A spectral technique for random satisfiable 3CNF formulas

Let I be a random 3CNF formula generated by choosing a truth assignment ? for variables x₁, x_n uniformly at random and including every clause with i literals set true by ? with probability p_i, independently. We show that for any constants 0 ≤ η₂,η₃ ≤ 1 there is a constant d_min so that for all d ≥ d_min a spectral algorithm similar to the graph coloring algorithm of Alon and Kahale will find a satisfying assignment with high probability for p₁ = d/n², p₂ = η₂d/n², and p₃ = η₃d/n². Appropriately setting the η_i's yields natural distributions on satisfiable 3CNFs, not‐all‐equal‐sat 3CNFs, and exactly‐one‐sat 3CNFs. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Process sampling module coupled with purge and trap-GC-FID for in situ auto-monitoring of volatile organic compounds in wastewater

An automatic sampling device, i.e., process sampling module (PSM), connected with a purge and trap-GC-FID system has been developed for real-time monitoring of VOCs in wastewater. The system was designed to simultaneously monitor 17 compounds, including one polar compound, i.e., acetone, and 16 non-polar compounds. The trapping tube is packed with two adsorbents, Carbopack B and Carbosieve III, to trap target compounds. For the purpose of in situ monitoring, the flush valve of the sampling tube is composed of two two-way valves and a time controller to prevent absorption interference of the residue. The optimal conditions for the analytical system include a 12 min purge time at a temperature of 60 °C, and 4 min of desorption time with a desorption temperature of 260 °C. Good chromatograms have been obtained with the analytical system even if a cryogenic device and de-misting were not used. The relative standards deviation (RSD) of the system is between 2% and 13.4%, and accuracies between 0.3 and 23.5% have been achieved. The detection limits of the method range from 0.32 to 2.39 ppb. In this system, the four parts, i.e., PSM, P&T, GC, and FID, were simple, reliable and rugged. Also, the interface of these four parts was simple and dependable.     

关于n进制中非零数字之积函数的几何均值

给出了n进制中非零数字之积函数几何均值的精确计算公式．     

Note on Wong's paper

Using the method of interval integral average, we establish some new oscillation criteria which improve the oscillation criteria due to James S.W. Wong.     

A General Class of Change Point and Change Curve Modeling for Life Time Data

Change point hazard rate models arise in many life time data analysis, for example, in studying times until the undesirable side effects occur in clinical trials. In this paper we propose a general class of change point hazard model for survival data. This class includes and extends different types of change point models for survival data, e.g. cure rate model and lag model. Most classical approach develops estimates of model parameters, with particular interest in change point parameter and often the whole hazard function, but exclusively in terms of asymptotic properties. We propose a Bayesian approach, avoiding asymptotics and provide inference conditional upon the observed data. The proposed Bayesian models are fitted using Markov chain Monte Carlo method. We illustrate our proposed methodology with an application to modeling life times of the printed circuit board.     

Improved Roundoff Error Analysis for Precomputed Twiddle Factors

The accurate precomputation of the twiddle factors is necessary in order to perform discrete trigonometric transforms. This paper presents both worst case and average case analysis of roundoff errors occurring in eight precomputation methods of twiddle factors. We are interested in methods with small roundoff errors, low complexity and using only little computer memory. Numerical tests confirm the theoretical results.     

从刚体的转动角谈地球的自转周期

从刚体转动角的计算入手，结合地球自转和公转运动的几种周期，分析了地球自转的真正周期－恒星日的长度，纠正了某些献和日常生活中关于地球自转周期的错误说法。     

趋近平均法测量普朗克常量

为解决光电效应实验中的测量误差较大问题,提出了“趋近平均法”对普朗克常量进行测量,可使测量误差由使用拐点法的34%降至13.5%.