General criteria were derived for the linear dependence of arithmetic functions over the complex field as well as severalother criteria for arithmetic functions that were solutions of additive, multiplicative, exponential, and logarithmic equations. Anumber of examples were worked out in order to ...
Linear Dependence/Independence 线性相关/无关 令y1(x),y2(x),···,yn(x) 为在区间 I 上定义的 n(n≥2) 个函数 线性无关,若方程 c1y1(x)+c2y2(x)+···+cnyn(x)=0 仅在c1=c2=···=cn=0 时成立 若不是线性无关那么就是线性相关 Wronskian of n functions n个函数的Wronskian 若p_...
So we suppose our functions f1, f2, . . .,fn to be analytic. For general m, a condition equivalent to linear dependence is the vanishing of all...Kenneth Wolsson. A condition equivalent to linear dependence for functions with vanishing wron- skian. Linear Algebra and its Applications, ...
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Comments on an article about the linear independence of testing functions used in the method of moments. Description of the pulse testing functions used; Purpose of the half-pulses at the ends of the straight wire; Proof of linear independence or dependence. 关键词: LINEAR dependence (Mathematics...
Linear Dependence and Independence(线性相关和线性无关) 2.1 Basic concept 2.1.1 Linear combinations of vectors(线性组合) 2.1.2 linearly represented(线性表示) 2.1.3 linear dependence and Independence(线性相关和线性无关) 2.2 ...
Valiant's (2007) model of evolvability models the evolutionary process of acquiring useful functionality as a restricted form of learning from random examples. Linear threshold functions and their various subclasses, such as conjunctions and decision lists, play a fundamental role in learning theory and...
LYAPUNOV functionsDEPENDENCE (Statistics)TOPOLOGYFor families of n -dimensional linear differential systems ( n ≥ 2) whose dependence on a parameter ranging in a metric space is continuous in the sense of the uniform topology on the half-line, we obtain a complete description of the i th ...
(y) ~ 1 + x1 + x4 + x5 Distribution = Poisson Estimated Coefficients: Estimate SE tStat pValue (Intercept) 0.17604 0.062215 2.8295 0.004662 x1 1.9122 0.024638 77.614 0 x4 0.98521 0.026393 37.328 5.6696e-305 x5 0.61321 0.038435 15.955 2.6473e-57 100 observations, 96 error degrees of freedom ...
In the 20th century the emphasis shifted to the solution of boundary-value problems, and the theory itself remained relatively dormant until the middle of the century when new results appeared concerning, among other things, Saint-Venant’s principle, stress functions, variational principles, and ...