可微性

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。

The maximum principle of the optimal control for the stochastic systems described by Zakaj stochastic partial sifferential equationis proved by approximately minimum point theorem of E. Ekeland. The convexity and compactness of the set of control values is not assumed, and it is not necessary for the maximum principle about differentiability in control variables included in drift term of the stoch astic system and the integrand in index functional, and costate process satisfies the stochastic partial ...

在不假便定控制变量取值的集合是凸的和紧的，不要求随机系统的漂移项和指标泛函的被积函数关于控制变量具有可微性的情况下，用E，Ekeland的近似极小点定理证明了Zakai随机偏微分方程描述的随机系统的最优控制的最大值原理，和用很简洁的方法证明了协态过程满足一个随机偏微分方程。

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。

The research content of this project is mainly the study of the differentiability of Lipschitz mapping and its appilications.

本项目以无穷维Banach空间上Lipschitz映射的可微性问题及其应用为主要研究课题。

The example that ultimately drove home the distinction between continuity and differentiability was given by him.

最终讲明白连续性和可微性之间的区别的例子是由他给出的。

Finally, we study the eventual differentiability of a C_0-semigroup associated to a waveequation with boundary dissipation.

最后，我们讨论了一类具边界耗散的线性双曲型方程生成的算子半群的最终可微性，并利用这个结果得到了方程的解具有最终正则性以及半群满足谱决定增长条件。

Our results generalize and improve some existing ones because our method abandons the typical assumptions on boundedness, differentiability and monotonicity of activation functions.

由于我们的方法去除了关于激活函数的有界性、可微性和单调性的常用假设，因此我们的结果是某些现有结果的推广和改进。

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。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。