Automorphisms of finite order on Gorenstein del Pezzo surfaces

In this note we shall determine all actions of groups of prime order p with p > 3 on Gorenstein del Pezzo (singular) surfaces Y of Picard number 1. We show that every order-p element in Aut(Y) (= Aut(Y'), Y' being the minimal resolution of Y) is lifted from a projective transformation of the projective plane. We also determine when Aut(Y) is finite in terms of the self intersection of the canonical divisor of Y, Sing(Y) and the number of singular members in the anti-canonical linear system of Y. In particular, we show that either |Aut(Y)| = 2^a 3^b for some 0 3 there is at least one element g_p of order p in Aut(Y) (hence |Aut(Y)| is infinite).Comment: 18 pages, Transactions of the American Mathematical Society, to appea

Laser wakefield and direct acceleration in the plasma bubble regime

Laser wakefield acceleration (LWFA) and direct laser acceleration (DLA) are two different kinds of laser plasma electron acceleration mechanisms. LWFA relies on the laser-driven plasma wave to accelerate electrons. The interaction of ultra-short ultra-intensive laser pulses with underdense plasma leads the LWFA into a highly nonlinear regime (“plasma bubble regime”) that attracts particular interest nowadays. DLA accelerates electrons by laser electromagnetic wave in the ion channel or the plasma bubble through the Betatron resonance. This dissertation presents a hybrid laser plasma electron acceleration mechanism. We investigate its features through particle-in-cell (PIC) simulations and the single particle model. The hybrid laser plasma electron acceleration is the merging concept between the LWFA and the DLA, so called laser wakefield and direct acceleration (LWDA). The requirements of the initial conditions of the electron to undergo the LWDA are determined. The electron must have a large initial transverse energy. Two electron injection mechanisms that are suitable for the LWDA, density bump injection and ionization induced injection, are studied in detail. The features of electron beam phase space and electron dynamics are explored. Electron beam phase space appears several unique features such as spatially separated two groups, the correlation between the transverse energy and the relativistic factor and the double-peak spectrum. Electrons are synergistically accelerated by the wakefield as well as by the laser electromagnetic field in the laser-driven plasma bubble. LWDA are also investigated in the moderate power regime (10 TW) in regarding the effects of laser color and polarization. It is found that the frequency upshift laser pulse has better performance on avoiding time-jitter of electron energy spectra, electron final energy and electron charge yield. Some basic characters that related to the LWDA such as the effects of the subluminal laser wave, the effects of the longitudinal accelerating field, the electron beam emittance, the electron charge yield and potentially applications as radiation source are discussed.Physic

Human gait recognition with matrix representation

Human gait is an important biometric feature. It can be perceived from a great distance and has recently attracted greater attention in video-surveillance-related applications, such as closed-circuit television. We explore gait recognition based on a matrix representation in this paper. First, binary silhouettes over one gait cycle are averaged. As a result, each gait video sequence, containing a number of gait cycles, is represented by a series of gray-level averaged images. Then, a matrix-based unsupervised algorithm, namely coupled subspace analysis (CSA), is employed as a preprocessing step to remove noise and retain the most representative information. Finally, a supervised algorithm, namely discriminant analysis with tensor representation, is applied to further improve classification ability. This matrix-based scheme demonstrates a much better gait recognition performance than state-of-the-art algorithms on the standard USF HumanID Gait database

Scale disparities and magnetohydrodynamics in the Earth’s core

Fluid motions driven by convection in the Earth’s fluid core sustain geomagnetic ­ fields by magnetohydrodynamic dynamo processes. The dynamics of the core is critically influenced by the combined effects of rotation and magnetic ­ fields. This paper attempts to illustrate the scale-related difficulties in modelling a convection-driven geodynamo by studying both linear and nonlinear convection in the presence of imposed toroidal and poloidal ­ fields. We show that there exist three extremely large disparities, as a direct consequence of small viscosity and rapid rotation of the Earth’s fluid core, in the spatial, temporal and amplitude scales of a convection-driven geodynamo. We also show that the structure and strength of convective motions, and, hence, the relevant dynamo action, are extremely sensitive to the intricate dynamical balance between the viscous, Coriolis and Lorentz forces; similarly, the structure and strength of the magnetic field generated by the dynamo process can depend very sensitively on the fluid flow. We suggest, therefore, that the zero Ekman number limit is strongly singular and that a stable convection-driven strong-­field geodynamo satisfying Taylor’s constraint may not exist. Instead, the geodynamo may vacillate between a strong ­field state, as at present, and a weak ­ field state, which is also unstable because it fails to convect sufficient heat

Optimal funding and investment strategies in defined contribution pension plans under Epstein-Zin utility

A defined contribution pension plan allows consumption to be redistributed from the plan member’s working life to retirement in a manner that is consistent with the member’s personal preferences. The plan’s optimal funding and investment strategies therefore depend on the desired pattern of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member has an Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution, and we also take into account the member’s human capital. We show that a stochastic lifestyling approach, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches is an optimal investment strategy. In addition, the optimal contribution rate each year is not constant over the life of the plan but reflects trade-offs between the desire for current consumption, bequest and retirement savings motives at different stages in the life cycle, changes in human capital over the life cycle, and attitude to risk