Clifford分析中κ-双正则函数的一些性质(英文)

k-双正则函数是双正则函数的推广。尽管许多k-双正则函数不是双正则函数,双正则函数的许多性质可以推广到k-双正则函数。本文研究了k-双正则函数的一些性质,包括Cauchy-Pompeiu公式,高阶Cauchy积分公式,平均值定理和级数的收敛定理。     

加权正则函数的一些性质

正则函数是Clifford分析中的一类重要函数,加权正则函数是正则函数的进一步发展,也是一类重要的函数,因此具有一定的研究意义.在正则函数的研究基础上,并利用加权正则函数自身的性质,讨论了加权正则函数的平均值定理,最大模原理,Weierstrass定理以及一些其它推论.     

k-超正则函数及其相关函数的性质

给出了k -超正则函数的开拓定理和唯一性定理,由唯一性定理证明了超正则函数列的内闭一致收敛性; 由k -超正则函数的P 部和Q 部满足的两个微分方程,讨论了此方程与k -超正则函数及其相关函数的关系.     

Clifford分析中双正则函数的Taylor展式及其性质

首先借助实Clifford分析中双正则函数的累次积分的换序公式,给出了双正则函数的Cauchy积分公式,然后由特征边界的Cauchy积分公式,得到了双正则函数的Taylor展式,并由此给出了双正则函数的唯一性定理,柯西不等式和Weierstrass定理.     

一种改进的Heaviside函数与Dirac函数的C-V图像分割研究

C-V模型中Heaviside函数和Dirac函数正则化逼近影响对目标图像的分割,根据Heaviside函数和Dirac函数的性质,提出了新的正则化Heaviside函数和Dirac函数.首先分析了C-V模型中正则化的Heaviside函数和Dirac函数在图像分割中所起的作用,在此基础上提出了新的正则化的Heaviside函数和Dirac函数,改进了C-V模型.实验结果表明,运用正则化的Heaviside函数和Dirac函数的图像分割效果较好.     

函数的次微分连续性与邻近正则性

研究了函数和集在某点的邻近正则性与次微分连续性,给出邻近正则函数的次微分在某种意义下的单调性及函数的邻近正则性与其上图的邻近正则性的关系．     

基于改进的变分水平集C-V图像分割模型研究

为解决C-V模型中弱边缘或边缘模糊图像分割问题,提出了用边缘停止函数代替正则化Dirac函数的C-V图像分割模型.首先对正则化Heaviside函数和正则化Dirac函数中的参数进行了讨论,然后利用图像边缘信息将梯度算子引入正则化Driac函数中,对C-V模型进行改进,最后,用边缘停止函数代替C-V模型中的正则化Dirac函数.实验结果显示,提出的模型比C-V模型对图像的分割效果更好.     

复Clifford分析中几类函数的等价描述

第一部分借助黄沙老师拟置换的思想,得到了复正则函数,复超正则函数的等价条件,定义了复超调和函数并讨论了它的等价条件,第二部分讨论了复超正则函数的若干性质.     

Clifford分析中广义超正则函数的一个非线性边值问题

讨论了Cliffrd分析中广义超正则函数的一个非线性边值问题.首先将广义超正则函数分解为两个奇异积分算子,然后给出了广义超正则函数的Plemelj公式及相关奇异积分算子的性质,最后利用Schauder不动点原理证明了广义超正则函数的一个非线性边值问题的解的存在性及积分表达式.     

实Clifford分析中超正则函数列和函数空间的性质

定义了实Clifford分析中超正则函数列的一致有界、内闭一致有界及内闭一致收敛等概念,并讨论了超正则函数列及超正则函数空间的几条性质.     

Rolling in the Higgs model and elliptic functions

Asymptotic methods in nonlinear dynamics such as, for example, the Krylov-Bogoliubov averaging method and the KAM theory are commonly used to improve perturbation theory results in the regime of small oscillations. But for a series of problems in nonlinear dynamics, in particular, for the Higgs equation in field theory, not only the small-oscillation regime but also the rolling regime is of interest. Both slow- and fast-rolling regimes are important in the Friedmann cosmology. We present an asymptotic method for solving the Higgs equation in the rolling regime. We show that to improve the perturbation theory in the rolling regime, expanding a solution known in terms of elliptic functions not in trigonometric functions (as with the averaging method in the small-oscillation regime) but in hyperbolic functions turns out to be effective. We estimate the accuracy of the second approximation. We also investigate the Higgs equation with damping.     

Asymptotic behavior of the correlation coefficients of transverse momenta in the model with string fusion

In the framework of the model with fusion of quark–gluon strings on the transverse lattice, we find the asymptotic behavior of the correlation coefficients between observables in separated rapidity intervals with a high string density in a realistic case with an inhomogeneous distribution of strings in the impact parameter plane. We calculate the asymptotic forms for three types of correlations: between the average transverse momenta of particles with rapidity in these intervals, between the average transverse momentum of particles in one rapidity interval and the multiplicity of particles in another, and also between the multiplicities of charged particles in these intervals. We show that the previously found independence of the asymptotic form of the correlation coefficient between the average transverse momenta from the variance in the number of particles produced in string fragmentation holds only in the case of a uniform distribution of strings in the transverse plane. We also show that the found general expressions for the long-range correlation coefficients in the particular case with a uniform distribution of strings in the transverse plane become the formulas previously obtained by another method applicable only in this simple case.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

On Problems in the Calculus of Variations in Increasingly Elongated Domains

This paper deals with minimization problems in the calculus of variations set in a sequence of domains, the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain constant. The authors study the asymptotic behavior of minimizers in various situations and show that they converge in an appropriate sense toward minimizers of a related energy functional in the constant directions.     

Interpretations of National Curricula: the case of geometry in textbooks from England and Japan

This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13–14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks.     

基于平行DEA模型的我国小学教育资源配置效率分析

小学教育是教育阶段的基础,也是我国强制教育的一部分。但如何在各省份性别比例相差较大的情况下,更加有效的提高各省份小学教育资源配置效率是一个值得思考的问题。为了避免性别带来的影响,可以通过平行结构DEA模型根据学生性别分为两个平行子系统,来衡量我国2012~2018年各省份小学教育的资源配置情况。研究发现大部分省份小学教育资源配置的总系统效率未达到有效边界,仍有需要改进的地方。男学生在小学教育阶段的效率通常优于女学生在小学教育阶段的效率,但随着近些年我国教育体制的日益完善,女学生在小学教育阶段的效率呈上升趋势。此外,我国西部地区的小学教育资源配置效率在一些年份普遍优于东部和中部地区,而中部地区和东部地区小学教育总系统效率相对稳定,西部地区小学教育总系统效率波动较大。     

Nonlinear features in protein circuitry

The noise involved in protein circuit can result in fluctuations in protein concentrations. Then we have explored the effect of such noise on the feedback loop between p53 and its repressor Mdm2, the negative feedback dynamics and oscillatory activities are presented. Recent experimental results show that under certain conditions, the activity of the average protein level of p53 behaves with dampened oscillation in response to DNA damage, and it has non-decaying oscillatory behavior in individual cells, and we show that the dampening is induced by intrinsic noise, namely the uncertainty associated with chemical kinetics in dealing with when and in what order reactions take place in the p53 system. Furthermore, the experimental results are reproduced in this paper.