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A quantified logic of clarity and vagueness is developed, based on the pattern of the G delian system T of modal logic, a clarity operator replacing the necessity operator.

基于哥德尔模式的模态逻辑系统T，本文提出了一种关于清晰性和模糊性的量化逻辑，其中利用清晰性算子来代替必然性算子。

A eugenic evolution strategy genetic algorithm,which integrates random evolution operation and deterministic optimization operation,is adopted in this paper to realize global optimization in high efficiency.

采用优进遗传算法，将确定性与随机性寻优操作相融合，实现了高效全局搜优，它所基于的优进策略包括设计Powell寻优算子、改进交叉算子、自适应地调整交叉率和变异率等。

For the sake of predicting the detection effect of differential operator s,the frequency features of common operators are analyzed from the view point of frequency domain.

为了预测微分算子边缘提取能达到的效果，从频域角度出发，分析了边缘检测中常用微分算子的频谱特性。

Based on traditional Fourier differentiation matrix and some modifications of the original differentiation operator, this paper refers to a new kind of method——staggered-grid Fourier pseudospectral differentiation operator.

本文在传统傅里叶微分矩阵的基础上，对原始微分算子进行改进，引入了错格微分算子的傅里叶伪谱方法。

A comparison with the analytic result for vertical displacement in homogeneous medium demonstrates that the staggered-grid differentiation operator almost achieves as the same accuracy as the analytic method.

在均匀介质中，将错格伪谱微分算子计算的结果和解析解进行比较，结果表明本文算子几乎达到了解析解的精度。

In the second chapter we first present a decomposition of divided difference operators on non-uniform knots.

在本文的第二章我们从差商算子分解的角度出发，首先给出差商算子的细分格式，然后进一步给出了非均匀B样条级数的细分算法。

4 We show that the Dirac operator in an external field has the same essential spectrum as the free Dirac operator provided the potential vanishes at infinity.

在4.3.4节，我们证明了狄拉克算子在外场中有着对应着无穷远处时零势能极限的自由狄拉克算子的相同的本质谱。

In addition, the discrete Euler operator and homotopy operator of order zero are preliminarily studied.

另外，初步研究了离散化的零阶欧拉算子和同伦算子。

Let P be a Markov operator in, and Q any ergodic Markov operator possessing finite invariant measure. In this note a simple and direct proof of the equivalence of the mixing property for Q and the ergodicity for Cardesian product PQ is given.

设P是L上的Markov算子，Q是任一具有有限不变测度并且遍历的Markov算子，在这篇注记中我们给出了P的混和性和Cartesian积P×Q的遍历性相互等价这一结果的直接而简单的证明。

K_ωby a finite sum of finite products of Toeplitz operators on L_α~2, and define the operator L_ω.

K_w表示为有限个Toeputz算子乘积的有限和形式，同时定义了L_a~2(D~n~⊥上的算子L_w。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。