浅谈代数问题中的数形结合

对数与形的结合在代数解题中的广泛应用作了一些归纳和扩充,主要概括了它在求函数值域与极值(最值)、解不等式(不等式组)、解方程(方程组)三个方面的应用.通过一些典型例题,提出了相应的方法与常用的技巧,因此,数与形不再是分离的主体,而是紧密地结合在一起,并渐渐形成了许多新型数学分支.     

Among- and within-population variation in sperm quality in the simultaneously hermaphroditic land snail Arianta arbustorum

Sperm competition models on the evolution of sperm size assume associations with another sperm quality trait, sperm longevity. Sperm length can also provide an indication of possible mechanisms affecting motility and thus fertilization success. Despite their importance, however, detailed mechanisms of sperm competition at the gamete level are poorly understood. In simultaneously hermaphroditic land snails, sperm traits and cryptic female choice are assumed to be crucial in determining fertilization success. We examined the variation in sperm length and number among individuals from four natural populations of the land snail Arianta arbustorum, a species with multiple mating and long-term sperm storage. We also assessed variation in velocity, motility and longevity of sperm in snails from two of the four populations. Independent of shell size, sperm length differed among populations and, to a minor extent, even among individuals within populations. Mean sperm length of a snail was not correlated with the number of sperm delivered in a spermatophore. The mean sperm velocity (=VCL) did not differ between snails from two populations. However, VCL varied among snails. Percentage motility and longevity of sperm differed between snails from the two populations. No correlations were found between length, velocity, percentage motility and longevity of sperm. To conclude, individual snails differed in sperm quality, and this variation may partly explain the differential fertilization success between A. arbustorum snails. Moreover, our findings did not support the positive association between sperm length and longevity assumed by sperm competition models for internally fertilizing species.     

Emergence of increased division of labor as a function of group size

Empirical evidence suggests that division of labor in insect societies is positively related to group size both within and across taxa. Response threshold models (RTM) have been commonly used to analyze patterns of division of labor. However, these models have been explored empirically and theoretically for only a limited number of tasks, and few studies have examined predictions of the model as colony size and work availability change. We theoretically examine how group size influences division of labor using a fixed response-threshold model. We simultaneously explore how expected by-products of increased colony size, including demand (total work need relative to total work force available) and task number, affect this relationship. Our results indicate that both low demand and high task number positively influence division of labor. We suggest that these changes parallel what is observed within social groups as their size increases, and that, in part, the commonly observed increased division of labor with increasing group size is emergent.     

郑州市大气监测优化布点的研究

利用物元分析法，在大气污染普查基础上，以郑州市污染最严重的季节（冬季）的数据为准，构造大气环境监测的标准物元矩阵，求出关联函数值，进行了大气监测点的优选，并与用模糊聚类选出的点位相比较，来验证郑州市目前已有测子丫建立的合理性，并以此证明物元分析法是环境监测优化布点的一种可靠的方法。     

Application of nanoparticle tracking analysis for characterising the fate of engineered nanoparticles in sediment-water systems

Novel applications of nanotechnology may lead to the release of engineered nanoparticles (ENPs), which result in concerns over their potential environmental hazardous impact. It is essential for the research workers to be able to quantitatively characterise ENPs in the environment and subsequently to assist the risk assessment of the ENPs. This study hence explored the application of nanoparticle tracking system (NTA) to quantitatively describe the behaviour of the ENPs in natural sediment-water systems. The NTA allows the measurement of both particle number concentration (PNC) and particle size distribution (PSD) of the ENPs. The developed NTA method was applied to a range of gold and magnetite ENPs with a selection of surface properties. The results showed that the positively-charged ENPs interacted more strongly with the sediment than neutral and negatively-charged ENPs. It was also found that the citrate coated Au ENPs had a higher distribution percentage (53%) than 11-mercaptoundecanoic acid coated Au ENPs (20%) and citrate coated magnetite ENPs (21%). The principles of the electrostatic interactions between hard (and soft) acids and bases (HSAB) are used to explain such behaviours; the hard base coating (i.e. citrate ions) will interact more strongly with hard acid (i.e. magnetite) than soft acid (i.e. gold). The results indicate that NTA is a complementary method to existing approaches to characterise the fate and behaviour of ENPs in natural sediment.     

