Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition

We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling $g^2$ and a gauge index $N$, as a system passes through a large $N$ phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlev\'e II equation, and also away from the transition point using the pre-string difference equation. Here we present a complementary analysis of the transition at all coupling and all finite N, in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painlev\'e III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms `condense' at the transition point to match with the double-scaling limit trans-series. We also define a uniform large N strong-coupling expansion (a non-linear analogue of uniform WKB), which is much more precise than the conventional large N expansion through the transition region, and apply it to the evaluation of Wilson loops.Comment: 46 pages; 20 figure

A generic framework for the development of standardised learning objects within the discipline of construction management

E-learning has occurred in the academic world in different forms since the early 1990s. Its use varies from interactive multimedia tools and simulation environments to static resources within learning management systems. E-learning tools and environments are no longer criticised for their lack of use in higher education in general and within the construction domain in particular. The main criticism, however, is that of reinventing the wheel in order to create new learning environments that cater for different educational needs. Therefore, sharing educational content has become the focus of current research, taking e-learning into a whole new era of developments. This era is enabled by the emergence of new technologies (online and wireless) and the development of educational standards, such as SCORM (Sharable Content Object Reference Model) and LOM (Learning Object Metadata) for example. Accordingly, the broad definition of the construction domain and the interlocking nature of subjects taught within this domain, makes the concept of sharing content most appealing. This paper proposes a framework developed to describe the various steps required in order to enable the application of e-learning metadata standards and ontology for sharable learning objects to serve the construction discipline. The paper further describes the application of the proposed framework to a case study for developing an online environment for learning objects that are standardised, sharable, transparent and that cater for the needs of learners, educators and curricula developers in Construction Management. Based on the framework, a learning objects repository is developed incorporating educational and web standards. The repository manages objects as well as metadata using ontology and offers a set of services such as storing, retrieving and searching of learning objects using Semantic Web technologies. Thus, it increases the reusability, sharability and interoperability of learning objects

Higgs boson production through bbˉb \bar b annihilation at threshold in N3^3LO QCD

We present threshold enhanced N$^3$LO QCD corrections to inclusive Higgs production through bottom anti-bottom annihilation at hadron colliders using threshold resummed cross section. The resummed cross section is obtained using factorization properties and Sudakov resummation of the inclusive cross section. We use the recent results on threshold N$^3$LO corrections in QCD for Drell-Yan production and three loop QCD corrections to Higgs form factor with bottom anti-bottom quark to achieve this task. This is the first step towards the evaluation of complete N$^3$LO result. We have numerically demonstrated the importance of such corrections at the LHC.Comment: 15 pages, 1 figur

A requirements engineering framework for integrated systems development for the construction industry

Computer Integrated Construction (CIC) systems are computer environments through which collaborative working can be undertaken. Although many CIC systems have been developed to demonstrate the communication and collaboration within the construction projects, the uptake of CICs by the industry is still inadequate. This is mainly due to the fact that research methodologies of the CIC development projects are incomplete to bridge the technology transfer gap. Therefore, defining comprehensive methodologies for the development of these systems and their effective implementation on real construction projects is vital. Requirements Engineering (RE) can contribute to the effective uptake of these systems because it drives the systems development for the targeted audience. This paper proposes a requirements engineering approach for industry driven CIC systems development. While some CIC systems are investigated to build a broad and deep contextual knowledge in the area, the EU funded research project, DIVERCITY (Distributed Virtual Workspace for Enhancing Communication within the Construction Industry), is analysed as the main case study project because its requirements engineering approach has the potential to determine a framework for the adaptation of requirements engineering in order to contribute towards the uptake of CIC systems

ADVERTISING-PRICING CONDUCT IN MEAT RETAILING

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Quantum Hall Droplets on Disc and Effective Wess-Zumino-Witten Action for Edge States

We algebraically analysis the quantum Hall effect of a system of particles living on the disc ${\bf B}^1$ in the presence of an uniform magnetic field $B$. For this, we identify the non-compact disc with the coset space $SU(1,1)/U(1)$. This allows us to use the geometric quantization in order to get the wavefunctions as the Wigner ${\cal D}$-functions satisfying a suitable constraint. We show that the corresponding Hamiltonian coincides with the Maass Laplacian. Restricting to the lowest Landau level, we introduce the noncommutative geometry through the star product. Also we discuss the state density behavior as well as the excitation potential of the quantum Hall droplet. We show that the edge excitations are described by an effective Wess-Zumino-Witten action for a strong magnetic field and discuss their nature. We finally show that LLL wavefunctions are intelligent states.Comment: 18 pages, clarifications and misprints corrected, version published in IJGMM