带有凹凸非线性项的Kirchhoff型方程解的多重性

利用集中紧性原理和对偶喷泉定理,研究了一类带有凹凸非线性项的Kirchhoff方程{-(a+b∫Ω|▽u|~2dx )Δu=|u|~4u+μ|u|~(q-2)u x∈Ω u=0 x∈?Ω获得了该方程有无穷多个解.其中Ω为R~3中边界光滑的有界开集,且a,b0,1q 2,μ0.     

渐近半伪压缩映射合成隐迭代序列的强收敛性

参照Banach压缩映照原理,合理引进了一涉及有限族渐近半伪压缩映射的具误差的合成隐迭代序列.在一致凸Banach空间中,研究该合成隐迭代序列的强收敛性,得到了具误差的合成隐迭代序列强收敛于有限族渐近半伪压缩的公共不动点的充要条件.     

基于凸壳的在线单类学习机

传统的基于支持向量机的单类分类器因计算复杂度高而无法满足大规模数据实时处理的需求,在线学习方法为解决该问题提供了一种有效途径.本文在挖掘样本数据在特征空间分布性状的基础上,提出了一种基于凸壳的在线单类学习机(One-class Online Classifier based on Convex Hull,OOCCH).该方法首先使用凸壳的定义选择能代表特征空间中数据分布的凸壳向量对应的原始样本作为训练样本来缩减训练集的规模;其次在分类器在线更新阶段利用凸壳向量动态地调整分类器的训练样本.理论分析证明了OOCCH的有效性,与现有的在线单类分类器的实验比较,OOCCH在训练时间和分类性能方面有显著优势.     

凸函数Steiner对称化的一个等价特征

函数Steiner对称化的经典定义是根据函数水平集的Steiner对称化以及函数的分层表示定义的.给出了强制凸函数Steiner对称化的一个解析表达式,它是经典Steiner对称化的一个等价特征.这个新的定义不依赖于函数水平集的Steiner对称化,而是将定义转化为一维的类似抛物线函数的Steiner对称化,这更有助于函数不等式的证明.函数的Blaschke-Santalo不等式是一个重要的函数形式的仿射等周不等式,它的几何背景是凸体的BlaschkeSantalo不等式.首先利用Steiner对称化的新的定义,证明了对于任意的强制凸函数经过一次Steiner对称化后积分值变小了;然后利用Prekopa-Leindler不等式证明了径向函数的Blaschke-Santalo不等式.由于任何凸函数经过不断的Steiner对称化总可以在Lp范数意义下收敛于它的对称递减重排,而对称递减重排即为径向函数,因此证明了函数形式的Blaschke-Santalo不等式.     

水稻第6染色体短臂谷壳硅含量QTL的分解

报道了水稻谷壳硅含量QTLqHUS6的分解研究。针对前期定位的qHUS-6区域,应用在第6染色体短臂RM587-RM19784区间分离、背景基本纯合的F2:3群体,将qHUS-6分解为2个QTL;其中,qHUS-6-1位于目标区间的上部,qHUS-6-2位于下部。同时,筛选出在目标区间内携带更小杂合片段的3个单株。其中,2株覆盖qHUS-6-1区间,各自交产生了1个F2:3群体,应用这2个群体将qHUS-6-1定位于RM510和RM19417之间约147.0kb的区间内;另1株覆盖qHUS-6-2区间,自交产生了1个F2:3群体,从中挑选出在qHUS-6-2区间具有不同基因型组成的5套F3株系,将qHUS-6-2分解为qHUS-6-2a和qHUS-6-2b,分别位于RM19706-RM19795和RM314-RM19665区间。     

花生壳纤维素提取及半纤维素与木质素脱除工艺探讨

为了获取优质的纤维素,以花生壳为原料,通过对纤维素提取工艺的探讨,确定了既能保持纤维素提取量,又可较多脱除半纤维素和木质素的工艺条件。试验结果表明,在NaOH溶液的质量分数为4%、反应温度为55℃、反应时间为2 h条件下,半纤维素的脱除率为80.67%;在15 g/L NaClO2和31 mL/L乙酸联合处理、处理温度75℃条件下,木质素脱除率为47.29%。提取出的花生壳纤维素含量可达40%以上。说明在此工艺条件下,能够提取出含半纤维素和木质素较少的优质纤维素。     

