EXTENDING POMPEIU OPERATOR AND THE COMPACTNESS OF SOLUTION SET FOR A CLASS OF HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS

This paper discusses chiefly the compactness of solution set of following equationswhere △ is the Laplacian in Sobolev’s sense, a;（x）,i= 0,1,…n, n≥ 3, are real square matrices of dimen-sion N×V , bounded and measurable in a bounded multiply connected domain Ω, the boundary S is as-sumed to be sufficiently smooth, u（x） is unknown vector, z = （x1,x2,…,xn） Ω Rz,m≥1,|S1|issuperficial measure of the unit sphere of RZ, |i|=i1+ i2 +… + i., △m=△(△m-1). ,（Ω）, ,（Ω）, … denote the classes of vectors or matrices whose elements belong to L,（Ω）,W,（Ω）,…. A vector or a matrix is said to be continuous differentiable, bounded and measurable if so are its ele-

Genetic Variation and Differentiation of Larix decidua Populations in Swiss Alps

Genetic diversity within and among six subpopulations of Larix decidua Mill. from two altitudinal transects of Swiss Alps was investigated using 6 enzyme systems coding for 8 loci. Globally, the mean proportion of polymorphic loci was 22.9%, the average number of alleles per locus was 1.3, and the mean expected heterozygosity was 0.095. Only 5.8% of the genetic variation resided among populations. The mean genetic distance was 0.006. Several significant differences of gene frequencies were found between different age classes. Positive values of the species mean fixation index observed in this study suggested a considerable deficit of heterozygotes in the populations of L. decidua of Swiss Alps. At one of the sites (Arpette), the highest subpopulation in elevation gave the lowest level of genetic diversity (as evidenced by the lowest proportion of polymorphic loci and the lowest mean expected heterozygosity) and the largest value of genetic distance when compared to other subpopulations. The genetic differences between the highest subpopulation and the other ones suggest that the founder effect may be an important factor influencing genetic differentiation of L. decidua populations at Arpette transect.

LEIBNIZ′FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN′S FUNCTION

In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.

BLOW-UP OF A CLASS OF SEMILINEAR PARABOLIC VARIATIONAL INEQUALITIES

In this paper we study the blow-up behavior for a class of semilinear parabolic variational inequalities;whereK = {u ∈L2（0,T;H01（Ω））|u（x,t）≥ψ（x） a. e. （x,t） ∈Ω×（0,T）, u（x,0） = （x）},andis a uniformly elliptic operator.We prove the following main theorem.Theorem Let u（x,t） be a local solution of problem （I）,u∈C（0,T;H2（Ω）∩H01（Q））,ui∈L2（0,T;L2（Ω））, and following conditions are satisfied.（1） There exists a continuously differentiable function G（x,s） and a positive number α,such

Game analysis of endogenous force in developing cooperatives in the village: A case study

With village elite fl ow as the clues, this study mainly describes the development of the Hongqi village cooperative organization. Through analyzing the fl ow condition in development process of the village elite personnel in the village cooperatives, this paper explores the struggle and cooperation between the developments of cooperatives of endogenous force in rural structure. The study found that under the limited situation of rural elite capacity, as an embedded base village bottom-up formation of cooperatives, the internal forces are constantly in a tension structure, the various forces in the different development period are conversion between the symbiotic and opposition; Combination, differentiation, struggle of various forces within the cooperative are supported by their own wealth, genetic, factional social capital; the splits and realignments of malignant competition forces caused by internal cooperatives are the key power to restrict the development of village cooperatives. The base-level countryside and cooperatives needs limited elite unity and equilibrium of internal forces to obtain effective governance and long-term development.

Discrete Exterior Calculus of Proteins and Their Cohomology

This paper proposes a novel application of cohomology to protein structure analysis. Since proteins interact each other by forming transient protein complexes, their shape (e.g., shape complementarity) plays an important role in their functions. In our mathematical toy models, proteins are represented as a loop of triangles (2D model) or tetrahedra (3D model), where their interactions are defined as fusion of loops. The purpose of this paper is to describe the conditions for loop fusion using the language of cohomology. In particular, this paper uses cohomology to describe the conditions for “allosteric regulation”, which has been attracted attention in safer drug discovery. I hope that this paper will provide a new perspective on the mechanism of allosteric regulation. Advantages of the model include its topological nature. That is, we can deform the shape of loops by deforming the shape of triangles (or tetrahedra) as long as their folded structures are preserved. Another advantage is the simplicity of the “allosteric regulation” mechanism of the model. Furthermore, the effect of the “post-translational modification” can be understood as a resolution of singularities of a flow of triangles (or tetrahedra). No prior knowledge of either protein science, exterior calculus, or cohomology theory is required. The author hopes that this paper will facilitate the interaction between mathematics and protein science.

