(2,m,n)-groups with Euler characteristic equal to −2asb-2^as^b

We study those $(2, m, n)$-groups which are almost simple and for which the absolute value of the Euler characteristic is a product of two prime powers. All such groups which are not isomorphic to $PSL_2 (q)$ or $PGL_2(q)$ are completely classified

Perfect countably infinite Steiner triple systems

We use a free construction to prove the existence of perfect Steiner triple systems on a countably infinite point set. We use a specific countably infinite family of partial Steiner triple systems to start the construction, thus yielding 2ℵ0 non-isomorphic perfect systems

Collaborative Development of Open Educational Resources for Open and Distance Learning

Open and distance learning (ODL) is mostly characterised by the up front development of self study educational resources that have to be paid for over time through use with larger student cohorts (typically in the hundreds per annum) than for conventional face to face classes. This different level of up front investment in educational resources, and increasing pressures to utilise more expensive formats such as rich media, means that collaborative development is necessary to firstly make use of diverse professional skills and secondly to defray these costs across institutions. The Open University (OU) has over 40 years of experience of using multi professional course teams to develop courses; of working with a wide range of other institutions to develop educational resources; and of licensing use of its educational resources to other HEIs. Many of these arrangements require formal contracts to work properly and clearly identify IPR and partner responsibilities. With the emergence of open educational resources (OER) through the use of open licences, the OU and other institutions has now been able to experiment with new ways of collaborating on the development of educational resources that are not so dependent on tight legal contracts because each partner is effectively granting rights to the others to use the educational resources they supply through the open licensing (Lane, 2011; Van Dorp and Lane, 2011). This set of case studies examines the many different collaborative models used for developing and using educational resources and explain how open licensing is making it easier to share the effort involved in developing educational resources between institutions as well as how it may enable new institutions to be able to start up open and distance learning programmes more easily and at less initial cost. Thus it looks at three initiatives involving people from the OU (namely TESSA, LECH-e, openED2.0) and contrasts these with the Peer-2-Peer University and the OER University as exemplars of how OER may change some of the fundamental features of open and distance learning in a Web 2.0 world. It concludes that while there may be multiple reasons and models for collaborating on the development of educational resources the very openness provided by the open licensing aligns both with general academic values and practice but also with well established principles of open innovation in businesses

Searching and ranking ontologies on the Semantic Web

The number of ontologies available online is increasing constantly. Tools that are capable of searching, retrieving, and ranking ontologies are becoming crucial to facilitate ontology search and reuse. In this document, we describe OntoSearch, which is a tool for capturing and searching ontologies on the Semantic web. We also briefly describe AKTiveRank which is used to rank OWL ontologies based on certain ontology-structure analysis.

World. An anthropological examination (part 2)

This paper is the second of a two-part essay that aims to examine anthropologically the category “world.” The first part argued in favor of a single-world approach and for the unavoidable centrality of personhood in the human condition. In this second part of the essay, I address the metaphysical implications of the category “world” and relate them to the process of “worlding,” thus defending the continued heuristic value of the old anthropological category of worldview. I suggest that a consideration of the Ontological Proof of God’s existence, developed by St. Anselm of Canterbury in the late eleventh century, helps us develop a comparative theory of personhood by showing how the experience of transcendence is inherent in personal ontogenesis

A Modified Distortion Measurement Algorithm for Shape Coding

Efficient encoding of object boundaries has become increasingly prominent in areas such as content-based storage and retrieval, studio and television post-production facilities, mobile communications and other real-time multimedia applications. The way distortion between the actual and approximated shapes is measured however, has a major impact upon the quality of the shape coding algorithms. In existing shape coding methods, the distortion measure do not generate an actual distortion value, so this paper proposes a new distortion measure, called a modified distortion measure for shape coding (DMSC) which incorporates an actual perceptual distance. The performance of the Operational Rate Distortion optimal algorithm [1] incorporating DMSC has been empirically evaluated upon a number of different natural and synthetic arbitrary shapes. Both qualitative and quantitative results confirm the superior results in comparison with the ORD lgorithm for all test shapes, without any increase in computational complexity

Finite scattering amplitudes in field theory

In this thesis we explore the infrared problem perturbatively in massless field theory. We review the current conventional methods and theorems that are applied in the calculation of QCD jet observables and then discuss the formulation of an alternative approach called the Asymptotic Interaction Picture (AIP). The AIP is based on a unitary transformation such that long-ranged interactions are present in the asymptotic Lagrangian and thus the states associated with this picture are no longer free Fock states but are asymptotic states containing soft and collinear interactions. Under the guidance of the AIP we are led to modifying conventional perturbation theory, cutting up amplitudes in a manner that allows for the construction of infrared finite amplitudes that are in correspondence with the asymptotic states of the AIP. We apply this formalism to several NLO corrections to QCD observables and construct dressed states who's amplitudes are finite in all regions of phase space. Using these amplitudes we compute several observables and show agreement with the conventional calculations in infrared safe regions. Higher-order calculations are then investigated in ϕ (^3)theory and the infrared pole structure is shown to behave as expected such that NNLO corrections to dressed states are obtained. Finally we present part of the NNLO correction to the dressed two-parton amplitude in QCD and show that, with several provisos, this approach may potentially be applied to the precision calculations of observables at the International Linear Collider (ILC). We therefore give a possible alternative to current subtraction methods at NNLO when no initial state radiation is present

Development of a viable concrete printing process

A novel Concrete Printing process has been developed, inspired and informed by advances in 3D printing, which has the potential to produce highly customised building components. Whilst still in their infancy, these technologies could create a new era of architecture that is better adapted to the environment and integrated with engineering function. This paper describes the development of a viable concrete printing process with a practical example in designing and manufacturing a concrete component (called Wonder Bench) that includes service voids and reinforcement. The challenges met and those still to be overcome particularly in the evaluation of the manufacturing tolerances of prints are also discussed

Ladder operators and endomorphisms in combinatorial Physics

Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of Combinatorics. These may be expressed in terms of infinite, but row-finite, matrices, which may also be considered as endomorphisms of C[x]. This leads us to consider endomorphisms in more general spaces, and these in turn may be expressed in terms of generalizations of the ladder-operators familiar in physics

Extended Bell and Stirling numbers from hypergeometric exponentiation

Exponentiating the hypergeometric series 0FL(1,1,...,1;z), L = 0,1,2,..., furnishes a recursion relation for the members of certain integer sequences bL(n), n = 0,1,2,.... For L >= 0, the bL(n)'s are generalizations of the conventional Bell numbers, b0(n). The corresponding associated Stirling numbers of the second kind are also investigated. For L = 1 one can give a combinatorial interpretation of the numbers b1(n) and of some Stirling numbers associated with them. We also consider the L>1 analogues of Bell numbers for restricted partitions