连续可微性

This paper investigates the absolute convergence of the Fourier Laplace series concerning of some smooth functions defined on the unit sphere in R n,hereinto shows that:if f is 2([n4]+1) th continuously differentiable function on H r P,then the series ∑∞k=0Y kf converges uniformly to f.

讨论了n 维球面上某些可微函数类的Fourier Laplace级数的绝对收敛性，其中指出：设f是Hrp上 2 ( [n4 ]+1)次连续可微函数，则级数∑∞k =0 Ykf一致收敛到f参

The continuity and differentiability for composite function are the important content in advanced mathematics.

对高等数学中复合函数的连续性条件进行了弱化改进，得到了类似复合函数连续及在x0处极限存在的充分条件，对复合函数的可微性条件进行改进，得到了复合函数可微以及在x0处存在左右导数的充分条件。

In section 2, the integral expression, continuity and twice continuous differentiability and integro-differential equation satisfied by the expected discounted penalty at ruin Ф〓 are derived.

在第二节，我们得到了Ф〓的积分表达，连续性及二次连续可微性和积分-微分方程。

Institute of Statistics and Actuary, Shandong Economic UniversityAbstract We consider the risk process perturbed by diffusion under interest force in this article. The integral expressions, continuities, twice continuous differentiability and integro-differential equations about $F_{\delta}$, the distribution of the surplus immediately before ruin, and $H_{\delta}$, the joint distribution of the surplus immediately before ruin and the deficit at ruin are obtained.

我们考虑既带有随机干扰又带有确定投资回报的风险过程，得到了破产前瞬间盈余的分布$F_{\delta}$及破产前瞬间盈余和破产时赤字的联合分布$H_{\delta}$所满足的积分表达，连续性及二次连续可微性和积分--微分方程。

Chaikin algorithm is the simplest discrete curve modeling method.In thepaper planar Chaikin algorithm is generalized into sphere,and the practicability ofthe algorithm as well as the continuous differentiable property of the generatingcurve is proved.It is shown that the curve generated by Chaikin algorithm is apiecewise spherical Bezier curve of second kind of order two.Furthermore,generalspherical corner-cutting algorithms are discussed,and it is pointed out that thecurve generated through corner-cutting has"Spherical Variation DiminishingProperty".3Curve interpolation method restricted on a smooth surface based ontransformation.

Chaikin算法是最简单的离散曲线造型方法，文中将Chaikin算法推广到球面，证明了算法的可行性和生成曲线的连续可微性，指出球面Chaikin算法得到的曲线是分段的二次第二类球面Bezier曲线，并给出了用球面Chaikin算法构造球面插值曲线的算法；进一步，文中讨论了一般的球面割角算法，指出由球面割角算法得到的曲线具有"球面变差缩减性质"。3基于变换的约束在光滑曲面上的曲线插值方法。

In section 2 of chapter 2, we obtain the integral expression of Ф and prove the twice-continuous differentiability in (0,+∞).

在第三章第二节，我们得到了Ф的积分表达并证明了其二次连续可微性。

In section 3, we take account of Ф〓,Ф〓. Their integral expressions and twice-continuous differentiability are also obtained.

在第三节中，我们考虑Ф〓，Ф〓，它们的积分表达和二次连续可微性也被得到。

And their twice-continuous differentiability are proved.

并且它们的二次连续可微性也得到证明。

Surface blending in terms of geometric continuous is more practical and welcome with view of geometric interpretation which is different to the traditional differential method based on algebra.

几何连续是对参数曲面中参数连续度量进一步深刻的认识和研究。它是可微性的代数概念的几何抽象，克服了参数连续对曲面苛刻，高阶及结果失真等缺点。

The nonlinearity and discrete gradient inherited in CAViaR model is a conundrum for parameter estimation. We take the asymmetric Laplace distribution with scale parameter as the error process; indicate the variance has a minimum positive value when the scale parameter is a constant, conflicting with the distribution of real financial data. Further we estimate the parameters of indirect TARCH-CAViaR model base on Bayesian framework and Markov chain Monte Carlo method. The optimal scale parameter can also be obtained by Markov chain Monte Carlo method.

CAViaR一般模型中递归分位回归方程的非线性和非连续可微性是参数估计的一个难题，基于含有尺度参数的不对称拉普拉斯分布作为误差过程，指出将尺度参数固定为常数会导致不对称拉普拉斯分布随机变量的方差存在最小正值的限制，与实际金融数据分布不符；进而提出采用贝叶斯分析和马尔科夫链蒙特卡罗模拟方法，估计间接TARCH-CAViaR模型的参数，并可获得尺度参数的合理估计。

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。