decomposition. The continuity of the core inverse can be derived as a particular case. Secondly, we study perturbation bounds for the core-EP inverse under prescribed conditions. Perturbation bounds for the core inverse can be derived as a particular case. Also, as corollaries, the sufficient (and necessary) conditions for the continuity of the core-EP inverse are obtained. Thirdly, a numerical example is illustrated to compare the derived upper bounds. Finally, an application to semistable matrices is provided.

math.RA↗
arXiv2018

Power law rheology of generalised Maxwell and Kelvin-Voigt models

We analyse the rheological behaviour of the generalised Maxwell and Kelvin-Voigt models with a power law spectrum of relaxation or retardation times, ${\cal H}\sim 1/τ^α$ or ${\cal L}\sim τ^α$, respectively. When $0<α<1$, both models have the same weak power law behaviour, which occur in a variety of soft materials, including living cells. Beyond this region, for other values of $α$, the two models have different and distinctive rheological behaviours, converging continuously to the 1-element Maxwell and Kelvin-Voigt models, respectively, for $α<-1$ or $α>2$.

physics.bio-ph↗
arXiv2016

Characterizations and representations of core and dual core inverses

In this paper, double commutativity and the reverse order law for the core inverse are considered. Then, new characterizations of the Moore-Penrose inverse of a regular element are given by one-sided invertibilities in a ring. Furthermore, the characterizations and representations of the core and dual core inverses of a regular element are considered.

math.RA↗
arXiv2016

Centralizer's applications to the inverse along an element

In this paper, we first prove that the absorption law for one-sided inverses along an element holds, deriving the absorption law for the inverse along an element. We then apply this result to obtain the absorption law for the inverse along different elements. Also, the reverse order law and the existence criterion for the inverse along an element are given by centralizers in a ring. Finally, we characterize the Moore-Penrose inverse by one-sided invertibilities in a ring with involution.

math.RA↗
arXiv2016

Reverse order law for the inverse along an element

In this paper, we introduce a new concept called left (right) g-MP inverse in a $*$-monoid. The relations of this type of generalized inverse with left inverse along an element are investigated. Also, the reverse order law for the inverse along an element is studied. Then, the existence criteria and formulae of the inverse of the product of triple elements along an element are investigated in a monoid. Finally, we further study left and right g-MP inverses, the inverse along an element in the context of rings.

math.RA↗
arXiv2015

Rheology of fractal networks

We model the cytoskeleton as a fractal network by identifying each segment with a simple Kelvin-Voigt element, with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel, which may support stress, without relaxing. By considering a very simple regular self-similar structure of segments in series and in parallel, in 1, 2 or 3 dimensions, we are able to express the viscoelasticity of the network as an effective generalised Kelvin-Voigt model with a power law spectrum of retardation times, $\cal L\simτ^α$. We relate the parameter $α$ with the fractal dimension of the gel. In some regimes ($0<α<1$), we recover the weak power law behaviours of the elastic and viscous moduli with the angular frequencies, $G'\sim G''\sim w^α$, that occur in a variety of soft materials, including living cells. In other regimes, we find different power laws for $G'$ and $G''$.

physics.bio-ph↗
arXiv2014

The inverse along a product and its applications

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and expressions of the inverse along a matrix.

math.RA↗
arXiv2010

Scaling of the elastic contribution to the surface free energy of a nematic on a sawtoothed substrate

We characterize the elastic contribution to the surface free energy of a nematic in presence of a sawtooth substrate. Our findings are based on numerical minimization of the Landau-de Gennes model and analytical calculations on the Frank-Oseen theory. The nucleation of disclination lines (characterized by non-half-integer winding numbers) in the wedges and apexes of the substrate induces a leading order proportional to qlnq to the elastic contribution to the surface free energy density, q being the wavenumber associated with the substrate periodicity.

cond-mat.soft↗