有界函数

Different from the former study, the value region of projective operator in the neural network which they study was a general dosed convex subset of n demensional Euclidean space and it wasn＇ t a compact convex set in general, that is, the value region of projective operator was probably unbounded.

与以前研究投影算子的值域一般是n维欧氏空间中的紧凸子集不同，而是n维欧氏空间中未必有界的闭凸子集，同时目标函数也是一般的连续可微函数，未必为凸函数。

Property 2 Let be a continuous function of several variables on a closed region D, then can obtain any number between its absolute maximum M and its absolute minimum m.

性质2在有界闭区域D上的多元连续函数，必定在D上取得界于最大值M与最小值m之间的任何值。

Based on Lyapunov stability theory, a kind of bounded robust controller is develowd by introducing hyperbolic tangent functions plus proper auxiliary ones into constructed storage function.

基于李雅普诺夫稳定性理论，通过在构造存储函数的过程中引入双曲正切函数和适当的辅助函数，设计了一种有界的鲁棒控制器。

Compared with deterministic systems, the infinitesimal generator for the system is a second-order differential operation. In this dissertation, we designed the quartic control Lyapunov function and systematically design the state-feedback and output feedback adaptive controller using integrator backstepping methodology. The closed-loop system is asymptotically stable in the large.

与确定性系统相比，随机系统的Lyapunov函数的微分运算包含二阶导，所以设计适当形式的控制Lyapunov函数十分关键，本文设计了四次型的控制Lyapunov函数，并应用积分反推技术，给出了状态反馈及输出反馈自适应控制器和鲁棒自适应控制器的设计方法，证明了闭环系统概率意义下的渐近稳定性和有界稳定性。

The growth of functions in these spaces depends on a weighted function ρ. We investigate the relation between growth and boundary values of the functions, and prove that a function or its radial derivative is in one of the spaces if and only if the p'integral average of the difference of its boundary value function is integrable or bounded.

研究这些函数空间中函数的增长性与边界值的关系，得到了函数或其径向导数属于相应空间的充分必要条件是其边界值差分的p次积分平均应具备一定的可积性或有界性。

Thirdly, the problems of institution investor'optimal liquidation strategy and optimal liquidation time were investigated with the conditions that the price of risky asset followed arithmetic Brown motion and liquidation velocity was limited. The problems involved the following scenes: price impact function was linear expression of liquidation velocity which was boundary closed set with an isolated point; price impact function was stochastic; price impact function was nonlinear.

接着，当风险资产的价格服从算术布朗运动，且对投资者的变现速度做出限制时，研究机构投资者的最优变现策略和最优变现时间问题，其中包括：价格冲击函数为变现速度的线性函数，变现速度是一带有孤立点的有界闭集；价格冲击是随机形式；价格冲击是变现速度的非线性函数。

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

Each generator offers a piecewise linear supply function, within his capacity of generation, into the market and wishes to maximize his expected profit.

当电力市场需求函数表示为市场价格与有界随机需求冲击的非线性函数时，每个发电商在其发电容量范围内向电力市场提交一个分段线性供应函数，以获取最大化利润。

If theharmonic index is finite,then each end may be represented by a non-constant positiveharmonic function,and these functions compose a partition of unity.For minimalhypersurfaces with finite total scalar curvature,we can explicitly estimate the harmonicindex.Moreover,the space of bounded harmonic functions are exactly generated bythose functions associated to each end.This gives geometric interpretations of the ends.

若调和指标有限，则每个端均可由一非常值的调和函数代表，它们形成了一个单位分解，对于全纯量曲率有限的极小超曲面，我们明确地估计了调和指标，进一步，有界调和函数正好由代表端的那些调和函数所生成，这就给出了端的几何解释。

An Ellipsoidal Basis Function can make the partition of input space and make a limitary and bounded.

椭球基函数（Ellipsoidal Basis Function，EBF）使网络划分输入空间成为封闭有界的局部作用的空间，与径向基函数（Radial Basis Function，RBF）神经网络的高斯函数相比，它对空间的划分更明确。

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 。