极限集

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

By getting Lebesgue characteristic of integrable function of Riemann from the definition of Gather zero measure, discussing the relation between almost continuous everywhere and existent of limit, it gets the theory which is from the function integrability to the consecution and from consecution to the limit existence .i.e. the almost limit existence is equal to the almost continuous everywhere in the integrable function of Riemann. It also gets a unified condition which has a wider range than regulated function and comes to the conclusion that the function of bounded variation is the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征，讨论了其几乎处处连续与极限存在的关系，从而得到了从函数可积性到连续性，从连续性到极限存在性的函数特性理论，即可积函数中极限的几乎处处存在与几乎处处连续是等价的，得出比正规函数更加宽泛的统一条件，得出了有界变差函数是可积函数的结论。

On this basis, we give the characterization of the compact set in E〓,τ

引入了模糊数网的最终等度左连续概念，利用它得到了模糊数序列在水平收敛意义下存在极限的一个充要条件，在此基础上给出了空间E〓，τ(l中紧集的特征刻画，即空间E〓，τ(l中的闭集U是紧的当且仅当U一致支集有界，且U的每个网有在（0，1上最终等度左连续、在λ=0处最终等度右连续的子网。

By getting Lebesgue characteristic of integrable function of Riemann from the definition of gather zero measure, it discusses the relation between almost continuous everywhere and existent of limit, and gets that the almost continuous everywhere is equal to the almost limit existence everywhere in the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征，讨论了其几乎处处连续与极限存在的关系，即可积函数中几乎处处连续与极限的几乎处处存在是等价的，得出了比正规函数更加广泛的统一条件，得出了有界变差函数是可积函数的结论。

LetJbe a continuous map of a unit square into itself and f can be descendent. This paperpresents slecific featrue for f with homochinic points.

设f是可降的二维自映射，本文给出了这类自映射有异状点的特征──存在f的链回归点，但不是周期点，并且f的队极限点集与周期点集的交非空。

We firstly discuss minimal sets characterizations of closed-set lattice , then systematically study the categorical properties of categories CL and PairCL by the means of the join-semilattices closed-set-latticefies, and the constructions of monomorphism, epimor-phism, extremal monomorphism, extremal epimorphism, section, retraction, subob-ject, quotient object, product, co-product, equalizer, coequalizer, inverse limits and direct limits in the categories CL and PairCL are given.

首先讨论了闭集格的极小集刻划，然后通过并半格的闭集格化这种方法，较为系统地研究了范畴CL及范畴PairCL的性质，给出了范畴CL和范畴PairCL的单态射、满态射、极端单态射、极端满态射、截节、收缩、子对象、商对象、极端子对象、极端商对象等特殊态射和特殊对象的具体刻划，并且研究了它们的等化子和余等化子、乘积和余积、逆极限和定向极限的具体构造。

We firstly discuss minimal sets characterizations of closed-set lattice , then systematically study the categorical properties of categories CL and PairCL by the means of the join-semilattice's closed-set-latticefies, and the constructions of monomorphism, epimor-phism, extremal monomorphism, extremal epimorphism, section, retraction, subob-ject, quotient object, product, co-product, equalizer, coequalizer, inverse limits and direct limits in the categories CL and PairCL are given.

首先讨论了闭集格的极小集刻划，然后通过并半格的闭集格化这种方法，较为系统地研究了范畴CL及范畴PairCL的性质，给出了范畴CL和范畴PairCL的单态射、满态射、极端单态射、极端满态射、截节、收缩、子对象、商对象、极端子对象、极端商对象等特殊态射和特殊对象的具体刻划，并且研究了它们的等化子和余等化子、乘积和余积、逆极限和定向极限的具体构造。

This course mainly contents real number muster and function, limit of number sequence, limit of function, continuity, derived number and differential, differential mean value theorem and its application, completeness of real number, integral, series(including positive series and Fourier series), multiple- differential, double integral, integral with parameter, curve integral, camber integral and so on.

理解和掌握《数学分析》的概念、理论和方法，对于学生加深理解数学的基本思想和方法，培养抽象思维能力和逻辑思维能力，提高数学素养具有重要的意义。主要内容包括：实数集和函数，数列极限，函数极限，连续性，导数和微分，微分中值定理及其应用，实数完备性，积分、级数(包括幂级数、Fourier级数)、多元微分学、重积分、含参变量积分、曲线积分、曲面积分等。

In this paper,the definition modes of Lebesgue integral of non-negative measurable functions are studied by the way of cutting defining and valued rids,approaching with simple function series.The four definitions of Lebesgue integral of non-negative measurable functions are given.Furthermore,their e- quivalence properties are proved by elementary knowledge.

文献〔1」利用非负可测函数在Ef镇司上积分的极限定义了f在有界可测集E上的L积分；文献[2」利用非负递增简单函数列积分的极限定义了非负可测函数的L积分；文献[3]给出了L积分的一种统一定义；文献〔4一6〕分别证明了测度

Firstly, some basic properties of the limit shadowing are given; Secondly, we give the characterization of both lin-ear automorphisms and linear flows on R~ with the limit shadowing property; Thirdly, as applications we prove that the hyperbolic endomorphisms on T~ have the limit shadowing properties, Smale "horseshoes" have the same prop-...

首先，给出了极限跟踪性的一些基本性质；其次，得到了n维欧氏空间上线性自同构及线性流具有极限跟踪性的特征；最后，作为应用证明了双曲环面自同态以及Smale&马蹄&在其不变集上具有极限跟踪性。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。