Soft Gluons in Logarithmic Summations

We demonstrate that all the known single- and double-logarithm summations for a parton distribution function can be unified in the Collins-Soper resummation technique by applying soft approximations appropriate in different kinematic regions to real gluon emissions. Neglecting the gluon longitudinal momentum, we obtain the $k_T$ (double-logarithm) resummation for two-scale QCD processes, and the Balitsky-Fadin-Kuraev-Lipatov (single-logarithm) equation for one-scale processes. Neglecting the transverse momentum, we obtain the threshold (double-logarithm) resummation for two-scale processes, and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (single-logarithm) equation for one-scale processes. If keeping the longitudinal and transverse momenta simultaneously, we derive a unified resummation for large Bjorken variable $x$, and a unified evolution equation appropriate for both intermediate and small $x$.Comment: 14 pages in Latex, 1 figure in postscript fil

Evaluating Callable and Putable Bonds: An Eigenfunction Expansion Approach

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and put dates, the callable and putable bond pricing function is the value function of a stochastic game with stopping times. Under some technical conditions, it is shown to have an eigenfunction expansion in eigenfunctions of the pricing operator with the expansion coefficients determined through a backward recursion. For popular short rate diffusion models, such as CIR, Vasicek, 3/2, the method is orders of magnitude faster than the alternative approaches in the literature. In contrast to the alternative approaches in the literature that have so far been limited to diffusions, the method is equally applicable to short rate jump-diffusion and pure jump models constructed from diffusion models by Bochner's subordination with a L\'{e}vy subordinator

Identification of Frequency Ranges for Subharmonic Oscillations in a Relay Feedback System

This paper examines the behaviour of a single loop relay feedback system (RFS) which is driven by an external signal. It is well known that such a RFS exhibits a variety of oscillation patterns including forced and subharmonic oscillations (SO). This paper focuses on the conditions for SO. It will be shown that for an external signal with a fixed amplitude, it is possible for SO with different orders to occur simply by changing the frequency of the external signal. Similarly, for an external signal with a fixed frequency, it is possible for SO with different orders to occur when the amplitude of the external signal is varied. The conditions under which these different scenarios will occur are explored. An analysis of these conditions identifies the frequency ranges where certain orders of SO are possible for a given amplitude of the external signal. The effects of the initial conditions on the SO are illustrated and discussed. Simulation studies are presented to illustrate the result

Modelling and Parameter Identification Using Reduced I-V Data

No abstract available

Evaluation of the Students' Learning Experience and Competency Gain with YACRS

No abstract available

Face Recognition Technique Using Gabor Wavelets And Singular Value Decomposition

Gabor Wavelets (GWs) (also known as Gabor filter) and Singular Value Decomposition (SVD) have been studied extensively in the area of face recognition. In this project, face recognition system is developed using combination of GWs and SVD. Both techniques are used to extract facial features from the human facial image and presented in the form of feature vector. For GWs, only 12 out of 40 GWs are selected to extract facial features from the facial images. This offers the advantage of reducing computational time of feature extraction. As for SVD, only the first five singular values are selected and its associated right singular vectors are used as the facial feature vectors. The use of SVD in addition to the GWs increases the reliability of the face recognition system. In the face verification and matching stage, the similarity level between facial images is determined by computing the distance between the resulting facial feature vectors obtained from GWs and SVD respectively. Overall, the Gabor-SVD based face recognition technique showed constructive and promising result in recognizing the valid user and rejecting invalid users on the JAFFE database