数学概论讲演（1943～2004）

本书作者B．埃克曼是瑞士当代著名数学家，以研究拓扑、微分几何、同调代数和群论而著称。他毕业于瑞士苏黎世著名学府EHT（联邦技术学院），后来曾在瑞士洛桑大学及美国普林斯顿高等研究所任教和从事科研工作，1948年起任EHT的数学教授，     

Wavelet Numerical Solutions for Weakly Singular Fredholm Integral Equations of the Second Kind

Daubechies interval wavelet is used to solve numerically weakly singular Fredholm integral equations of the second kind. Utilizing the orthogonality of the wavelet basis,the integral equation is reduced into a linear system of equations. The vanishing moments of the wavelet make the wavelet coefficient matrices sparse,while the continuity of the derivative functions of basis overcomes naturally the singular problem of the integral solution. The uniform convergence of the approximate solution by the wavelet method is proved and the error bound is given. Finally,numerical example is presented to show the application of the wavelet method.     

Excitatory effect of histamine on neuronal activity of rat cerebellar fastigial nucleus Jn vitro

The cerebellar fastigial nucleus （FN） holds an important role in motor control and body balance. Previous studies have revealed that the nucleus is innervated by direct hypothalamocerebellar hletaminergic fibers. However, the functional role of histaminergic projection in cerebellar FN has never been established. In this study, we investigated the effect of histamine on neuronal firing of cerebellar FN by using slice preparations. Sixty-five FN cells were recorded from 47 cerebellar slices, and a vast majority of the cells responded to histamine stimulation with an excitatory response （58/65, 89.2%）. Perfusing slices with low-Ca^2＋/high-Mg^2＋ medium did not block the histamine-induced excitation （n=10）, supporting a direct postsynaptic action of histamine on the cells. Furthermore, the excitatory effect of histamine on FN neurons was not blocked by selective histamine H1 receptor antagonist triprolidine （n=15） or chlorpheniramine （n=10）, but was effectively suppressed by ranitidine （n=15）, a highly selective histamine H2 receptor antagonist. On the other hand, highly selective histamine H2 receptor agonist dimaprit （n=20） instead of histamine HI receptor agonist 2-pyridylethylamine （n=16） mimicked the excitatory effect of histamine on FN neurons. The dimaprit-induced FN neuronal excitation was effectively antagonized by selective histamine H2 receptor antagonist ranitidine （n=13） but not influenced by selective histamine H1 receptor antagonist triprolidine （n=15）. These results demonstrate that histamine excites cerebellar FN cells via the histamine H2 receptor mechanism and suggest that the hypothalamocerebellar histaminergic fibers may modulate cerebellar FN-mediated sensorimotor integration through their excitatory innervations on FN neurons.     

Mechanism of the interaction between Au nanoparticles and polymerase in nanoparticle PCR

Nanoparticle PCR is a novel method to optimize DNA amplification. It performs well in improving specificity, enhancing sensitivity and speed. Several mechanisms were proposed in previous studies: one was based on the interaction between gold nanoparticles (AuNPs) and DNA while the other was attributed to the heat transfer property of AuNPs. In this paper, we propose that the interaction between AuNPs and DNA polymerase can significantly influence PCR. First, the addition of DNA polymerase can eliminate the inhibitory effects of excess AuNPs. Second, the addition of AuNPs will increase yield of the desired PCR product and make the optimum concentration of DNA polymerase move to higher value. Third, while excess polymerase might inhibit amplification efficiency, AuNPs can reverse this process and the yield of PCR amplification. Based on these results we propose a possible mechanism that AuNPs might modulate the activity of polymerase and improve PCR amplification.     

