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 compare the results ...
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_...
The model in equation (1) is ‘linear’ if the functions f and h are linear functions, that is, matrix operations of the form f(x) = Ax and h(x) = Cx where Am×m and Cn×m are constant (or even time-varying, but state-independent) matrices. Throughout the field of ...
The system of equations for this stress formulation is still rather complex, and analytical solutions are commonly determined by making use of stress functions. This concept establishes a representation for the stresses that will automatically satisfy the equilibrium equations. For the two-dimensional cas...
Both the Jacobian linearization description, as in (5), and the quasi-LPV description, as in (21), lead to a parameter-dependent family of linear systems. In some cases, we can model or approximate the parameter dependence in the LPV system as a linear fractional transformation (LFT). The...
2. 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) ...
(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 ...
Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonal...
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 ...