Elliptic polynomials orthogonal on the unit circle with a dense point spectrum

We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of the Jacobi elliptic functions. We find explicit expression for these polynomials in terms of elliptic hypergeometric functions. We show that the obtained polynomials are orthogonal on the unit circle with respect to a dense point measure. We also construct corresponding explicit systems of polynomials orthogonal on the interval of the real axis with respect to a dense point measure. They can be considered as an elliptic generalization of the Askey-Wilson polynomials of a special type.      

On the amicability of orthogonal designs

Although it is known that the maximum number of variables in two amicable orthogonal designs of order 2ⁿp, where p is an odd integer, never exceeds 2n+2, not much is known about the existence of amicable orthogonal designs lacking zero entries that have 2n+2 variables in total. In this paper we develop two methods to construct amicable orthogonal designs of order 2ⁿp where p odd, with no zero entries and with the total number of variables equal or nearly equal to 2n+2. In doing so, we make a surprising connection between the two concepts of amicable sets of matrices and an amicable pair of matrices. With the recent discovery of a link between the theory of amicable orthogonal designs and space‐time codes, this paper may have applications in space‐time codes. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 240‐252, 2009     

On the index of Fredholm pairs of idempotents

Using the technique of block-operators, in this note, we prove that if P and Q are idempotents and （P - Q）^2n＋1 is in the trace class, then （P - Q）^2m＋1 is also in the trace class and tr（P - Q）^2m＋1 = dim（k（P） ∩ k（Q）^⊥） -dim（k（P）^⊥ N k（Q））, for all m ≥ n. Moreover, we prove that dim（k（P）∩ k（Q）^⊥） = dim（k（P）^⊥ ∩k（Q）） if and only if there exists a unitary U such that UP = QU and PU = UQ, where k（T） denotes the range of T. Keywords Fredholm, orthogonal projection, positive operator     

Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians

It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.      

基于S-R和分解定理的无网格Galerkin法求解几何非线性问题

针对几何非线性问题,基于S-R和分解定理与更新拖带坐标描述法,从运动变换的角度出发,由虚功率原理建立全局弱式积分方程.采用无网格Galerkin法(EFG)求得该问题的数值解.对于非线性问题的数值计算,通常采用增量和迭代法.S-R和分解定理给出了一种新的应变张量,该应变张量能合理地反映大位移大转动情况下物体的应变状态及转动情况,而且有利于求解几何非线性问题.数值算例验证了该方法的合理性和有效性.     

微生物固定法降解含聚废水的最佳条件

利用从含聚废水中分离纯化得到的单一菌株R4-1,R4-2,R4-3,R4-5,H4-3,以海藻酸钠-PVA为包埋剂,采用包埋固定法对5种菌的混合菌进行固定化实验.通过单因素实验和正交实验,系统考察了湿菌体与包埋剂的体积比、氯化钙质量分数、硼酸质量分数和交联时间等因素对聚丙烯酰胺降解率的影响.实验得到微生物固定法降解含聚废水的最佳制备条件:4%海藻酸钠,4%的PVA,湿菌体与包埋剂体积比1∶1,2%氯化钙,3%硼酸,分段交联时间为氯化钙4h后硼酸20h.湿菌体与包埋剂的体积比对聚丙烯酰胺降解率的影响十分显著.追加实验最佳制备条件,得到微生物固定化颗粒对含聚废水的降解率可达到83.1%.     

基于演变谱和正交化HHT法的类谐和长周期地震动合成

结合演变谱理论和正交化HHT法的优点,建立了一种能同时反映强度和频率非平稳特性的地震动人工合成方法.选取1999年台湾集集地震中的2条类谐和长周期地震动记录作为原始地震动进行了人工合成,并进行了局部功率谱密度分析和反应谱分析.分析结果表明,本文建立的地震动合成方法能实现对地震动频率非平稳性的模拟,合成的类谐和长周期地震动时程与原始地震动时程在能量时频分布上具有较好的一致性,且弹性反应谱及弹塑性反应谱的拟合精度较高,可供工程结构地震反应分析使用.     

改进的遗传算法在球面点分布问题中的应用

球面点的分布问题,是世界性数学难题.对基本遗传算法进行了改进.采用实数编码,同时在遗传算法中引入了正交算子、变维子空间算子、灾变算子等高效演化算子,形成了自适应遗传算法.这样改进的算法极大地促进了个体多样性,并能促进优秀基因型的杂交和遗传,在收敛和鲁棒性方面优于一般的遗传算法,将它应用于球面点分布问题取得了较好的效果.     

水驱油藏转注CO_2驱油参数优化与效果评价

以大港油田某断块为研究对象,基于正交试验设计原理,以提高采收率程度和换油率为评价指标,运用数值模拟方法,开展水驱油藏转注CO2驱油注采参数优化与效果评价研究.研究结果表明:转注CO2驱油能够有效提高水驱油藏采收率,最优注气段塞大小为0.05 PV,气水体积比为1∶2,注气速度为40 000 m3/d,注采比为1∶0.9;适当提高注采比有利于保持地层压力,增加原油与CO2混相程度,提高气体波及系数,有效改善CO2驱油效果;气水交替驱能够获得良好的CO2埋存效果,注入的CO2大约有50%被封存在油藏中.     

FSAE赛车发动机谐振进气系统仿真及设计

采用GT-power软件建立JH600发动机模型,模拟全负荷时发动机转速与有效功率的关系,通过与试验结果对比,模拟结果与试验数据吻合良好,为进气系统的设计与仿真提供了重要依据.利用正交实验法结合GT-power软件对谐振进气系统进行匹配计算,从而确定了进气管直径、谐振腔直径和限流阀位置等参数.匹配设计结果能有效地提高发动机中高转速下的动力性,弥补了因安装限流阀而导致的赛车发动机功率损失.