查询词典 continuous differentiability

The experiment and the research indicate that:(1) Through the Hot-Continuous-Rolling production technics under small reduction ratio of 4.04 and 5.08, the rectangular continuous-casting billet of 235×265mm can be used to produce big size steel stick of Φ140mm and Φ 125mm whose macrostructure and mechanical properties meet the standards, this technics is viable;(2) This rolling technics can make the deformation penetrate to the center of the billet by low temperture and low velocity and big roller diameter and large reduction quantity at every pass and optimum design and arrangement of rollers, which is the key of Hot-Continuous-Rolling technics under small reduction ratio;(3) The sending technics used in Xining Special Steel Co.,Ltd can not use waste-heat of billet adequately, but the sensitive temperature section of A1N or sulphides or inclusions separating out is avoided, creating a favorablecondition for insuring good surface quality of final rolled steel;(4) The Hot-Continuous-Rolling technics under small reduction ratio has a close relationship with the billet quality control and the hot sending process control and the cooling control after rolling.

通过实验研究表明：(1) 235×265mm矩形连铸坯分别采用4.04和5.08的小压缩比热连轧生产工艺，所生产的Φ140mm和Φ125mm的大规格棒材，其低倍组织和机械性能均符合标准要求，该工艺是可行的；(2)本实验所采取的低温低速、大辊径大道次压下量轧制工艺加上轧辊孔型的优化设计与配置，可以使加工变形渗透到铸坯的中心，这一点是实现小压缩比热连轧生产工艺的关键；(3)西宁特钢在红送过程中虽然铸坯余热未能得到充分的利用，但是有效地避开了A1N、硫化物的析出及夹杂物偏析的敏感温度区，为保证最终轧材良好的表面质量创造了有利的条件；(4)小压缩比热连轧生产与铸坯质量控制，热送过程控制以及轧后冷却控制密不可分。

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。

This article uses the implicit function theorem and the properties of analytic functions,with less limitations for the uniqueness,continuity,continuous differentiability of the implicit functions,and gets the sufficient and necessary conditions of the existence of implicit functions by simplifying them.

从常用隐函数存在性定理出发，放宽对隐函数唯一、连续、连续可微等性质的限制，利用解析函数的性质将其展拓，得到广义隐函数存在的充分必要条件和广义隐函数的分布特征。

Gerber and Shiu (1998a) and Tsai and Willmot (2002) all consider the renewal equation for the expected discounted penalty function at ruin Ф and its decomposition in this risk process. In their proceeding, they assumed the twice continuous differentiability of Ф,Ф〓,Ф〓 as a premise but its proof isn't obvious.

Gerber and Landry（1998）及Tsai andWillmot（2002）考虑了此模型下的破产时罚金折现期望Ф所满足的更新方程及其分解后的因子Ф〓和Ф〓，但它们的推导过程都是在假定Ф，Ф〓，Ф〓连续且二次连续可微的前提条件下进行的，但实际上此前提假定的成立并非显然。

Furthermore, the first-order optimality condition and its equivalent reformulations for generalized semi-infinite max-min programming with a non-compact set are presented using the lower-Hadamard directional derivative and subdifferential.2. Chapter 3 studies the gradient-type methods for unconstrained optimization problems. Section 1 proposes a new class of three-term memory gradient methods. The global convergence property of the method is established. Furthermore, in order to improve the convergence property of the method, a new class of memory gradient projection methods is presented with the property that the whole sequence of iterates converges to a solution to the problem under the conditions such as pseudo-convexity and continuous differentiability of objective function. In section 2, two new classes of methods, called gradient-type method with perturbations and hybrid projection method with perturbations, are proposed. In these methods, non-monotone line search technique is employed, which makes them easily executed in computer.

第3章研究了无约束优化问题的梯度型算法，第1节提出了一类新的三项记忆梯度算法，讨论了算法的全局收敛性，进一步提出了一类新的具有更好收敛性质的记忆梯度投影算法，并证明了该算法在函数伪凸的情况下具有整体收敛性，第2节在非单调步长搜索下提出了带扰动项的梯度型算法及其混合投影算法，这两类算法的一个重要特征就是步长采用线搜索确定而不象许多文献中那样要求步长趋于零，这样更容易在计算机上实现，在较弱的条件下证明了这些算法的全局收敛性，数值算例表明了算法的有效性。

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。

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。

Then the method make every subdomains lubricous and conquer non-differentiability of the problems.2. Through introducing the continuous conditions on internal boundary, a distributed optimal control model is established.

通过区域分解及在内边界上引入连续性条件，将分片光滑分布参数系统的抛物型方程定解问题转化为一个最优控制模型。

Fostering the concept of multi-culture firmly and mastering the development of advanced culture correctly are conductive to resisting terrorism, separatism of nationalities and ultraism of religion, which is of great academic theoretical, immediate and profound historical si...

牢固树立多元文化的理念和正确把握先进文化的发展方向，有助于在世界范围内自觉地抵制恐怖主义，民族分裂主义和宗教极端主义。不仅具有重大的学术理论意义，而且也具有重大的现实意义和深远的历史意义。

But if anyone walks in the night, he stumbles, because the light is not in him.

11：10 若在黑夜行走，就必碰跌，因为那光不在他里面。