Dynamics of the periodic type-K competitive Kolmogorov systems

For time-periodic dissipative and irreducible type-K competitive Kolmogorov systems, it is proved that there is a canonically defined countable family F of unordered, disjoint invariant sets with the property that, for every persistent trajectory whose ω-limit set is not a cycle, there exists a unique trajectory in some element of F such that these two trajectories are asymptotic and the corresponding points in these two trajectories are K-related.     

具有控制系数的高阶线性微分方程复振荡的一个结果

该文考虑具有控制系数 A\-0 和系数仅有有限个极点的高阶线性齐次微分方程（1.1）。得到了一个复振荡结果，该结果是J. K. Langley［11］等作者在整系数下相应结果的推广。     

Probability Inequalities and Limit Theorems for Generalized L-Statistics

We obtain exponential upper bounds for tails of distributions of generalized L-statistics based on a sample from an exponential distribution. We prove the asymptotic normality of generalized L-statistics based on a sample from the uniform distribution on [0,1] and of L-statistics with decomposed kernels (without any restrictions on the sample distribution type).     

NCD系统的数学理论

无索赔折扣系统(No Claim Discount system,简记为NCD系统)是世界各国机动车辆险中广泛采用的一种经验费率厘定机制.本文尝试建立了NCD系统严谨的数学理论, 重点讨论了NCD系统的数学建模和稳态分析.此外,作为本文必要的数学前提,首先在第2节着重探讨了随机矩阵间的随机优序关系,并将所得结论运用至齐次不可约且遍历的马尔科夫链的研究中,这些内容也有其独立的数学上的兴趣.     

OSCILLATION RESULTS FOR A SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.     

Multiple Window and Cluster Size Scan Procedures

Researchers apply scan statistics to test for unusually large clusters of events within a time window of specified length w, or alternatively an unusually small window w that contains a specified number of events. In some cases, the researcher is interested in testing for a range of specified window lengths, or a set of several specified number of events k (cluster sizes). In this paper, we derive accurate approximations for the joint distributions of scan statistics for a range of values of w, or of k, that can be used to set an experiment-wide level of significance that takes into account the multiple comparisons involved. We use these methods to compare different ways of choosing the window sizes for the different cluster sizes. One special case is a multiple comparison procedure based on a generalized likelihood ratio test (GLRT) for a range of window sizes. We compare the power of the GLRT with another method for allocating the window sizes. We find that the GLRT is sensitive for very small window sizes at the expense of moderate and larger window sizes. We illustrate these results on two examples, one involving clustering of translocation breakpoints in DNA, and the other involving disease clusters.     

High‐order accurate numerical solutions of incompressible flows with the artificial compressibility method

A high‐order accurate, finite‐difference method for the numerical solution of incompressible flows is presented. This method is based on the artificial compressibility formulation of the incompressible Navier–Stokes equations. Fourth‐ or sixth‐order accurate discretizations of the metric terms and the convective fluxes are obtained using compact, centred schemes. The viscous terms are also discretized using fourth‐order accurate, centred finite differences. Implicit time marching is performed for both steady‐state and time‐accurate numerical solutions. High‐order, spectral‐type, low‐pass, compact filters are used to regularize the numerical solution and remove spurious modes arising from unresolved scales, non‐linearities, and inaccuracies in the application of boundary conditions. The accuracy and efficiency of the proposed method is demonstrated for test problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Pseudo-Isotherms Using a Second Order Kinetic Expression Constant

The kinetics of four sorption systems, Cu/tree fern, Pb/tree fern, AB9/activated clay and BR18/activated clay have been studied based on the assumption of a pseudo-second order rate law. Pseudo-isotherms using the pseudo-second order kinetic expression constant have been developed to describe the four liquid-solid sorption systems. The experimental results have been analyzed using a pseudo-Langmuir and a pseudo-Redlich-Peterson isotherm. Both isotherms were found to represent the measured sorption data well. According to the evaluation using the pseudo-Langmuir equation, the monolayer sorption capacities were obtained to be 13.9, 46.6, 124 and 105 mg g^–1 for copper, lead, AB9 and BR18 respectively.     

Baker＇s Yeast Mediated Reduction of Optically Active Diketone

Baker‘s yeast mediated reduction of optically active diketone is described. The two keto groups are efficiently differentiated and the ee value of the recovered material is considerably raised. It affords highly optically active key intermediates efficiently for the synthesis of natural polyhydroxylated agarofuran products.     

An Unusual Reductive Ring-opening Reaction of Phthalimide with Sodium Hydride in DMF

An unusual reductive ring-opening reaction of phthalimide with sodium hydride in anhydrous DMF was observed for the first time. The presumed mechanism was described in detail.