Assumptions that imply quantum dynamics is linear

A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system but must allow the system to be described as part of a larger system. The basic linearity is linked with previously established results to complete a simple derivation of the linear Schrodinger equation. For this it is assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease.Comment: 10 pages. Added references. Improved discussion of equations of motion for mean values. Expanded Introductio

Compatible relations on filters and stability of local topological properties under supremum and product

An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Frechetness, strong Frechetness, countable tightness and countable fan-tightness, some of which recover or refine classical results, some of which are new. The reader may find other applications as well.Comment: 28 page

Lithostratigraphy, sedimentation and evolution of the Volta Basin in Ghana

We present a revised lithostratigraphy for the Voltaian Supergroup of Ghana, based on a review of existing literature, interpretations of remotely sensed data and reconnaissance field survey of the Volta Basin. These strata thicken eastwards, to a maximum of between 5 and 6 km adjacent to the Pan-African Dahomeyide orogen. They began to accumulate some time after about 1000 Ma, along the margin of an epicontinental sea. Initial sedimentation, comprising the age-equivalent Kwahu and Bombouaka Groups, shows a cyclical mode of deposition controlled by eustatic changes in sea-level that produced a range of nearshore marine, littoral and terrestrial environments. A major erosional interval was followed by deposition of the 3–4 km thick Oti-Pendjari Group. Basal tillites and associated sandy diamictons are correlated with the Marinoan (end-Cryogenian) glaciation, indicating a maximum depositional age of about 635 Ma. The overlying cap carbonates and tuffs were deposited within a shallow epeiric sea bordered by a volcanically active rift system. The main part of the group records the transition from a rifted passive margin to a fully developed foreland basin receiving marine flysch in the form of argillaceous strata interbedded with highly immature wacke-type sandstones and conglomerates. Maximum accommodation space was developed within a foredeep adjacent to the Dahomeyide belt. Towards the end of the orogenic phase, the foredeep succession became partially inverted and then was buried under coarse terrestrial, red-bed molasse of the Obosum Group

Social media, social capital and adolescents living in state care: A multi-perspective and multimethod qualitative study

Social media are used daily by billions to communicate. Adolescents living in state care are no different, yet the potential implications of their social media use are. Despite the global use of social media and evidence highlighting their role in social capital cultivation, how adolescents living in state care make use of social media remains unknown with discussions tending to focus exclusively on risk. Using data from a four-year Digital Life Story work (DLSW) research programme, this paper explores adolescents’ and social care professional’s (n=45) perspectives on the everyday use of social media by adolescents living in state care. Using an ethnographic multimethod approach, extracts of conversations from the four English residential homes engaged in the DLSW programme were thematically analysed. Three major themes emerged; contacts as currency, promoting and protecting the self and transitions. Analysis illustrate how adolescents living in state care use social media as active digital agents and the need to reframe this usage to enable benefits to be enacted. The paper concludes that urgent research is needed to enable practitioners and policy makers to show a deeper appreciation of the potentials of social media enabling a more balanced approach to succeed in practice