OSCILLATORY CRITERIA FOR A CLASS OF EVEN ORDER NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATION

In this paper we consider the following nth order nonlinear functional differential equation xn（t）+integral from n=1 to ∞p（t,ξ）f（x（t）,x[g（t,ξ）]）do（ξ）=0（n even,n≧2,b】a） （1） Oscillations of this equation are studied.We make

第二课堂助力常微分方程教学的实践研究

第二课堂是课堂教学的有效拓展.常微分方程课程在教学中存在内容抽象和教学用时不足等问题.开展常微分方程第二课堂有利于拓展教学时间和空间,利用数学实验进行数学求解与数学建模.通过实践发现,常微分第二课堂有利于激发学生的数学思维、数学兴趣和合作能力等.在实践中要注重问题创设、实验条件优化和实验辅助支持等,保证常微分方程第二课堂的顺利实施.

以创新能力为导向的研究性教学模式改革与实践——以高等数学为例

本文将对分课堂和五星教学模式的优势相结合,以一流课程建设为切入点,借助现代信息技术,提出了以创新能力培养为导向的研究性教学方法.并以高等数学中微元法和无穷限积分教学为例,展示了问题驱动+同伴讨论的研究性教学设计.

三孩政策下家庭教育期望及其生育效应

随着经济社会发展和生育观念转变,家庭生育决策进入日益理性化和成本约束的阶段。父母较高的教育期望和激烈的教育竞争影响着家庭生育意愿和行为。通过构建家庭资源约束条件下教育期望、培育策略与生育效应的分析框架,并基于大样本调查数据,考察了教育期望对家庭生育的影响效应。研究发现,家庭教育期望显著提升了生育一孩的概率,但降低了家庭生育二孩的概率,较高的教育期望引致家庭采取“质量替代数量”的生育决策。异质性分析发现,教育期望对不同阶层生育数量和再生育意愿的影响形成分化效应。较高的教育期望显著降低了中低收入阶层家庭二孩和三孩的生育意愿及行为;但在高收入阶层,较高的教育期望并未对家庭二孩和三孩的生育意愿及行为产生挤压效应。进一步研究发现,育龄夫妇受教育程度与家庭教育期望形成替代效应,育龄夫妇受教育程度越低,教育期望对二孩生育的挤压效应越大。机制分析发现,较高的教育期望显著降低了家庭的男孩偏好,说明父母对子女的教育期望越高,越重视孩子的质量而非性别和数量,带来少子化的生育决策。家庭教育期望具有一定程度的不可逆性和不同群体的趋同性,必须降低家庭的养育成本和缓解家庭养育焦虑。通过发展普惠性学前教育和义务教育,提高城乡教育均等化水平,提供多元化的市场养育服务,改善家庭的生育预期,进而提高家庭生育率。

民本班与汉本班学生课堂适应的差异化研究——以新疆工程学院为例

该研究选取新疆工程学院490名学生进行跟踪调查,民本班发放问卷245份,汉本班发放问卷245份。民本班回收问卷243份,问卷有效率为99.2%,汉本班回收问卷240份,问卷有效率为98.0%,符合统计要求。基于490份问卷得到的数据,选出问卷中差异性比较大的题目,对其进一步全面剖析少数民族大学生课堂学习适应的现状。研究表明,一方面,民本班的学生学习兴趣不浓,对待教师和课程不够重视,学生作业质量有待提升。汉本班学生相对于民本班学习态度比较端正,学习过程更具有主动性,自主学习意识强;另一方面,民本班学生相对于汉本班学生缺少学习计划,在学习方法上有所欠缺,但是从民本班学生的实验课程课堂情况来看,民本班学生动手能力强,团队协作能力强。

青花椒雄蕊调控基因ZaPI的克隆、鉴定与表达模式分析

【目的】探究青花椒雄蕊分化关键B类基因及其核酸和蛋白序列特性,并分析其在雌雄花分化过程的表达模式,为青花椒花芽性别分化的遗传调控机制提供候选基因和数据支撑。【方法】基于青花椒转录组和基因组数据库,提取雌雄花分化过程中差异表达的所有B类MADS-box家族基因,并分析获取关键成员;克隆关键成员基因编码序列,全面剖析核酸和蛋白序列特性;并解析其在11种不同组织器官以及雌雄花分化过程的表达模式。【结果】青花椒雌雄花分化过程的差异基因中共有11个B类MADS-box家族基因,其中Zardc17043(ZaPI)的表达量最高,且在雄花中极显著特异表达。该ZaPI编码序列全长624 bp,共编码207个氨基酸,含有77个氨基酸组成的MADS-box结构域和84个氨基酸组成的K-box结构域,蛋白相对分子量为24.29 kD,是位于11号染色体包含4个外显子和3个内含子且定位于细胞核的亲水性蛋白;系统进化分析显示,青花椒ZaPI与同为芸香科(Rutaceae)的克莱门柚(Citrus clementina)和甜橙(Citrus sinensis)亲缘关系最近。此外,青花椒ZaPI基因编码序列共预测到54个转录因子结合位点,主要涉及植物生殖生长和抗逆过程等多种调控途径。顺式作用元件分析发现,ZaPI启动子区富含光信号、植物激素、逆境胁迫等相关的顺式作用元件。同时,该基因在根茎叶刺等营养器官中几乎不表达,雌花分化过程的表达量也相对较低,但在雄花分化过程中呈极显著上调趋势。【结论】研究所获得的ZaPI基因与雄蕊的分化显著相关,可能与植物激素等多种信号分子互作参与了青花椒的雄蕊形成过程。研究所获结果对于进一步探究青花椒雄蕊形成的分子机制,培育高产青花椒种质资源提供了丰富的理论支撑。

