充要条件；[数] 充分必要条件
We discuss the properties of an interval judgment matrix with transitivity and propose a sufficient and necessary condition that a consistent interval judgment matrix is of transitivity.
讨论了具有序传递性的区间数判断矩阵的性质，给出了一致性区间数判断矩阵具有序传递性的一个充要条件。
The sufficient and necessary condition of controllability and reachability of a class of linear switching systems which has the same systematic matrix and different input matrixes is given.
给出一类线性切换系统能控性、能达性的充分必要条件，此类系统的特征是具有相同的系统矩阵和不同的输入矩阵。
Moreover, a judgement condition for live and bound WAC net system is given, and the sufficient and necessary condition for WAC net liveness monotonicity is shown.
同时，提出了活的有界的WAC网系统的判定条件，进而给出了WAC网活性满足单调性的充分必要条件。
The paper proposed a sufficient and necessary condition for the problem to admit an exact penalty function approach.
给出了这类双层规划具有恰当罚函数的充要条件，以及这类问题的解的一些性质。
At the same time, a new proof is given for the sufficient and necessary condition of the SOR method applied to symmetric and positive definite system.
进一步丰富了SOR理论，同时给出了SOR方法在对称正定条件下收敛的充要条件的又一新证明。
This paper present a sufficient and necessary condition of constructing quintic PH curves and analyze the geometric meaning of the control polygon.
本文给出了构成五次PH曲线的充要条件，分析了其控制多边形的几何意义。
This paper deals with the system of linear equations with matrix variables and gives the sufficient and necessary condition of consistency.
本文讨论以矩阵为变量的线性方程组，给出相容性的充要条件。
In this paper, we introduce the concept of the weak efficiency. Some of its properties are discussed and a sufficient and necessary condition of the weak efficiency is obtained.
本文引入生产技术的弱有效性概念，讨论了它的若干性质，得出一个弱有效性的充要条件。
A sufficient and necessary condition in terms of the compactness of super-distance space is given based on the property of super-distance space and the related theory of compactness.
利用超距空间的基本性质及拓扑空间紧致性的相关理论，给出超距空间为紧致空间的充分且必要条件，并讨论了一些相关性质。
The sufficient and necessary condition for complete inertial force balancing of open-chain spatial linkages is derived and the concept of relative balancing is presented in this paper.
本文导出空间开链型机构惯性力完全平衡的充分必要条件，提出相对平衡的概念。
Meanwhile, the sufficient and necessary condition for the orientation of an arbitrary ****** polygon is given.
同时，给出了任意简单多边形走向的充要条件。
This paper gives the concept and some properties of partition symmetric anti-circulate matrix, and the sufficient and necessary condition is discussed.
给出了分块对称反循环矩阵的概念，讨论了分块对称反循环矩阵的性质，给出了分块对称反循环矩阵的若干充分必要条件。
After a sufficient and necessary condition of phase interferometer unambiguous direction finding is proved, two methods of ambiguity resolution by combination of long baselines are presented.
在证明了多基线的相位干涉仪不产生测向模糊的充要条件后，讨论了两种用长基线组合解测向模糊的算法。
Finally, a sufficient and necessary condition of the diagonalizable block compound matrices is proved.
最后让明了块复合矩阵可对角化的一个充要条件。
The sufficient and necessary condition of approximation order is obtained by studying M - band multiscaling functions in frequency domain.
就M带多小波的多尺度函数逼近阶在频域里进行研究，给出了M带多尺度函数具有逼近阶m的频域充要条件。
The present paper deals with the sufficient and necessary condition of the final positive solutions of non-linear partial-difference equations and first presents the comparison theorem.
建立关于具有连续变量非线性偏差分方程存在最终正解的充要条件。
In this paper, we give sufficient and necessary condition and some sufficient conditions of oscillate for neutral differential equations with piecewise constant argument.
研究了一类具有分段常数变元的中立型微分方程组的振动性，并给出了所有解振动的充分必要条件和若干充分条件。
A sufficient and necessary condition is given that the algebraic immunity of a Boolean function is not more than a fixed value.
借助覆盖向量刻画了代数免疫布尔函数的特征，给出布尔函数代数免疫不大于某确定值的充要条件。
We use the global bifurcation result of compact operators to get a sufficient and necessary condition for the existence of positive periodic solutions.
利用紧算子的全局分歧结果给出了这个方程正周期解存在的充分必要条件。
The sufficient and necessary condition of possession justice is the both justice of acquirement and transfer.
持有正义的充要条件是获取与转让同时是正义的。
Besides, this paper gives a sufficient and necessary condition of the existence of normal process under the strictly nonnegative definiteness condition.
此外本文还给出了严格非负定条件下实正态过程存在的一个充要条件。
In this paper, we obtain the sufficient and necessary condition for the stability by two-dimensional random walk approach.
本文用二维随机游动方法得到了其稳定性的充分必要条件。
In this paper, we present a discriminating criterion of continuous stack filters, then obtain a sufficient and necessary condition for the equivalence of two weighted threshold filters.
本文给出了连续层叠滤波的判别准则，继而得到了两个加权阈值滤波相等的充要条件。
在逻辑学和数学领域中，“充分且必要条件”（sufficient and necessary condition）是一个核心概念，用于描述两个命题之间的严格等价关系。以下从定义、实例与应用场景三方面展开说明：
1. 定义与解析
2. 形式化表达
充要条件可表示为：
$$
A text{ 是 } B text{ 的充要条件} iff (A Rightarrow B) land (B Rightarrow A)
$$
这一关系在数学证明中广泛用于定理的等价性描述，例如“三角形三边相等”与“三角形三个角均为60度”互为充要条件。
3. 实际应用
在计算机科学中，充要条件用于算法设计的条件判断；在工程学中，则用于系统稳定性分析，例如“特征根实部全为负”是“线性系统稳定”的充要条件（参考：IEEE Control Systems Society）。
"Sufficient and necessary condition"（充分且必要条件）是逻辑学和数学中的重要概念，用于描述两个命题之间的严格等价关系。以下为详细解释：
充分条件（Sufficient Condition）
必要条件（Necessary Condition）
充分且必要条件（Sufficient and Necessary Condition）
数学表达式对比： $$ begin{aligned} text{充分条件} & : A Rightarrow B text{必要条件} & : B Rightarrow A text{充要条件} & : A Leftrightarrow B end{aligned} $$
应用场景：常见于定理证明（如几何定理）、算法条件判断（如循环终止条件）和逻辑推理中。例如在证明充要性时，需要分别验证充分性（A→B）和必要性（B→A）。
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