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Motivated by Baker\'s result, we introduce a functional index‖E‖_∞to prove that if a mapping f which is from a normed space to a normed algebra satisfying‖ab‖=‖a‖‖b‖satisfies that‖E‖_∞is bounded,then either f is bounded or f is exponential.

受到Baker的结论启发，通过引入一个泛函指标‖E‖∞，证明了从赋范空间到满足范数可乘性的赋范代数的映射f，只要满足‖E‖∞是有界的，则f要么是有界的，要么是指数的。

We first introduce the positive real spectrum function and bounded spectrum function then establish the parametrization of the power spectrum by the Levinson polynomials associated with the autocorrelation matrix of the output and bounded spectrum function.

首先引入正实谱函数的和有界谱函数的概念，利用正实函数和有界实函数理论，通过和过程自相关矩阵相关联的Levinson多项式和有界谱函数，建立了功率谱参数化的表达式。

In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.

在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。

We first characterize the groups in which all m∈cdq〓 contain at most 4 prime divisors; and then show the following: if any m∈cdq〓 is nth-power-free then the derived length of solvable group G is bounded by a function f depended only on n; also if cdq〓 has k different p-parts then the p-length of solvable group G is bounded by a function g depended only on k.

首先研究了非线性不可约特征标对应的特征标次数的商至多含有4个素因子的有限群结构。其次，我们证明：若每m∈cdq〓是n次方自由的，则有限可解群G的的导长及p-长都被仅依赖于n的函数所界定；若cdq〓中共有k个两两不同的p-部分，则有限可解群G的p-长能被仅依赖于k的函数所界定。

In the study of the Lagrange stability of impact motion, we give some conditions of the bouncing solution of the asymptotically linear equation which is bounded or unbounded. Outside of a large disc, using the symplectic transformation of the Hamilton system to estimate the iteration of the successor map. Applying the Moser's small twist theorem, we get the invariant curves and then give the proof of the bouncing solutions which is bounded. We will estimate the successor map of the equation directly for proving the unboundedness of the bouncing solutions.

在碰撞运动的Lagrange稳定性的讨论中，给出了渐近线性方程碰撞解有界或无界的条件，在充分大的圆盘外，通过Hamilton系统的辛坐标变换的角度平均来估计后继映射的迭代，应用Moser小扭转定理得到不变曲线从而给出在一定条件下碰撞解有界的证明，碰撞解无界性的证明将采用直接估计后继映射的方法给出。

Since the set of the centres of these balls is finite, it has finite diameter, from which it follows that every totally bounded space is bounded.

因为这些球的中心的集合是有限的，它有有限半径，从而得出所有完全有界空间是有界的。

A sufficient condition is derived to ensure that the switched nonlinear systems are uniformly bounded and uniformly ultimate bounded.

给出了无激励非线性切换系统一致有界和一致最终有界的充分条件。

This article chiefly introduces some results about vector measure and gives an asymptotic martingale which is L1 bounded amart,not-bounded.

主要介绍向量测度中的一些结论，并给出一个渐近鞅是L_1有界渐近鞅而不是有界的。

Taking household\'s land use preference as classification rule, household agent types were divided though classification tree. Different choosing process of current production strategies and theirs probabilities after expiration of GFGP chosen by various types of household agents\' were put forward by experience-weighted attraction model based on bounded -rational approach. Finally, forecasting the results of households\' recultivation behaviour after the expiration of GFGP by scenario analysis method. The results show that relative policies are useful to rectify deviation of households\' bounded-rational behaviours and reinforce outcomes of GFGP.

以农户家庭户主的土地利用选择偏好作为分类依据，采用分类树方法对农户智能体类型进行划分；基于有限理性决策理论，引用经历—权重吸引模型，对农户智能体的目前生产策略决策过程和退耕还林政策期满后农户对不同生产策略的选择概率进行了分析；最后，在ERDAS环境下对退耕还林政策期满后农户的复垦行为进行了情景分析，认为政府制定并实施的相关政策措施对于纠正农户的有限理性行为偏差，维持和巩固退耕还林政策成果具有重要作用。

This paper presents a new analysis method for model reference adaptive control with arbitrary bounded input nonlinearities, which does not require the stability of plants. The plant can have unmodeled dynamics and bounded disturbances.

余文提出了一种分析具有任意非线性输入的模型参考自适应的新方法，它不要求对象是稳定的，允许系统存在未建模动态和有界扰动。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。