可微的

Key words: partial differential equation; Lewy equation; real analytical; infinitely differential solution; compactly supported set

引用格 式：吴小庆。Lewy方程的无穷可微解。中国科技论文在线精品论文，2010，3(1)：19～27。

According to Liouville's theorem , any bounded complex analytic function defined on the whole complex plane is constant.

如上所述，实或复解析函数均在实变量的意义上无穷可微。

In chapter 4, a kind of multivariate compactly supported infinitely differentiablefunctions is constructed.

第四章我们主要构造了一类具有紧支集的无穷次可微径向函数。

The results of micro-indentation and fracture show that the influence of compressibility can not be ignored.

结果显示在微压痕和断裂问题中可压缩性的影响不可忽略。

The results of micro-indentation andfracture show that the influence of compressibility can not be ignored.

结果显示在微压痕和断裂问题中可压缩性的影响不可忽略。

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。

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 addition, the applications of the directional derivative and differential of the fuzzy mappings from 〓 to Ein convex fuzzy programming, the applications of the fixed point theorems of increasing fuzzymappings in fishery production and the applications of the integral over a directional linesegment of the fuzzy mappings are also studied.

另外，还给出了从〓到〓的模糊映射的方向可导性及可微性在凸模糊优化中的应用、增模糊映射的不动点定理在鱼业生产中的应用及模糊映射在有向线段上积分在获取统计数字方面的应用。

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。

However, to construct a tensor product orthonomal wavelet basis in L〓, 2〓-1 different functions are used. Furthermore, it is concluded that the family, obtained by dilations and translations from this radial wavelet as well as their linear combinations, can constitute an orthonomal basis in L〓. The conclusion is a major breakthrough in multidimensional wavelet analysis.

从而得到：由一个径向小波的伸缩、平移系及其线性组合可以构成n维平方可积函数空间L〓的规范正交基，这个结果将当前利用张量积方法构造n维正交小波基所需要的2〓-1个不同的函数降为仅需要一个径向小波函数，这在理论上是一个重大突破；构造了同时具备局部支撑和无穷次连续可微性质的高维不可分小波的例子，这是不同于I。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。