Jacobi-Predictor-Corrector Approach for the Fractional Ordinary Differential Equations

We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t. the Jacobi-weight function $\omega(s)=(1-s)^{\alpha-1}(1+s)^0$. This method has the computational cost O(N) and the convergent order $IN$, where $N$ and $IN$ are, respectively, the total computational steps and the number of used interpolating points. The detailed error analysis is performed, and the extensive numerical experiments confirm the theoretical results and show the robustness of this method.Comment: 24 pages, 5 figure

Immunogens and Antigen Processing: Report from a Global HIV Vaccine Enterprise Working Group

The Global HIV Vaccine Enterprise convened a meeting of a Working Group in July 2009 to discuss recent progress in rational design of the components of an HIV vaccine, such as inserts, vectors and adjuvants,and in understanding antigen processing and presentation to T and B cells. This Report summarizes the key points of that discussion, and subsequent discussions with the Chairs of the other Enterprise Working Groups, the Enterprise Science Committee, the Enterprise Council and the broader scientific community during open sessions at scientific conferences

Techno-economic evaluation of reducing shielding gas consumption in GMAW whilst maintaining weld quality

A new method of supplying shielding gases in an alternating manner has been developed to enhance the efficiency of conventional gas metal arc welding (GMAW). However, the available literature on this advanced joining process is very sparse and no cost evaluation has been reported to date. In simple terms, the new method involves discretely supplying two different shielding gases to the weld pool at predetermined frequencies which creates a dynamic action within the liquid pool. In order to assess the potential benefits of this new method from a technical and cost perspective, a comparison has been drawn between the standard shielding gas composition of Ar/20%CO2, which is commonly used in UK and European shipbuilding industries for carbon steels, and a range of four different frequencies alternating between Ar/20%CO2 and helium. The beneficial effects of supplying the weld shielding gases in an alternating manner were found to provide attractive benefits for the manufacturing community. For example, the present study showed that compared with conventional GMAW, a 17 per cent reduction in total welding cost was achieved in the case of the alternating gas method and savings associated with a reduction in the extent of post-weld straightening following plate distortion were also identified. Also, the mechanical properties of the alternating case highlighted some marginal improvements in strength and Charpy impact toughness which were attributed to a more refined weld microstructure

The political economy of private firms in China

The sweeping change in political economy associated with the spectacular growth of the private sector in China is not much studied in economics literature. This paper fills in this gap. The central subject of this paper is the political economy nature of the Chinese private sector and of the CPC. Empirically, we examine the dynamics of rent creation from the party membership and other political connections when the regime is changed from anti-capitalistic to pro-capitalistic. Endogeneity problems are addressed. We identify the causality of rents and private entrepreneurs’ political connections, and explore the implications of these political elites’ rents for social welfare in terms of productivity.postprin

Time and Time Functions in Parametrized Non-Relativistic Quantum Mechanics

The ``evolving constants'' method of defining the quantum dynamics of time-reparametrization-invariant theories is investigated for a particular implementation of parametrized non-relativistic quantum mechanics (PNRQM). The wide range of time functions that are available to define evolving constants raises issues of interpretation, consistency, and the degree to which the resulting quantum theory coincides with, or generalizes, the usual non-relativistic theory. The allowed time functions must be restricted for the predictions of PNRQM to coincide with those of usual quantum theory. They must be restricted to have a notion of quantum evolution in a time-parameter connected to spacetime geometry. They must be restricted to prevent the theory from making inconsistent predictions for the probabilities of histories. Suitable restrictions can be introduced in PNRQM but these seem unlikely to apply to a reparametrization invariant theory like general relativity.Comment: 18pages, 1postscript figure in separate file, uses REVTEX 3.

Chern-Simons theory and three-dimensional surfaces

There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is extrinsic and uses the connection associated with the gauging of normal rotations. As such, the two theories appear to describe very different aspects of the surface geometry. Remarkably, at a classical level, they are equivalent. In particular, it will be shown that their stress tensors differ only by a null contribution. Their Euler-Lagrange equations provide identical constraints on the normal curvature. A new identity for the Cotton tensor is associated with the triviality of the Chern-Simons theory for embedded hypersurfaces implied by this equivalence. The corresponding null surface stress capturing this information will be constructed explicitly.Comment: 10 pages, unnecessary details removed, typos fixed, references adde

Constraints on Beta Functions from Duality

We analyze the way in which duality constrains the exact beta function and correlation length in single-coupling spin systems. A consistency condition we propose shows very concisely the relation between self-dual points and phase transitions, and implies that the correlation length must be duality invariant. These ideas are then tested on the 2-d Ising model, and used towards finding the exact beta function of the $q$-state Potts model. Finally, a generic procedure is given for identifying a duality symmetry in other single-coupling models with a continuous phase transition.Comment: LaTeX, 6 page