Property Price Modelling: The Regression Model and The Neural Newtwork Model

Hedonic regression models are widely used in housing price studies. However, incorrect identification of the functional relationship may lead to potential bias. This research studies the neural network model in modeling housing price. A neural network model is regarded as a nonlinear regression model without a predetermined functional form. The adoption of the neural network model could overcome the biasness inherent in the hedonic price regression model. The performance of neural network models and hedonic regression models are discussed based on the Hong Kong property price data

The Origin of Gamma-Rays from Globular Clusters

Fermi has detected gamma-ray emission from eight globular clusters. We suggest that the gamma-ray emission from globular clusters may result from the inverse Compton scattering between relativistic electrons/positrons in the pulsar wind of MSPs in the globular clusters and background soft photons including cosmic microwave/relic photons, background star lights in the clusters, the galactic infrared photons and the galactic star lights. We show that the gamma-ray spectrum from 47 Tuc can be explained equally well by upward scattering of either the relic photons, the galactic infrared photons or the galactic star lights whereas the gamma-ray spectra from other seven globular clusters are best fitted by the upward scattering of either the galactic infrared photons or the galactic star lights. We also find that the observed gamma-ray luminosity is correlated better with the combined factor of the encounter rate and the background soft photon energy density. Therefore the inverse Compton scattering may also contribute to the observed gamma-ray emission from globular clusters detected by Fermi in addition to the standard curvature radiation process. Furthermore, we find that the emission region of high energy photons from globular cluster produced by inverse Compton scattering is substantially larger than the core of globular cluster with a radius >10pc. The diffuse radio and X-rays emitted from globular clusters can also be produced by synchrotron radiation and inverse Compton scattering respectively. We suggest that future observations including radio, X-rays, and gamma-rays with energy higher than 10 GeV and better angular resolution can provide better constraints for the models.Comment: Accepted by ApJ, Comments may send to Prof. K.S. Cheng: [email protected]

The Fundamental Plane of Gamma-ray Globular Clusters

We have investigated the properties of a group of $\gamma$-ray emitting globular clusters (GCs) which have recently been uncovered in our Galaxy. By correlating the observed $\gamma$-ray luminosities $L_{\gamma}$ with various cluster properties, we probe the origin of the high energy photons from these GCs. We report $L_{\gamma}$ is positively correlated with the encounter rate $\Gamma_{c}$ and the metalicity $\left[{\rm Fe/H}\right]$ which place an intimate link between the gamma-ray emission and the millisecond pulsar population. We also find a tendency that $L_{\gamma}$ increase with the energy densities of the soft photon at the cluster location. Furthermore, the two-dimensional regression analysis suggests that $L_{\gamma}$, soft photon densities, and $\Gamma_{c}$/$\left[{\rm Fe/H}\right]$ possibly span fundamental planes which potentially provide better predictions for the $\gamma$-ray properties of GCs.Comment: 17 pages, 4 figures, 3 tables, published in Ap

The Impact of Waiting Time and Other Service Factors on Customer Satisfaction and Repurchase Frequency

Although repurchase intention and customer satisfaction have attracted a lot of attention in service management research, relatively few studies have discussed the impact of waiting time on repurchase frequency. In this study, we investigate the effect of waiting time and other service quality factors on customer satisfaction and repurchase frequency. Using the Generalized Linear Model as a tool, a Return Frequency Model was developed to describe the relationship between number of return visits in certain time period and the waiting time and different service factors in the fast food service setting. Using Polytomous Logistic Regression, an Overall Satisfaction Model was developed to demonstrate the relationship between customer’s overall satisfaction level, waiting time and service quality

Coherence Length of Excitons in a Semiconductor Quantum Well

We report on the first experimental determination of the coherence length of excitons in semiconductors using the combination of spatially resolved photoluminescence with phonon sideband spectroscopy. The coherence length of excitons in ZnSe quantum wells is determined to be 300 ~ 400 nm, about 25 ~ 30 times the exciton de Broglie wavelength. With increasing exciton kinetic energy, the coherence length decreases slowly. The discrepancy between the coherence lengths measured and calculated by only considering the acoustic phonon scattering suggests an important influence of static disorder.Comment: 4 Pages, 4 figure

