necessary and sufficient conditions

Based on the pricniple of dividing resistance unit and the equations for calculating the resistance of river bed given by the Einstein,this paper discussed the existence and uniqueness of the solutions of resistance equations and gave the sufficient and essential condition for derivation of the uniquesolation.

根据爱因斯坦划分阻力单元的原理和计算河床和河岸阻力的方程组，从数学的角度上讨论了阻力方程组解的存在性和唯一性，给出了方程组存在唯一解的充分必要条件，即爱因斯坦处理综合阻力的方法，事实上是阻力方程组存在唯一解的充分必要条件，而姜国干处理综合阻力的方法，只有存在ｎ＝ｎｂ＝ｎｗ时，阻力方程组才有解。

By applying the topology theory,the necessary and sufficient condition for the existence and uniqueness of the equilibrium point of GHNN was obtained.

应用拓扑理论,得到了广义Hopfield神经网络平衡点的存在性和唯一性的充分必要条件;利用矩阵的性质,通过构造Lurie型Liapunov函数,得到了广义Hopfield神经网络绝对指数稳定的充分条件以及几类特殊神经网络绝对指数稳定的充分必要条件。

The main results are: if A=(a_(ij))_(3×3), Reλ(A)<0, and c~Tb·trA~2-c~TA~2b≤0, the necessary and sufficient condition for absolute stability of the system is that c~Tb≤0, c~TA~(-1)b≥0; especially when A=(diag(-ρ_1, -ρ_1, -ρ_2),) the necessary and sufficient condition for absolute stability of the system is c~Tb≤0, (c~TA~(-1)b≥0.

利用popov频率法,讨论了三阶直接控制系统dXdt=AX+bf(σ),σ=cTX零解的绝对稳定性,获得了A在cTb·trA2-cTA2b≤0的条件下,其零解绝对稳定的充分必要条件为cTb≤0,cTA-1b≥0;特别是当A=diag(-ρ1,-ρ1,-ρ2)时,零解绝对稳定的充分必要条件为cTb≤0,cTA-1b≥0。

A solvable necessary and sufficient condition: P(x)=bG(x)-G′(x)/G(x)-2F(x)Q(x)=F~2(x)-F′(x)-F(x)(bG(x)-G′(x)/G(x))+cG~2(x).

利用降阶法研究了变系数二阶线性微分方程y″+P(x)y′+Q(x)y=f(x)的可解性,得到了一个可解的充分必要条件:存在有限形式的可微函数F(x)、G(x),G(x)≠0及常数b和c使得P(x)=bG(x)-G′(x)/G(x)-2F(x),Q(x)=F2(x)-F′(x)-F(x)(bG(x)-G′(x)/G(x))+cG2(x)。

The Condition of Existence Solve of Sufficient and Necessary on a Class of Diophantine Equations;

一类不定方程组有解的充分必要条件

Research on Necessary and Sufficient Conditions of Industrial Clusters;

产业集群形成的必要条件和充分条件

Necessary and Sufficient Condition for the Existence of Positive Solutions of Nonlinear Second-Order Ordinary Differential Systems;

非线性二阶常微分系统边值问题正解存在的充分必要条件

A Necessary and Sufficient Condition for the Existence of Positive Solutions of Fourth Order Singular Differential Equations

一类四阶奇异微分方程正解存在的充分必要条件

Some Necessary and Sufficient Conditions of Abelian Groups and Cyclic Groups

交换群和循环群的若干充分必要条件

Dual Consecutive Number is the Necessary and Sufficient Condition of a Square Integer;

二重连整数是平方数的充分必要条件

A necessary and sufficient condition of(m,n)-tree;

(m,n)-树的一个充分必要条件

sufficient-necessary condition about proportionalityof mean value premium principle;

平均值原理成比例性的充分必要条件

On fully essential condition of Hamilton Graph;

关于Hamilton图的充分必要条件

The Necessary and Sufficient Condition for[D,φ(x),λ]=0

[D,φ(x),λ]=0的充分必要条件

A Necessary and Sufficient Condition for the Existence of Positive Solutions to Impulsive Singular Mixed Boundary Value Problems

脉冲奇异混合边值问题正解存在的充分必要条件

Results A necessary and sufficient condition for the temopral stability of steady state is provided and the necessary conditon for the bifurcation of this steady state to spatially non-uniform solution is also given.

结果获得了该类反应模型平衡态局部稳定的充要条件与系统产生一致分歧解的必要条件。

A sufficient and necessary condition for the generalized Moore-Penrose inverse of a factorization matrix

分解矩阵具有广义Moore-Penrose逆的充要条件

Necessary and Sufficient Conditions for Oscillations of a Class of Functional Differential Equations of Delayed Type;

一类滞后型泛函微分方程振动的充分必要条件

A Sufficient And Necessay Condition For Integrability Of Two-order Linear Differential Equation;

二阶线性常微分方程可积的一个充分必要条件

Once again, the trivial necessary condition is, in fact, sufficient.

事实上，这个平凡的必要条件也是充分的。

On the Definition of Life and the Prerequisite of the Origins of Life;

生命的定义和生命起源的充分必要条件

A New Proof of the Necessary and Sufficient Condition of the Trigonometric Polynomial Identically Equals Zero;

三角多项式T(x)恒为零的充分必要条件的证明