We show that the only way of changing the framing of a link by ambient isotopy in an oriented $3$ -manifold is when the manifold has a properly embedded non-separating $S^{2}$ . This change of framing is given by the Dirac trick, also known as the light bulb trick. The main tool we use is based on McCullough’s work on the mapping class groups of $3$ -manifolds. We also relate our results to the theory of skein modules.

In December, 2019, an infectious outbreak of unknown cause occurred in Wuhan, which attracted intense attention. Shortly after the virus was identified as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the epidemic of coronavirus disease 2019 (COVID-19) broke out, and an information storm occurred. At that time, 2 important aspects, that is, the stages of spread and the components of the epidemic, were unclear. Answers to the questions (1) what are the sources, (2) how do infections occur, and (3) who will be affected should be clarified as the outbreak continues to evolve. Furthermore, components of the epidemic and the stages of spread should be explored and discussed. Based on information of SARS, Middle East respiratory syndrome (MERS), and COVID-19, the components of the epidemic (the sources, the routes of infection, and the susceptible population) will be discussed, as well as the role of natural and social factors involved. Epidemiologic characteristics of patients will be traced based on current information.

For a smooth manifold N denote by Em(N) the set of smooth isotopy classes of smooth embeddings N → ℝm. A description of the set Em(Sp × Sq) was known only for p = q = 0 or for p = 0, m ≠ q + 2 or for 2m ⩾ 2(p + q) + max{p, q} + 4. (The description was given in terms of homotopy groups of spheres and of Stiefel manifolds.) For m ⩾ 2p + q + 3 we introduce an abelian group structure on Em(Sp × Sq) and describe this group ‘up to an extension problem’. This result has corollaries which, under stronger dimension restrictions, more explicitly describe Em(Sp × Sq). The proof is based on relations between sets Em(N) for different N and m, in particular, on a recent exact sequence of M. Skopenkov.

We consider orientable closed connected 3-manifolds obtained by performing Dehn surgery on the components of some classical links such as Borromean rings and twisted Whitehead links. We find geometric presentations of their fundamental groups and describe many of them as 2-fold branched coverings of the 3-sphere. Finally, we obtain some topological applications on the manifolds given by exceptional surgeries on hyperbolic 2-bridge knots.

The dynamics of a mechanical manipulator have the inherent characteristics of being highly non-linear and strongly coupled due to the interaction of the inertial, centripetal, coriolis and gravitational forces.

These characteristics produce difficulties in predicting the dynamic behaviour of a given manipulator's structure. These interactive forces depend largely on the geometrical configuration and operational conditions of a manipulator. Therefore, it is essential to investigate the dynamics behaviour under different conditions in order to obtain an optimal design.

This paper presents a study of the dynamics behaviour of a robot's arm with particular reference to the mechanical manipulator being designed by the AEAC. A computer software package has been developed to facilitate the investigation of the potential dynamics behaviour of a robot's arm and provides the designer with useful information for the real time control of high performance robots. This package also enables the designer to closely monitor the implications of his design.

The software of this package is based on the Lagrangian model, taking advantage of the recursive formulation. A brief description of the types of velocity trajectories used in this study is also included in this paper.

The software for the modelling was written in FORTRAN 77 in single precision and run on a UNIVAC operating system.

One way to increase the flexibility (or versatility) of manipulators is to use links with time varying inertia. One can then control both the joint torques and the inertias of the links therefore more pliancy in the practical utilisation of the arm. The paper deals with the Lagrangian formulation of the corresponding inertia control problem which can be considered either in open loop or in closed loop form. The general equations are derived and it is shown that one so obtains a set of uncoupled Ricatti differential equations which define the dynamics of the structural inertias. Problems related to stabilization and to structural parameter uncertainty are also considered.

At the 2004 BIALL Conference the Legal Online Resources Directory (LORD) was launched. The Legal Information Group (LIG) is currently developing the Directory to meet the needs of today's information professionals. James Mullan, Chair of LIG, gives a history of the LORD project and an outline of its possible future.

Diane Raper describes the ongoing project at the University of Kent to upgrade the free Lawlinks portal established nearly ten years ago by Sarah Carter. The emphasis is on ensuring linking is working, establishing new links, and generally making the site more user-friendly, both to Kent law students and the outside world.

Dans le cas d'un produit unique et non évolutif, on ne rencontre que très peu de difficultés à la représentation des données le concernant. Cependant dans un contexte de forte diversité, il s'avèreimpossible de représenter explicitement chaque produit par une nomenclature spécifique. L'article présentéici porte sur la modélisation des familles de produits. Afin de représenter une grande diversité de produitsla structuration des données techniques est abordée par la codification des objets techniques et leurclassification. Les modèles de représentation basés sur les liens sont exposés. Les modèles génériques dereprésentation de la diversité sont montrés avec les modèles de configurations. Finalement les principauxpoints de consensus sont relevés ainsi que les manques quand à la dynamique de versionnement et à lareprésentation du processus.