
充要條件;[數] 充分必要條件
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.
讨論了具有序傳遞性的區間數判斷矩陣的性質,給出了一緻性區間數判斷矩陣具有序傳遞性的一個充要條件。
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.
給出一類線性切換系統能控性、能達性的充分必要條件,此類系統的特征是具有相同的系統矩陣和不同的輸入矩陣。
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.
同時,提出了活的有界的WAC網系統的判定條件,進而給出了WAC網活性滿足單調性的充分必要條件。
The paper proposed a sufficient and necessary condition for the problem to admit an exact penalty function approach.
給出了這類雙層規劃具有恰當罰函數的充要條件,以及這類問題的解的一些性質。
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.
進一步豐富了SOR理論,同時給出了SOR方法在對稱正定條件下收斂的充要條件的又一新證明。
This paper present a sufficient and necessary condition of constructing quintic PH curves and analyze the geometric meaning of the control polygon.
本文給出了構成五次PH曲線的充要條件,分析了其控制多邊形的幾何意義。
This paper deals with the system of linear equations with matrix variables and gives the sufficient and necessary condition of consistency.
本文讨論以矩陣為變量的線性方程組,給出相容性的充要條件。
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.
本文引入生産技術的弱有效性概念,讨論了它的若幹性質,得出一個弱有效性的充要條件。
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.
利用超距空間的基本性質及拓撲空間緊緻性的相關理論,給出超距空間為緊緻空間的充分且必要條件,并讨論了一些相關性質。
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.
本文導出空間開鍊型機構慣性力完全平衡的充分必要條件,提出相對平衡的概念。
Meanwhile, the sufficient and necessary condition for the orientation of an arbitrary ****** polygon is given.
同時,給出了任意簡單多邊形走向的充要條件。
This paper gives the concept and some properties of partition symmetric anti-circulate matrix, and the sufficient and necessary condition is discussed.
給出了分塊對稱反循環矩陣的概念,讨論了分塊對稱反循環矩陣的性質,給出了分塊對稱反循環矩陣的若幹充分必要條件。
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.
在證明了多基線的相位幹涉儀不産生測向模糊的充要條件後,讨論了兩種用長基線組合解測向模糊的算法。
Finally, a sufficient and necessary condition of the diagonalizable block compound matrices is proved.
最後讓明了塊複合矩陣可對角化的一個充要條件。
The sufficient and necessary condition of approximation order is obtained by studying M - band multiscaling functions in frequency domain.
就M帶多小波的多尺度函數逼近階在頻域裡進行研究,給出了M帶多尺度函數具有逼近階m的頻域充要條件。
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.
建立關于具有連續變量非線性偏差分方程存在最終正解的充要條件。
In this paper, we give sufficient and necessary condition and some sufficient conditions of oscillate for neutral differential equations with piecewise constant argument.
研究了一類具有分段常數變元的中立型微分方程組的振動性,并給出了所有解振動的充分必要條件和若幹充分條件。
A sufficient and necessary condition is given that the algebraic immunity of a Boolean function is not more than a fixed value.
借助覆蓋向量刻畫了代數免疫布爾函數的特征,給出布爾函數代數免疫不大于某确定值的充要條件。
We use the global bifurcation result of compact operators to get a sufficient and necessary condition for the existence of positive periodic solutions.
利用緊算子的全局分歧結果給出了這個方程正周期解存在的充分必要條件。
The sufficient and necessary condition of possession justice is the both justice of acquirement and transfer.
持有正義的充要條件是獲取與轉讓同時是正義的。
Besides, this paper gives a sufficient and necessary condition of the existence of normal process under the strictly nonnegative definiteness condition.
此外本文還給出了嚴格非負定條件下實正态過程存在的一個充要條件。
In this paper, we obtain the sufficient and necessary condition for the stability by two-dimensional random walk approach.
本文用二維隨機遊動方法得到了其穩定性的充分必要條件。
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.
本文給出了連續層疊濾波的判别準則,繼而得到了兩個加權阈值濾波相等的充要條件。
在邏輯學和數學領域中,“充分且必要條件”(sufficient and necessary condition)是一個核心概念,用于描述兩個命題之間的嚴格等價關系。以下從定義、實例與應用場景三方面展開說明:
1. 定義與解析
2. 形式化表達
充要條件可表示為:
$$
A text{ 是 } B text{ 的充要條件} iff (A Rightarrow B) land (B Rightarrow A)
$$
這一關系在數學證明中廣泛用于定理的等價性描述,例如“三角形三邊相等”與“三角形三個角均為60度”互為充要條件。
3. 實際應用
在計算機科學中,充要條件用于算法設計的條件判斷;在工程學中,則用于系統穩定性分析,例如“特征根實部全為負”是“線性系統穩定”的充要條件(參考:IEEE Control Systems Society)。
"Sufficient and necessary condition"(充分且必要條件)是邏輯學和數學中的重要概念,用于描述兩個命題之間的嚴格等價關系。以下為詳細解釋:
充分條件(Sufficient Condition)
必要條件(Necessary Condition)
充分且必要條件(Sufficient and Necessary Condition)
數學表達式對比: $$ begin{aligned} text{充分條件} & : A Rightarrow B text{必要條件} & : B Rightarrow A text{充要條件} & : A Leftrightarrow B end{aligned} $$
應用場景:常見于定理證明(如幾何定理)、算法條件判斷(如循環終止條件)和邏輯推理中。例如在證明充要性時,需要分别驗證充分性(A→B)和必要性(B→A)。
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