Plancherel-Rotach Asymptotics of Second-Order Difference Equations with Linear Coefficients

In this paper, we provide a complete Plancherel-Rotach asymptotic analysis of polynomials that satisfy a second-order difference equation with linear coefficients. According to the signs of the parameters, we classify the difference equations into six cases and derive explicit asymptotic formulas of the polynomials in the outer and oscillatory regions, respectively. It is remarkable that the zero distributions of the polynomials may locate on the imaginary line or even on a sideways Y-shape curve in some cases

Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States

In this paper, we study a family of orthogonal polynomials $\{\phi_n(z)\}$ arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of $\phi_n(z)$ as the polynomial degree $n$ tends to infinity. Our asymptotic results suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong's difference equation method. In addition, the limiting zero distribution of the polynomials $\phi_n(z)$ is provided

A Unified And Green Platform For Smartphone Sensing

Smartphones have become key communication and entertainment devices in people\u27s daily life. Sensors on (or attached to) smartphones can enable attractive sensing applications in different domains, including environmental monitoring, social networking, healthcare, transportation, etc. Most existing smartphone sensing systems are application-specific. How to leverage smartphones\u27 sensing capability to make them become unified information providers for various applications has not yet been fully explored. This dissertation presents a unified and green platform for smartphone sensing, which has the following desirable features: 1) It can support various smartphone sensing applications; 2) It is personalizable; 2) It is energy-efficient; and 3) It can be easily extended to support new sensors. Two novel sensing applications are built and integrated into this unified platform: SOR and LIPS. SOR is a smartphone Sensing based Objective Ranking (SOR) system. Different from a few subjective online review and recommendation systems (such as Yelp and TripAdvisor), SOR ranks a target place based on data collected via smartphone sensing. LIPS is a system that learns the LIfestyles of mobile users via smartPhone Sensing (LIPS). Combining both unsupervised and supervised learning, a hybrid scheme is proposed to characterize lifestyle and predict future activities of mobile users. This dissertation also studies how to use the cloud as a coordinator to assist smartphones for sensing collaboratively with the objective of reducing sensing energy consumption. A novel probabilistic model is built to address the GPS-less energy-efficient crowd sensing problem. Provably-good approximation algorithms are presented to enable smartphones to sense collaboratively without accurate locations such that sensing coverage requirements can be met with limited energy consumption

Study of Balance Equations for Hot-Electron Transport in an Arbitrary Energy Band (III)

By choosing an electron gas resting instead of drifting in the laboratory coordinate system as the initial state, the first order perturbation calculation of the previous paper (Phys. Stat. Sol. (b) 198, 785(1996)) is revised and extended to include the high order field corrections in the expression for the frictional forces and the energy transfer rates. The final expressions are formally the same as those in first order in the electric field, but the distribution functions of electrons appearing in them are defined by different expressions. The problems relative to the distribution function are discussed in detail and a new closed expression for the distribution function is obtained. The nonlinear impurity-limited resistance of a strong degenerate electron gas is computed numerically. The result calculated by using the new expression for the distribution function is quite different from that using the displaced Fermi function when the electric field is sufficiently high.Comment: 15 pages with 3 PS figures, RevTeX, to be published in Physica Status Solidi (b