Quasi-local energy and the choice of reference

A quasi-local energy for Einstein's general relativity is defined by the value of the preferred boundary term in the covariant Hamiltonian formalism. The boundary term depends upon a choice of reference and a time-like displacement vector field (which can be associated with an observer) on the boundary of the region. Here we analyze the spherical symmetric cases. For the obvious analytic choice of reference based on the metric components, we find that this technique gives the same quasi-local energy values using several standard coordinate systems and yet can give different values in some other coordinate systems. For the homogeneous-isotropic cosmologies, the energy can be non-positive, and one case which is actually flat space has a negative energy. As an alternative, we introduce a way to determine the choice of both the reference and displacement by extremizing the energy. This procedure gives the same value for the energy in different coordinate systems for the Schwarzschild space, and a non-negative value for the cosmological models, with zero energy for the dynamic cosmology which is actually Minkowski space. The timelike displacement vector comes out to be the dual mean curvature vector of the two-boundary.Comment: 21 pages; revised version to appear in CQ

How Much Does Money Matter in a Direct Democracy?

The fine-structure splitting of quantum confined InxGa1-x Nexcitons is investigated using polarization-sensitive photoluminescence spectroscopy. The majority of the studied emission lines exhibits mutually orthogonal fine-structure components split by 100-340 mu eV, as measured from the cleaved edge of the sample. The exciton and the biexciton reveal identical magnitudes but reversed sign of the energy splitting.Original Publication:Supaluck Amloy, Y T Chen, K F Karlsson, K H Chen, H C Hsu, C L Hsiao, L C Chen and Per-Olof Holtz, Polarization-resolved fine-structure splitting of zero-dimensional InxGa1-xN excitons, 2011, PHYSICAL REVIEW B, (83), 20, 201307.http://dx.doi.org/10.1103/PhysRevB.83.201307Copyright: American Physical Societyhttp://www.aps.org

Approximation learning methods of Harmonic Mappings in relation to Hardy Spaces

A new Hardy space Hardy space approach of Dirichlet type problem based on Tikhonov regularization and Reproducing Hilbert kernel space is discussed in this paper, which turns out to be a typical extremal problem located on the upper upper-high complex plane. If considering this in the Hardy space, the optimization operator of this problem will be highly simplified and an efficient algorithm is possible. This is mainly realized by the help of reproducing properties of the functions in the Hardy space of upper-high complex plane, and the detail algorithm is proposed. Moreover, harmonic mappings, which is a significant geometric transformation, are commonly used in many applications such as image processing, since it describes the energy minimization mappings between individual manifolds. Particularly, when we focus on the planer mappings between two Euclid planer regions, the harmonic mappings are exist and unique, which is guaranteed solidly by the existence of harmonic function. This property is attractive and simulation results are shown in this paper to ensure the capability of applications such as planer shape distortion and surface registration.Comment: 2016 3rd International Conference on Informative and Cybernetics for Computational Social Systems (ICCSS

Modeling the Effect of Oil Price on Global Fertilizer Prices

The main purpose of this paper is to evaluate the effect of crude oil price on global fertilizer prices in both the mean and volatility. The endogenous structural breakpoint unit root test, the autoregressive distributed lag (ARDL) model, and alternative volatility models, including the generalized autoregressive conditional heteroskedasticity (GARCH) model, Exponential GARCH (EGARCH) model, and GJR model, are used to investigate the relationship between crude oil price and six global fertilizer prices. Weekly data for 2003-2008 for the seven price series are analyzed. The empirical results from ARDL show that most fertilizer prices are significantly affected by the crude oil price, which explains why global fertilizer prices reached a peak in 2008. We also find that that the volatility of global fertilizer prices and crude oil price from March to December 2008 are higher than in other periods, and that the peak crude oil price caused greater volatility in the crude oil price and global fertilizer prices. As volatility invokes financial risk, the relationship between oil price and global fertilizer prices and their associated volatility is important for public policy relating to the development of optimal energy use, global agricultural production, and financial integration.volatility;crude oil price;global fertilizer price;non-renewable fertilizers;structural breakpoint unit root test