Largest 2-generated subsemigroups of the symmetric inverse semigroup

Proceedings of the Edinburgh Mathematical Society, nº50 (2007), p.551-561

Spatial neighborhood matrix computation: Inverse distance weighted versus binary contiguity

Paper presented at Geo-Spatial Crossroad GI_Forum, Salzburg, Austria.

Mathematical and numerical methods for inverse problems using fundamental solutions techniques

Fundação para a Ciência e a Tecnologia - SFRH/BD/27914/2006

The group inverse of a product

In this paper, we characterize the existence and give an expression of the group inverse of a product of two regular elements by means of a ring unit.

Further results on the inverse along an element in semigroups and rings

In this paper, we introduce a new notion in a semigroup $S$ as an extension of Mary's inverse. Let $a,d\in S$. An element $a$ is called left (resp. right) invertible along $d$ if there exists $b\in S$ such that $bad=d$ (resp. $dab=b$) and $b\leq_\mathcal{L}d$ (resp. $b\leq_\mathcal{R}d$). An existence criterion of this type inverse is derived. Moreover, several characterizations of left (right) regularity, left (right) $\pi$-regularity and left (right) $*$-regularity are given in a semigroup. Further, another existence criterion of this type inverse is given by means of a left (right) invertibility of certain elements in a ring. Finally we study the (left, right) inverse along a product in a ring, and, as an application, Mary's inverse along a matrix is expressed.

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.

Development of a subject-specific musculoskeletal shoulder model : inverse and forward dynamics applications

A prevalência de pessoas que referem dor no complexo articular do ombro, com concomitante limitação na capacidade para realizar atividades da vida diária, é elevada. Estes níveis de prevalência sobrecarregam quer os utentes, como a própria sociedade. A evidência científica atual indicia a existência de uma relação entre as alterações da articulação escápulo-torácica e as patologias associadas à articulação gleno-umeral. A capacidade de quantificar, cinemática e cineticamente, as disfunções ao nível das articulações escápulo-torácica e gleno-umeral, é algo de enorme importância, quer para a comunidade biomecânica, como para a clínica. No decorrer dos trabalhos desta tese foi desenvolvido, através do software OpenSim, um modelo tridimensional músculo-esquelético do complexo articular do ombro que inclui a representação do tórax/coluna, clavícula, omoplata, úmero, rádio, cúbito e articulações que permitem os movimentos relativos desses segmentos, assim como, 16 músculos e 4 ligamentos. Com um total de 11 graus de liberdade, incluindo um novo modelo articular escápulo-torácico, os resultados demonstram que este é capaz de reconstruir de forma precisa e rápida os movimentos escápulo-torácicos e glenoumerais, recorrendo para tal, à cinemática inversa, e à dinâmica inversa e direta. Conta ainda com um método de transformação inovador para determinar, com base nas especificidades dos sujeitos, os locais de inserção muscular. As principais motivações subjacentes ao desenvolvimento desta tese foram contribuir para o aprofundar do atual conhecimento sobre as disfunções do complexo articular do ombro e, simultaneamente, proporcionar à comunidade clínica uma ferramenta biomecânica de livre acesso com o intuito de melhor suportar as decisões clínicas e dessa forma concorrer para uma prática mais efetiva.

Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Internet au service du patrimoine. Cartographie dynamique de l'inventaire des géotopes d'importance nationale

L'inventaire des géotopes d'importance nationale, aujourd'hui proche de son état final, est le fruit d'un long travail de sélection, de documentation ainsi que de définition et de numérisation des périmètres des sites initié dans les années 1990 par le groupe de travail pour la protection des géotopes en Suisse (Strasser et al. 1995, Berger et al. 2008). Il représente un outil au service de la diffusion et à la promotion du géopatrimoine suisse, auprès de la population en général et des professionnels des géosciences en particulier, dans un but de valorisation patrimoniale et de protection et par une sensibilisation à la valeur particulière et à la vulnérabilité des géotopes.¦C'est dans cet objectif qu'a été développée une interface cartographique rendant accessible sur Internet le contenu de cet inventaire. L'outil de web mapping utilisé - GoogleMaps API - permet en effet d'enrichir une interface de navigation intuitive de diverses fonctions additionnelles offertes par la cartographie sur internet (Kraak 2004, Plewe 2007). La carte n'est donc pas seulement une représentation de la réalité permettant la localisation de différents objets, mais également un outil de recherche thématique et spatiale ainsi qu'un index reliant chaque objet cartographié à diverses informations.¦Porte d'accès aux données des site à une échelle individuelle ou globale, mais aussi outil d'exploration, cette interface propose plusieurs niveaux d'utilisation, correspondant aux diverses interactions possibles avec ces données : naviguer et découvrir les sites, réaliser des sélections multiples, comparer les géotopes à d'autres données, comme l'inventaire fédéral des paysages. L'utilisateur peut ainsi produire à chaque fois la carte qui répond à ses besoins et à ses questions. En donnant à tous accès au contexte et aux particularités de chaque site par delà la globalité abstraite de l'inventaire, cette application se veut avant tout un outil au service de la médiation du géopatrimoine.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.