ε不敏感损失函数支持向量机分类性能研究

将原先用于支持向量回归的ε不敏感损失函数引入到支持向量分类中,提出ε不敏感损失函数支持向量分类算法(-εSVC).同标准支持向量分类方法(C-SVC)和最小二乘支持向量分类方法(LS-SVC)相比较,试验结果表明:当赋予参数ε一个足够大的接近于1的值时,-εSVC的分类正确率略低于C-SVC和LS-SVC,但是-εSVC的训练、测试和参数选择的速度要高于C-SVC和LS-SVC.特别是对于大规模数据集,这种优势将更加明显.另外,通过精确选择参数ε的值,-εSVC能够获得比C-SVC和LS-SVC更高的分类正确率,但是训练、测试和参数选择的速度却随着ε的减小而降低.     

色多项式与图的着色性

1912年Birkhoff为解决著名的四色问题首次引进色多项式的概念，1932年Whitney进一步将此概念扩充到任意图上，并建立了一些基本结果，其后关于色多项式的研究深入开展积累了许多成果，并产生不少新课题，成为图论中一个热门研究领域。本书系统全面总结了基本成果，是第一本关于这个主题的专著。     

豆科锦鸡儿属云南锦鸡儿(Caragana franchetiana)染色体数目及核型研究

采取常规根尖压片法首次对豆科锦鸡儿属云南锦鸡儿进行了染色体数目和核型的分析统计。结果表明,云南锦鸡儿(Caragana franchetiana)为二倍体植物。其染色体数目2n=16,8对均为中部着丝粒染色体。核型公式为2n=2x=16=8m。最长染色体与最短染色体的长度比为1.2,臂比大于2的百分比为0,核型类别属于1A型,为较对称核型。没有观察到带随体的染色体。     

农民大规模转移中其子女义务教育经费保障机制研究

在工业化、城镇化进程中,农民大规模转移到城市,给进城农民在生产安置、经济收入、住房建设以及子女教育等方面带来了一系列问题。进城农民工子女的义务教育具有跨行政区域、准公共产品的属性,本文通过分析现行的农民工子女义务教育经费的政策设计不完善,区县经费责任不合理、公办学校自由裁量权过大和效果不理想等问题,提出在继续推动户籍制度改革背景下建立国家主导、流入地和流出地共同分担的经费负担体制,探索调整现有义务教育格局,合理配置国有公共教育资源,完善社会捐赠机制,多渠道筹措教育经费等相关对策及建议。     

生物模板法一步合成纳米金属磷酸盐

利用活体洋葱内表皮模板,在常温常压温和条件下,不利用任何表面活性剂和还原剂,以Zn(NO3)2、Na3PO4为原料,一步合成金属纳米磷酸锌.在相同条件下,选择不同的阳离子,制备出磷酸铅、磷酸铋和磷酸银等金属磷酸盐微/纳米材料,并研究了它们的性质.     

猪背最长肌PPARγ2基因Bsr1位点多态性与肉质关系的研究

采用RT-PCR、PCR-RFLP及测序技术,对山猪等背最长肌(LD)的品质及PPARγ2基因表达量和第一启动子Bsr1位点多态性进行研究.结果表明,LD上PPARγ2基因表达量较低,且与肌内脂肪(IMF)呈弱相关(R=0.22).对PPARγ2 Bsr1位点多态性研究发现,该位点可产生G/A突变,形成b、Bb和B型3种基因型.山猪LD PPARγ2 Bsr1位点包含3种基因型,二元杂交后b型比例下降,三元杂交会出现b型缺失.同时发现,长白和大约克LD b型不表达,长白猪仅有B型,而申农1号除B型外Bb型高表达,提示瘦肉猪定向选育过程中可能会使b型逐渐丢失或表达关闭,从而不利于脂肪细胞的增生.以PPARγ2基因型为主效因素与肉质性状拟合建立GLM模型,不同基因型间猪LD剪切力和IMF存在显著差异(P<0.05).b型的高表达有利于脂肪细胞分化和增生,故可维系较高的IMF和较好的肌肉嫩度,提示其可作为优质肉的目标基因.