K-Domain Splicing Factor OsMADS1 Regulates Open Hull Male Sterility in Rice

We identified the rice floral organ development mutant, termed as open hull and male sterile 1(ohms1), from the progeny of the indica restorer line Zhonghui 8015 treated with 60 Co γ-ray irradiation. The ohms1 mutant exhibited an open hull and lemma- and palea-like structure conversion between the anthers and stigma, which resulted in the ohms1 mutant spikelet showing ‘tridentate lemma'. The ohms1 mutant was entirely sterile but had 60%–70% fertile pollen. Genetic analysis and gene mapping showed that ohms1 was controlled by a single recessive gene, and the mutant gene was fine-mapped to a 42-kb interval on the short arm of chromosome 3 between markers KY2 and KY29. Sequence analysis of the four open reading frames in this region revealed that the mutant carried a single nucleotide transformation(A to G) at the last base of the fifth intron, which was likely corresponded to ohms1 phynotype, in an MIKC type MADS-box gene OsMADS1(LOC_Os03g11614). Enzyme digestion and c DNA sequencing further indicated that the variable splicing was responsible for the deletion of the sixth exon in ohms1, but no structural changes in the MADS domain or amino acid frame shifts appeared. Additionally, real-time fluorescent quantitative PCR analysis showed that the OsMADS1 expression level decreased significantly in the ohms1 mutant. The expression levels of rice flowering factors and floral glume development-related genes also changed significantly. These results demonstrate that OsMADS1 may play an important role in rice floral organ development, particularly in floral glume development and floret primordium differentiation.     

A Point Mutation in an F-Box Domain-Containing Protein Is Responsible for Brown Hull Phenotype in Rice

The accumulation of pigments affects the color of rice hulls while only limited information is known about its underlying mechanisms. In the present study, a rice brown hull 6(bh6) mutant was isolated from an ethane methyl sulfonate(EMS)-induced IR64 mutant bank. Brown pigments started to accumulate in bh6 rice hulls after heading and reached a higher level in mature seeds. Some major agronomic traits including panicle length and 1000-grain weight in bh6 were significantly lower than those in its corresponding wild type IR64, while other agronomic traits such as plant height, growth duration and seed-setting rate were largely similar between the two genotypes. The analysis of pigment content showed that the contents of total flavonoids and anthocyanin in bh6 hulls were significantly higher than those in IR64 hulls. Our results showed that the brown hull phenotype in bh6 was controlled by a single recessive gene which locates on the long arm of chromosome 9. Sequencing analysis detected a single base substitution(G/A) at position 1013 of the candidate gene(LOC_Os09g12150) encoding an F-box domain-containing protein(FBX310). Functional complementation experiment using the wild type allele can rescue the phenotype in bh6. Thus, we named this mutated gene as Os FBX310~(bh6), an allele of OsFBX310 functioning as an inhibitor of brown hull. The isolation of Os FBX310~(bh6) and its wild type allele can provide useful experimental materials and will facilitate the studies on revealing the mechanisms of flavonoid metabolism in monocot plants.     

平面上的逆Bonnesen型Minkowski不等式

研究了平面中形如A~2_(K,L)-A_KA_L≤U_(K,L)的Minkowski不等式的上界,即逆Bonnesen-型Minkowski不等式.设K,L是平面中的凸体,其面积分别为A_K,A_L,其中A_(K,L)为两凸体的混合面积,U_(K,L)为与K,L有关的几何不变量.利用平面上给定两凸体的支持函数,构造一类与给定凸体相关的新凸体.通过对新凸体几何性质的讨论,得到了一些新的加强的逆Bonnesen-型Minkowski不等式,并用此类不等式可推出一些已有结果.     

基于元胞自动机理论的紧急人员疏散模拟

基于元胞自动机原理,建立了紧急情况下人群疏散模型,并利用Visual Basic 6.0开发了可视化模拟仿真程序.在疏散模拟的仿真实现中,为了简化算法,使用墙体和障碍物把复杂建筑平面分割成凸多边形区域,然后利用门道把各个凸多边形区域联系起来构成一个整体的疏散平面空间.利用程序对建筑设计方案进行人员疏散模拟,可以找出建筑方案出现严重拥堵现象的临界人数,以论证建筑布局是否符合安全设计要求,并为建筑布局的改进提供参考.