Base-controlled mechanical systems and geometric phases

In this paper, we carry a detailed study of mechanical systems with configuration space $Q\longrightarrow Q/G$ for which the base $Q/G$ variables are being controlled. The overall system's motion is considered to be induced from the base one due to the presence of general non-holonomic constraints. It is shown that the solution can be factorized into dynamical and geometrical parts. Moreover, under favorable kinematical circumstances, the dynamical part admits a further factorization since it can be reconstructed from an intermediate (body) momentum solution, yielding a reconstruction phase formula. Finally, we apply this results to the study of concrete mechanical systems.Comment: 44 pages, 1 figur

The Hopf bifurcation for nonlinear semigroups

Several authors, have shown by perturbation techniques that the Hopf theorem on the development of periodic stable solutions is valid for the Navier-Stokes equations; in particular, solutions near the stable periodic ones remain defined and smooth for all t ≥ 0 . The principal difficulty is that the Hopf theorem deals with flows of smooth vector fields on finite-dimensional spaces, whereas the Navier-Stokes equations define a flow (or evolution operator) for a nonlinear partial differential operator (actually it is a nonlocal operator). The aim of this note is to outline a method for overcoming this difficulty which is entirely different in appearance from the perturbation approach. The method depends on invariant manifold theory plus certain smoothness properties of the flow which actually hold for the Navier-Stokes flow

ALTERNATIVE TOBACCO PRODUCTS & DEPRESSIVE SYMPTOMS AMONG YOUNG ADULTS

The association between cigarette use and depression has been documented in many studies. Fewer studies have examined other tobacco products such as electronic cigarettes (e-cigarettes) and hookah that are used by young adults. This study examined whether increased frequency of use of these products was associated with depressive symptoms in a cohort of n=5,236 Texas college students followed from 2014 to 2017. A hierarchical model showed that increased frequency of single product use of cigarettes, refillable e-cigarettes and hookah was associated with depressive symptoms. Refillable and disposable e-cigarettes were examined separately and results did not provide evidence of a different association for each type of e-cigarette when cigarettes were not also used. Dual use of cigarettes with another product was also examined. Dual use was associated with higher depressive symptoms for most product combinations. However, infrequent dual use of disposable e-cigarettes and cigarettes may not be associated with depressive symptoms. Suggestions for further research are included

The antiquarian photography of Cosmo Innes

The article focuses on the photography of historian Cosmo Innes. The author provides a brief historical background on Innes, discusses his interest in photographing pre-Reformation Scottish churches, and contrasts his work depicting church architecture to his photographs of country mansions, including Cawdor Castle, Auldbar Castle, and Gordon Castle

A formula for the solution of the Navier-Stokes equation based on a method of Chorin

Recently, A. Chorin has found a numerical scheme for solving the Navier-Stokes equations which has the pleasing feature of not breaking down at high Reynolds numbers R . The purpose of this announcement is to present a formula which is designed to establish the convergence of Chorin's time step iteration procedure, assuming that the relevant equations (heat equation and Euler's equations) are solved exactly at each step

Bush, Obama and a faith-based US foreign policy

In a calculated move to appeal to his core constituency during his first term, President George W. Bush launched domestic and international faith-based initiatives designed to leverage public finance for religious groupings to carry out social and welfare functions formerly performed by government or secular organizations. In December 2002 the Center for Faith-Based and Community Initiatives (CFBCI) was extended to the United States Agency for International Development (USAID). The Center's intention was to 'create a level playing field' for faith-based and community groups to compete for foreign assistance funding. These presidential initiatives are problematic, however, calling into question the first amendment-the separation of church and state. Upon taking office Barack Obama set up the Office of Faith-based and Neighborhood Partnerships, promising a greater emphasis on community/neighbourhood programs. The CFBCI remains a fixture in USAID and Obama shows as much enthusiasm for the initiative as his predecessor. Faith-based international relations and political science scholars have sought to build on these initiatives and call for a greater role for faith in US foreign policy. On the eve of the 2012 presidential election, this article considers the claims for a faith-based foreign policy by examining the construction of a faith-based discourse by academics and successive presidents. Using faith-based initiatives and USAID as a case-study, the article discusses criticisms of the policy and focuses on the role of a conservative evangelical organization, Samaritan's Purse, to illustrate the advantages and disadvantages of faith-based approaches. © 2012 The Author(s). International Affairs © 2012 The Royal Institute of International Affairs

The multi modal study of transport investment plans.

In 1998 the UK Department for Transport commissioned a programme of 22 studies to examine the most acute congestion problems on the English road network. The studies promised a new approach to reducing road congestion by examining the contribution that all modes of transport could make to solve these problems. The studies have provided the most convincing evidence to date that road building alone will not be able to solve congestion and pollution problems. Extra road infrastructure will, in most cases, buy a few years’ respite from congestion on the inter-urban road network. The studies have proposed substantial packages of road and public transport improvements, combined with demand management and traffic restraint measures, to tackle the problems. The evidence suggests that some form of road-user charging will be required in many areas to ensure that the efficiency benefits gained from the extra road capacity will not simply be eroded by traffic growth as has been seen to date on routes such as the M25. The outcomes of the studies have prompted the Government to undertake a review of the potential for a national road-user charging system. The multimodal studies have undoubtedly brought about a more balanced and integrated approach to transport planning. There have been quite significant changes to the roads schemes that were initially remitted to the studies and evidence to suggest that significant environmental concerns are now playing a much stronger role in decisions taken by the Department for Transport. The challenge now is to ensure that all of the major parts of the integrated strategies proposed are delivered. A failure to do so will not only reduce the benefits the proposals offer but will also devalue the multi-modal approach taken to the studies

Brexit and the mythologies of nationalism: a warning for Wales

Richard Marsden explores the historical distinctions between nationalist movements in Scotland, Ireland and Wales - and what this means for the UK after Brexit