A Proof of the Kikuta–Ruckle Conjecture on Cyclic Caching of Resources

Suppose that a hider possesses a continuously divisible resource that he may distribute around a circle. The resources on a random arc in the circle are lost. The hider has a priori information on the length of the arc and he wants to maximize the probability that the retrieved portion exceeds a critical quantity, which is enough to survive on. We show that there exists an optimal resource distribution, which uses a finite number of point caches of equal size, establishing a conjecture of Kikuta and Ruckle. Our result is related to a conjecture of Samuels’ on-tail probabilities.     

A reversal index for tournament matrices *

Given a tournament matrix T, its reversal indexi_R (T), is the minimum k such that the reversal of the orientation of k arcs in the directed graph associated with T results in a reducible matrix. We give a formula for i_R (T) in terms of the score vector of T which generalizes a simple criterion for a tournament matrix to be irreducible. We show that i_R (T)≤[(n?1)/2] for any tournament matrix T of order n, with equality holding if and only if T is regular or almost regular, according as n is odd or even. We construct, for each k between 1 and [(n?1)/2], a tournament matrix of order n whose reversal index is k. Finally, we suggest a few problems.     

Model simulation and experiments of flow and mass transport through a nano-material gas filter

A computational model for evaluating the performance of nano-material packed-bed filters was developed. The porous effects of the momentum and mass transport within the filter bed were simulated. For the momentum transport, an extended Ergun-type model was employed and the energy loss (pressure drop) along the packed-bed was simulated and compared with measurement. For the mass transport, a bulk adsorption model was developed to study the adsorption process (breakthrough behavior). Various types of porous materials and gas flows were tested in the filter system where the mathematical models used in the porous substrate were implemented and validated by comparing with experimental data and analytical solutions under similar conditions. Good agreements were obtained between experiments and model predictions.     

高压LDMOS晶体管准饱和效应分析与建模

研究了高压LDMOS（lateral double-diffused MOS）晶体管中一种特殊的电流饱和现象——准饱和效应.借助于TCAD模拟工具,澄清了准饱和效应的物理机理是漂移区载流子的速度饱和.进而从本征漏极电压V_k入手,给出了描述LDMOS管电流饱和特性的数学模型.该模型已经通过了Matlab的编程验证,兼具准确性、计算速度和可扩展性等优点,并可进一步应用于SPICE电路模拟.关键词：LDMOS准饱和效应高压