The resurgence properties of the incomplete gamma function I

In this paper we derive new representations for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc. Lond. A 439 (1992) 373--396). Using these representations, we obtain a number of properties of the asymptotic expansions of the incomplete gamma function with large arguments, including explicit and realistic error bounds, asymptotics for the late coefficients, exponentially improved asymptotic expansions, and the smooth transition of the Stokes discontinuities.Comment: 36 pages, 4 figures. arXiv admin note: text overlap with arXiv:1311.2522, arXiv:1309.2209, arXiv:1312.276

Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal

In (Boyd, Proc. R. Soc. Lond. A 447 (1994) 609--630), W. G. C. Boyd derived a resurgence representation for the gamma function, exploiting the reformulation of the method of steepest descents by M. Berry and C. Howls (Berry and Howls, Proc. R. Soc. Lond. A 434 (1991) 657--675). Using this representation, he was able to derive a number of properties of the asymptotic expansion for the gamma function, including explicit and realistic error bounds, the smooth transition of the Stokes discontinuities, and asymptotics for the late coefficients. The main aim of this paper is to modify the resurgence formula of Boyd making it suitable for deriving better error estimates for the asymptotic expansions of the gamma function and its reciprocal. We also prove the exponentially improved versions of these expansions complete with error terms. Finally, we provide new (formal) asymptotic expansions for the coefficients appearing in the asymptotic series and compare their numerical efficacy with the results of earlier authors.Comment: 22 pages, accepted for publication in Proceedings of the Royal Society of Edinburgh, Section A: Mathematical and Physical Science

Error bounds and exponential improvement for the asymptotic expansion of the Barnes GG-function

In this paper we establish new integral representations for the remainder term of the known asymptotic expansion of the logarithm of the Barnes $G$-function. Using these representations, we obtain explicit and numerically computable error bounds for the asymptotic series, which are much simpler than the ones obtained earlier by other authors. We find that along the imaginary axis, suddenly infinitely many exponentially small terms appear in the asymptotic expansion of the Barnes $G$-function. Employing one of our representations for the remainder term, we derive an exponentially improved asymptotic expansion for the logarithm of the Barnes $G$-function, which shows that the appearance of these exponentially small terms is in fact smooth, thereby proving the Berry transition property of the asymptotic series of the $G$-function.Comment: 14 pages, accepted for publication in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science

Integrated rural development - The concept and its operation

Our paper explores, on a theoretical level, the reason for frequent failures of rural development policies and identifies some potential improvements in rural policy making in Europe. Our approach to des/integration concerns actors, resources, institutions, knowledge, the fundamental logic of development, and the interplay between two distinct levels of rural development: the level of policies, or central intervention; and the level of local aspirations aimed at improving everyday rural life. Along these lines, two characteristic systems of rural development – the central bureaucratic and the local heuristic – can be clearly identified. Ideally, these should work in co-operation, complementing each other, forming an integrated development system, where rural policy serves to (i) channel resources, establish strategic aims and development models in a top-down mode, and (ii) convey information and mediate social, economic, political interests in a bottom-up mode. However, lack of integration and divergence of interest can lead to dysfunction, conflict and dissipation within the system. We argue that rural development policies tend to fail because the central bureaucratic system imposes top-down control and objectives throughout the development process, thus failing to sufficiently promote the reconfiguration of local resources, which is better achieved through bottom-up processes and the local heuristic system. In other words, the tendency to disjunction between the two basic socio-political systems of rural development is the main reason for the failure of rural development policy. The paper offers analytical models of integrated and non-integrated rural development systems and illustrates the argument through some examples taken from the community initiatives and the pre-accession policies of the European Union. The study is in two halves. The first half elaborates the concept of ‘integrated rural development’. based on international literature. The second part offers a few new conceptions, as a contribution to the ‘new rural development theory’ and simple models of integrated and non-integrated development.Rural development, local development, rural policy, European Union, LEADER Programme, centre-periphery, local governance

First Results of a Detailed Analysis of p+p Elastic Scattering Data from ISR to LHC Energies in the Quark-Diquark Model

First results of a detailed analysis of p+p elastic scattering data are presented from ISR to LHC energies utilizing the quark-diquark model of protons in a form proposed by Bialas and Bzdak. The differential cross-section of elastic proton-proton collisions is analyzed in detailed and systematic manner at small momentum transfers, starting from the energy range of CERN ISR at $\sqrt{s}= 23.5$ GeV, including also recent TOTEM data at the present LHC energies at $\sqrt{s} = 7$ TeV. These studies confirm the picture that the size of protons increases systematically with increasing energies, while the size of the constituent quarks and diquarks remains approximately independent of (or only increases only slightly with) the colliding energy. The detailed analysis indicates correlations between model parameters and also indicates an increasing role of shadowing at LHC energies.Comment: Proceeding from conference material, which was presented by F. Nemes at the Wilhelm and Else Heraeus SummerSchool on Diffractive and Electromagnetic Processes at High Energies, Heidelberg, Germany, September 5-9, 201

LHC optics and elastic scattering measured by the TOTEM experiment

The TOTEM experiment at the LHC has measured proton-proton elastic scattering in dedicated runs at $\sqrt{s}=7$ and 8 TeV centre-of-mass LHC energies. The proton-proton total cross-section $\sigma_{\rm tot}$ has been derived for both energies using a luminosity independent method. TOTEM has excluded a purely exponential differential cross-section for elastic proton-proton scattering with significance greater than 7$\sigma$ in the $|t|$ range from 0.027 to 0.2 GeV$^{2}$ at $\sqrt{s}=8$ TeV.Comment: Proceedings, 17th Lomonosov Conferenc