Spectrum of Relativistic and Subrelativistic Cosmic Rays in the 100 pc Central Region

From the rate of hydrogen ionization and the gamma ray flux, we derived the spectrum of relativistic and subrelativistic cosmic rays (CRs) nearby and inside the molecular cloud Sgr B2 near the Galactic Center (GC). We studied two cases of CR propagation in molecular clouds: free propagation and scattering of particles by magnetic fluctuations excited by the neutral gas turbulence. We showed that in the latter case CR propagation inside the cloud can be described as diffusion with the coefficient $\sim 3\times 10^{27}$ cm$^2$ s$^{-1}$. For the case of hydrogen ionization by subrelativistic protons, we showed that their spectrum outside the cloud is quite hard with the spectral index $\delta>-1$. The energy density of subrelativistic protons ($>50$ eV cm$^{-3}$) is one order of magnitude higher than that of relativistic CRs. These protons generate the 6.4 keV emission from Sgr B2, which was about 30\% of the flux observed by Suzaku in 2013. Future observations for the period after 2013 may discover the background flux generated by subrelativistic CRs in Sgr B2. Alternatively hydrogen ionization of the molecular gas in Sgr B2 may be caused by high energy electrons. We showed that the spectrum of electron bremsstrahlung is harder than the observed continuum from Sgr B2, and in principle this X-ray component provided by electrons could be seen from the INTEGRAL data as a stationary high energy excess above the observed spectrum $E_x^{-2}$.Comment: 42 pages, 6 figures, accepted by Ap

Stationary Localized States Due to a Nonlinear Dimeric Impurity Embedded in a Perfect 1-D Chain

The formation of Stationary Localized states due to a nonlinear dimeric impurity embedded in a perfect 1-d chain is studied here using the appropriate Discrete Nonlinear Schr$\ddot{o}$dinger Equation. Furthermore, the nonlinearity has the form, $\chi |C|^\sigma$ where $C$ is the complex amplitude. A proper ansatz for the Localized state is introduced in the appropriate Hamiltonian of the system to obtain the reduced effective Hamiltonian. The Hamiltonian contains a parameter, $\beta = \phi_1/\phi_0$ which is the ratio of stationary amplitudes at impurity sites. Relevant equations for Localized states are obtained from the fixed point of the reduced dynamical system. $|\beta|$ = 1 is always a permissible solution. We also find solutions for which $|\beta| \ne 1$. Complete phase diagram in the $(\chi, \sigma)$ plane comprising of both cases is discussed. Several critical lines separating various regions are found. Maximum number of Localized states is found to be six. Furthermore, the phase diagram continuously extrapolates from one region to the other. The importance of our results in relation to solitonic solutions in a fully nonlinear system is discussed.Comment: Seven figures are available on reques

The B(Bs)→D(s)PB(B_s)\to D_{(s)} P, D(s)VD_{(s)} V, D(s)∗PD_{(s)}^{*}P and D(s)∗VD_{(s)}^{*}V decays in the perturbative QCD approach

Two-body non-leptonic charmed decays $B_{(s)} \to D_{(s)}P$, $D_{(s)}^*P$, $D_{(s)}V$ and $D_{(s)}^*V$ are analyzed in perturbative QCD approach, where $P$ and $V$ denote the light pseudoscalar meson and vector meson, respectively. We test the $D$ meson wave function by a $\chi^2$ fit with experimental data of six $B\to DP$ channels. We give the branching ratios of all the charmed B decay channels, most of which agree with experiments amazingly well. The predicted $B_s$ decays can be confronted with the future experimental data. By straightforward calculations, our pQCD approach gives the right relative strong phase of $a_2/a_1$ with experiments. We also predict the percentage of transverse polarizations in $B_{(s)} \to D^* V$ decay channels.Comment: 25 pages, 4 figure

Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts.

The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes