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

A mathematical model of photopolymerization in a batch reactor

A mathematical model of a photo initiated additionpolymerization in a batch reactor was developed. The model considered initiation, propagation and, termination to simulate the addition polymerization process, The model has the advantage that the concentration of any particular n-mer may be calculated without calculating all of its precursors. Other methods do not have this property. An analytical solution to the model for the photopolymerization of styrene was solved. The calculations were run on a VAX 8800 computer and the results were then compared with the experimental results. The calculated results fitted the experimental results to some extent. Effects from the variations of feed temperatures and light intensities were also discussed, the model predicted their influence very well

Proportional and Preemption-enabled Traffic Offloading for IP Flow Mobility:Algorithms and Performance Evaluation

IP Flow Mobility (IFOM) enables a user equipment to offload data traffic at the IP flow level. Although the procedure of IFOM-based flow offloading has been specified by 3GPP, how many IP flows should be offloaded and when offloading should be performed are not defined. Consequently, IP flows may be routed to a target access network which has a strong signal strength but with backhaul congestion or insufficient access capability. In this paper, we propose two algorithms, referred to as proportional offloading (PO), and proportional and preemption-enabled offloading (PPO), respectively, for IP flow offloading in hybrid cellular and wireless local area networks. The PO algorithm decides an optimal proportion of IP flows which could be offloaded by considering available resources at the target access network. In the PPO algorithm, both service continuity and network utilization are taken into consideration. Furthermore, a detailed analytical model is developed in order to evaluate the behavior of the proposed algorithms. The analytical model is validated through extensive simulations. The results show that by dynamically adjusting the percentage of traffic flows to be offloaded, PO can reduce blocking probability and increase resource utilization. PPO further improves the performance at the cost of slightly higher offloading overhead