基于AHP和比较可能度关系的列控车载系统安全可靠性分析

列控车载系统是保证行车安全的重要系统,其对安全可靠性的要求极高。从人、机和环境3个方面,针对列控车载系统的特点,在分析列控车载系统各安全影响因素的基础上,利用层次分析法建立各影响因素间的关联关系,并充分考虑指标环境的不确定性和决策者思维的模糊性,构建三角模糊数互补判断矩阵。其次,运用三角模糊数比较可能度关系理论,集结所有指标比较的可能度,构建可能度关系比较矩阵。利用三角模糊数矩阵转换关系将可能度关系比较矩阵转换为模糊一致性判断矩阵,在此基础上求解各指标的各层单排序及总排序向量。最后,结合具体算例指出列控车载系统安全可靠性的关键影响因素,以及实际运行当中可能存在的问题并提出决策优化建议。     

基于遗传集对分析的空气环境质量评价

集对分析是针对确定与不确定问题进行定量分析的一种方法,而表征差异度系数i的取值,一直没有确定的方法,即使在确定了同一度、差异度、对立度之后,整个联系数仍因i的不确定取值而呈现既确定又不确定的特征。文章将遗传算法应用于联系数表达式中i值的优化求解,使得联系数确定化,并结合实例对空气环境质量进行评价,评价结果与用其它方法评价结果比较表明该方法的可行性。     

地下水渗流补给-内源释放耦合作用下河流水质不确定模拟

针对河流-地下水环境系统的模糊性、不精确性及随机不确定性,采用梯形模糊数描述和表征河流水文、水质及水文地质参数,构建了集成地下水渗流补给与内源释放耦合影响的一维河流水质模糊模拟模型.在此基础上,就地下水渗流补给与内源释放的可能组合,设置5种情景,分别进行水质模拟,并对计算结果进行分析、对比.实例研究表明,对地下水渗流补给与内源释放耦合作用下的河流水质衰减变化规律,梯形模糊数有较好的模拟效果.     

近50a东江流域径流变化及影响因素分析

以1956—2005年降雨、径流与气象资料为基础,应用Mann-Kendall趋势检验、小波分析以及R/S分析等多种方法,探讨了东江流域径流年际变化特征及其对气候变化以及植被覆盖变化的响应。结果表明:①50 a来流域年径流序列变化趋势不明显,存在4 a、7~9 a、11~13 a、16~22 a等4类尺度的周期性变化规律;河源、岭下站径流序列具有较强的状态持续性,博罗站持续性很小。②厄尔尼诺现象出现的当年,东江流域年径流量普遍减少;厄尔尼诺现象出现的次年,年径流量普遍增加。太阳黑子数的急剧变化,与东江径流量的丰、枯也有良好的响应关系。③50 a来,在降雨量呈不显著减少趋势的背景下,河源、岭下站径流仍然呈不显著增加趋势的主要原因是蒸发量下降的缘故,是气候因素和流域植被退化共同作用的结果。     

Evaluation of the relationship between two different methods for enumeration fecal indicator bacteria： Colony-forming unit and most probable number

Most probable number (MPN) and colony-forming unit (CFU) estimates of fecal indicator bacteria (FIB) concentration are common measures of water quality in aquatic environments. Thus, FIB intensively monitored in Yeongsan Watershed in an attempt to compare two di erent methods and to develop a statistical model to convert from CFU to MPN estimates or vice versa. As a result, the significant di erence was found in the MPN and CFU estimates. The enumerated Escherichia coli concentrations in MPN are greater than those in CFU, except for the measurement in winter. Especially in fall, E. coli concentrations in MPN are one order of magnitude greater than that in CFU. Contrarily, enterococci bacteria in MPN are lower than those in CFU. However, in general, a strongly positive relationship are found between MPN and CFU estimates. Therefore, the statistical models were developed, and showed the reasonable converting FIB concentrations from CFU estimates to MPN estimates. We expect this study will provide preliminary information towards future research on whether di erent analysis methods may result in di erent water quality standard violation frequencies for the same water sample.