教育选择有限理性模型:教育选择阶层分化的两种范式之争及整合路径

关于教育选择阶层分化的机制,长期以来一直存在文化再生产和理性选择两种范式之争。在经验研究中,文化再生产理论占据了相对主导地位。回顾两种理论范式之争的历史,两者争论的焦点在于教育选择阶层分化的机制究竟是理性还是非理性因素占据主导。通过对两种理论范式的优势与缺点进行对比分析发现,单一的理论范式解释力有限,两种理论范式存在整合的可能性和必要性,但目前尚缺乏有效的整合路径。借助西蒙的有限理性模型,可以将两种分析范式整合成更有解释力的教育选择有限理性模型,为具体的经验研究和教育政策的改进提供更有效的理论工具。

基于MGWR模型的大城市房价空间分异特征及影响因素分析——以南京市主城区为例

文章以2022年南京市主城居住小区为基本单元,运用空间自相关和克里金插值分析法对主城区房价的空间分布与分异进行分析与模拟,然后引入住房阶层理论在划分不同居住阶层基础上,分析各阶层间的空间分异特征;最后利用混合地理加权回归模型(MGWR),探究住区属性、区位条件、交通特征和配套设施4类因素对主城区房价空间分异的影响。研究表明:(1)南京市主城区房价整体呈现由主城西向周边区域逐步递减的多组团模式;(2)主城区不同住房阶层表现出“西高东低”的空间集聚特征,阶层间虽未出现明显的空间隔离、对立或极化,但富裕阶层对主城优势资源和环境的剥夺现象显著;(3)各类因素对主城区房价具有差异化影响,其中住区属性的影响较稳定,区位条件的影响具有空间全局性,而交通特征和配套设施的影响则存在显著的空间边界效应,即房价与设施空间距离的负相关性具有空间范围界限。

基于学习通与小班个性化模式常微分方程的教学实践

常微分方程是本科阶段数学专业学生的一门必修课程,被广泛应用于物理、化学、生物、医学等方面,渗透于生活的方方面面。因此学好常微分方程显得尤为重要。将学习通平台与小班化教学相结合的教学模式运用到常微分方程的教学中,充分利用“超星学习通”这一平台,为小班中的每个学生定制个人错题本,针对其易错点,进行“培优补弱”,二者的结合能带来更好的教学效果。

阶层固化感分析:产生、挑战与应对

有研究指出,中国社会流动并不存在阶层固化,然而“阶层固化”却长期、广泛地占据舆论空间。之所以出现这一矛盾现象,主要是因为当前在社会成员中普遍存在一种“阶层固化感”。与已有概念不同,“阶层固化感”直接面对社会成员所感受到的“固化”因素,导致其形成的,既有现实因素,也有历史因素以及舆论渲染因素。这一社会感受的存在会给政治意见表达、政治稳定和政治认同等带来新的挑战。应对这一挑战,既要从经济发展和社会保障的实际出发进行调整,也要注意舆论引导,丰富社会评价标准,释放社会情绪。

基于随机森林的电网GIS数据分布式存储方法

内部电网地理信息系统(Geographic Information Systern,GIS)数据体量增加,对电网数据存储性能造成了极大的困难,为此,提出一种基于随机森林的电网GIS数据分布式存储方法。以跨域资源共享(Cross-Origin Resource Sharing,CORS)技术在电网GIS空间信息服务平台中获取的电网GIS数据为基础,根据类区分度数值选择电网GIS数据特征,引入随机森林算法分类处理电网GIS数据,将其合理分发给不同的服务器,采用并行处理手段存储分类数据,从而实现了电网GIS数据的分布式存储。实验数据显示:应用所提方法后,电网GIS数据分类精度达到了96.8%,电网GIS数据分布式存储时间最小值为5.2 s,充分证实了所提方法数据存储性能更佳。

基于多模式多用户的高速公路差异化收费方案及仿真研究

为探索多样化、精确化的高速公路差异化收费政策,收集山东省交通网络数据,采用TransCAD软件建立复杂路网仿真模型,在传统四阶段法的基础上,使用高速公路和国省道交通流量数据计算得到分配所需的OD矩阵,利用多模式多用户交通分配模型分析实例路段差异化收费前后交通流量的变化情况。以山东省内某高速公路为例,对分路段和分车型2类差异化收费方案进行比较。

Variational Approach for the Adapted Solution of Backw ard Stochastic Differential Equations with Locally Lipschitz Diffusion Coefficients

One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".

Weak WT_2-class of differential forms and weakly A-harmonic tensors

In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.