根的存在定理的推广及其应用（英文）

众所周知,在《数学分析》中会遇到连续函数的一个重要定理,即根的存在定理,此定理对方程根的存在性判别起着重要作用.将这方面已有的定理进行推广,并用例题说明其应用情况.     

分次Γ环在升链条件下的性质及其PG根

在Γ环的基础上给出群分次Γ环及分次Γ理想等相关 概念, 得到分次Γ环的某些重要性质. 证明分次情况下的Levitizki定理、 Xie定理和Herstein-Small定理; 并通过定义分次P_G根、 分次WP_G根和分次QPG根, 推广了在Γ环中的相关结论.     

分次Γ环在升链条件下的性质及其PG根

在Γ环的基础上给出群分次Γ环及分次Γ理想等相关 概念, 得到分次Γ环的某些重要性质. 证明分次情况下的Levitizki定理、 Xie定理和Herstein-Small定理; 并通过定义分次P_G根、 分次WP_G根和分次QPG根, 推广了在Γ环中的相关结论.     

整系数多项式有理根的讨论

通过研究多项式的系数来确定整系数多项式的有理根,进而得出整系数多项式的有理根的一个判定定理和根的存在定理.     

对Cayle-Hamilton定理的证明及推广研究

矩阵理论中的Cayle-Hamilton定理,具有重要的理论价值和实用价值.本文利用矩阵的标准形和有关矩阵的乘法运算法则,对Cayle-Hamilton定理提出一种新的简明证法;并在定理证明的基础上,将此定理进行推广,证明以方阵A为根的矩阵多项式的行列式也A以为根.此推论的应用更具广泛性和一般性.     

零点定理及介值定理的推广

在深入分析零点定理及介值定理的基础上,对这两个定理的结论进行了推广,得出两条更广泛的定理,使得零点定理和介值定理分别成为它们的特殊情况.并给出了所得定理在方程根的存在性证明中的应用实例.     

零点定理的活用

高等数学中的零点定理是闭区间上连续函数的一个重要性质，利用它既可以证明方程根的存在性或求根的近似值，即解“等式”问题，又可以解“不等式”问题，本文从生活中谈谈零点定理的几个应用，以达到在数学教育教学中理论与实践相结合的作用。     

关于一道智力题的数学模型

构造数学模型求解一道智力题，利用根的存在定理给出严格的数学证明．     

拉格朗日中值定理的三种用法

拉格朗日中值定理是一个相当重要的定理，我们可以将其应用于证明不等式、求方程根和极限。     

多项式的根对系数连续依赖性的一个简捷证明

“多项式的根对系数连续依赖”定理在微分方程性理论中占重要地位.本文以代数和分析的基本理论为依据证明这个定理,较一般书籍在复变函数儒歇定理之后所给出的证明更为简明,易于掌握.     

Thermoequilibrium statistics for a finite system with energy nonextensivity

A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution functions by regulating λ , and then explore the nontrivial relationship between these functions and energy nonextensivity, as well other system parameters such as system size. A variational entropy function is also derived from these distribution functions.     

方格星虫生物活性成分的研究进展

方格星虫(Sipunculus nudus)是重要的经济类底栖动物,具有重要的食用和药用价值,它含有多种生物活性成分,如多糖、多肽及蛋白质等,具有增加免疫、延缓衰老、抗疲劳等生理功能。本文对方格星虫中生物活性成分的提取分离、纯化、结构分析及药理作用等进行综述,为方格星虫资源的深入研究和开发提供借鉴。     

Polarity for a class of Levy processes

Polar set of Markov processes is an important concept in probabilistic potential theory, but it is not easy to judge the polarity of the sets. In this paper, we give some results which can be easily used to examine the polarity of the sets whenX _t belongs to a special class of Levy processes. We also give a result about polar functions of symmetric stable processes. Biography: Wu Chuan-ju(1974-), Ph. D candidate, research direction: theory and application of stochastic processes.     

Chrestenson spectrum and auto-correlation function of inverse permutations of quick trickle permutations

In this paper, a sufficient and necessary condition of quick trickle permutations is given from the point of inverse permutations. The bridge is built between quick trickle permutations and m-value logic functions. By the methods of the Chrestenson spectrum of m-value logic functions and the auto-correlation function of m-value logic functions to investigate the Chrestenson spectral characteristics and the auto-correlation function charac- teristics of inverse permutations of quick trickle permutations, a determinant arithmetic of quick trickle permutations is given. Using the results, it becomes easy to judge that a permutation is a quick trickle permutation or not by using computer. This gives a new pathway to study constructions and enumerations of quick trickle permutations.     

Localization of muscarinic acetylcholine receptor in plant guard cells

Acetylcholine (ACh), as an important neurotransmitter in animals, also plays a significant role in various kinds of physiological functions in plants. But relatively little is known about its receptors in plants. A green fluorescence BODIPY FL-labeled ABT, which is a high affinity ligand of muscarinic acetylcholine receptor (mAChR), was used to localize mAChR in plant guard cells. InVicia faba L. andPisum sativum L., mAChR was found both on the plasma membrane of guard cells. mAChR may also be distributed on guard cell chloroplast membrane ofVicia faba L. The evidence that mAChR localizes in the guard cells provides a new possible signal transduction pathway in ACh mediated stomata movement.     

Construction of DNA damage response gene pprI functiondeficient and function-complementary mutants in Deinococcus radiodurans

PprI, a DNA damage response factor from the extraordinary radioresistant bacterium Deinococcus radiodurans, plays a central regulatory role in multiple DNA damage repair. In this study, a fusion DNA fragment carrying kanamycin resistance gene with the D. radiodurans groEL promoter was cloned by PCR amplification and reversely inserted into the pprl locus in the genome of the wild-type strain R1. The resultingpprl-deficient strain, designated YR1,was very sensitive to ionizing radiation. Meanwhile, the recombinant DNA fragment was cloned into the shuttle vector pRADZ3, and resulted in plasmid pRADK with kanamycin resistance in D. radiodurans. The fragments containing complete pprl gene and 3‘-terminal deletion pprIΔ were cloned into plasmid pRADK. The resulted plasmids designated pRADKpprI and pRADKpprIΔ were then transformed to YR1. Results show that YR1 carrying pRADKpprI was able to fully restore the extreme radioresistance to the same level as the wild-type D. raiodurans R1, whereas YR1 pRADKpprIΔ failed to do so. Construction of DNA repair switch PprI function-deficient and function-complementary mutants in D. radiodurans is not only useful to elucidating the relationship between domains and functions of PprI protein, but also opens the door to the further studies of the biological functions of PprI protein in vivo.     

A class of rotation symmetric Boolean functions with optimum algebraic immunity

For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.     

强混合序列下非参回归函数加权核估计的强收敛速度

在误差项为强混合序列的条件下,利用随机变量部分和的矩不等式,讨论非参回归函数加权核估计的强相合性,给出其收敛速度.当样本矩足够大时,强相合的收敛速度约等于n-1/2.     

The properties of meromorphic functions of several complex variables

In this paper, by using the normality criteria forK-quasimeromorphic mapping of several complex variables, we get a normality criteria for families of holomorphic functions and of meromorphic functions family. Supported in part by the National Natural Science Foundation of China Zhou Zehua: born in 1964, Ph. D     

A new class of harmonic univalent functions by the generalized Salagean operator

A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.