首先引入了Rota-Baxter配对模系统以及弯曲Rota-Baxter配对模系统的概念,并由它们构造了pre-Lie模与树状模.最后,由半单Hopf代数中的积分分别构造了Rota-Baxter配对模系统与弯曲Rota-Baxter配对模系统.

莱布尼兹代数作为李代数的推广,已经发展到很高的水平和阶段.由莱布尼兹代数构造 3-莱布尼兹代数,以及由 3-莱布尼兹代数构造Rota-Baxter算子,是一个非常有意义和重要的课题.

本文主要给出Hopf cotruss的概念及其等价刻画,并建立Hopf cotruss与Hopf cobrace之间的联系.

为了深入了解和探索lincRNA的调控机制,建立了lincRNA高效识别模型,有助于为后续研究提供数据源.依据最小自由能(minimum free energy,MFE)和信噪比(signal-noise ratio,SNR)等特征,并通过特征贡献度大小剔除冗余特征,构建随机森林(random forest,RF)分类模型,有效地识别lincRNAs.经检验,模型的灵敏度、特异性和精确度分别达到94.1％、93.2％和93.7％,高于现有PhyloCSF、LncRNA-ID和CPC方法的各项识别指标.模型在识别过程中表现出较好的鲁棒性,可准确识别lincRNA.

本文主要由Sweedler四维代数及其子代数,构造无穷小Hopf代数及其拟三角结构.

主要由Sweedler四维Hopf代数及其子代数构造了权重为-1的非平凡Rota-Baxter算子.

结合数学分析课程的发展现状,对影响学生数学分析成绩的若干内外因素作抽样问卷调查,将收集的有效数据作SPSS主成分分析和差异性分析等,获取影响学生成绩的主要因素.提出了数学理论与教学软件相结合,充分体现专业特色,适当降低理论难度,增加应用性教学,完善考评制度,实施多元常态化考核等相应的教学改革措施.

[Objective] We identified 16S rRNA genes in genomes of prokaryotes.[Methods] We constructed a 3-layer filtering model based on the three features of GC bases content of the gene sequences,3-base periodicity and Markov chain to recognize the 16S rRNA genes from prokaryotic genomes.[Results] The specificity,sensitivity and Matthews correlation coefficients of the model were 99.58％,91.60％ and 91.49％,respectively.[Conclusion] The results showed that the 16S rRNA genes can be identified efficiently and accurately by using our model.

A sufficient and necessary condition for a Long skew Hopf quasigroup to be a quasidimodule algebra is giv-en,and the relation between the braided Hopf quasigroup and the Yetter-Drinfel’d quasimodule algebra is studied.At the end,the quantization of Long skew Hopf quasigroups is constructed by Harrison 2-cocycle,and the conclusion for a quantized Long skew Hopf quasigroup to be a quasidimodule algebras is proved.

启动子是调节基因表达的重要元件,对其的研究对于阐明基因转录调控机制具有重要意义.作者依据RNA聚合酶Ⅱ启动子序列特性选取高效的特征提取方法,构建了基于粒子群优化的支持向量机(particle swarm optimization-support vector machine,PSO-SVM)新方法,用以识别真核生物基因RNA聚合酶Ⅱ启动子.结合5-折交叉检验方法,得到启动子-外显子、启动子-内含子和启动子-基因间序列的分类准确率分别为97.1％、96.7％和98.8％,其马修斯相关系数分别为0.962、0.934和0.976.结果说明,对比其它启动子识别方法,PSO-SVM方法更能有效地识别真核生物基因启动子.

人类基因启动子识别是医学研究的基本需要.提取DNA序列碱基的PZ曲线特征、二核苷酸空间结构特征、保守信号似然得分,以及K联体似然得分,结合GC含量变化和非均匀指数,构建基于粒子群优化的支持向量机算法来识别人类基因启动子.利用粒子群优化支持向量机参数进行优化避免了人为选择的随机性,并且在分类问题中表现出较好的稳健性.对测试集的10-折交叉检验结果为:敏感性为92％,特异性为91％,马修斯关联系数为0.83.该结果表明,基于粒子群优化的支持向量机算法能有效识别启动子序列.

前体mRNA的剪接是真核基因表达的关键阶段,识别剪接位点对基因表达也起着至关重要的作用.作者用紧邻与非紧邻的位置关联权重矩阵及组成分的多样性增量得到的五维特征向量来表示序列,应用支持向量机对供体位点和受体位点进行识别.采用5-fold交叉检验,得到供体和受体位点的马修斯相关系数分别为0.924和0.947,ROC曲线下面积分别为99.08％和99.54％.与一些传统方法相比,这一方法考虑了位点之间的相关性和序列的生物信息,表现出特征少、精度高等优点.

基因预测是DNA序列分析的一项重要任务,真核生物基因外显子序列的识别是生物信息学中的难点,本研究提出一种基于3-周期性小鼠基因的预测方法.基于碱基幅角的功率谱,使小鼠外显子序列的频谱图具有更显著的3-周期性,且内含子的频谱图更加平稳,从而增大了序列中外显子与内含子的信噪比的区分度,使小鼠基因序列的预测获得更好的效果,在平均值法阈值R2下预测准确率达94.53％;在分布图法阈值R1下,准确率达94.50％,敏感性达99.45％.

The main of this paper is to study the structure of weak Hopf module coalgebras.

In this paper,based on total integral and Hopf Galois theory,we mainly investigative the afRneness criterion for weak Doi-Hopf modules.

Recently certain twisted Lie algebras, so-called Hom-Lie algebras, and their duals have been considered in the literature. In this paper we investigate boundary and quasi-triangular Hom-Lie bialgebras further. In particular, we characterize the quasi-triangularity of boundary Hom-Lie bialgebras in terms of both a certain Hom-Lie algebra morphism and a certain Hom-Lie coalgebra morphism. We also give a necessary and sufficient condition for a given Hom-Lie algebra and a given 2-tensor to admit a coboundary Hom-Lie bialgebra structure. Finally, we generalize the Drinfeld double of a Lie bialgebra to Hom-Lie bialgebras and discuss the dual codouble.

This paper is mainly devoted to a Maschke-type theorem for weak (A,B)-Doi-Hopf modules.

This paper,mainly gives the structure theorem for module coalgebras by a kind of new method,and deletes the condition that the antipode S of the Hopf algebra H is bijective.

The relationship of global dimensions between the H-bimodule algebra A and its twisted smash product A * H is established.