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In fact, a lot of sparse signals may satisfy the form of block-sparse signal in practice, such as multi-band signal, DNA array (DNA microarray), radar pulse signal, and multiple measurement vector problems [16].
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Suppose that a smooth solution u of (1.2) exists locally and the initial value (g x,y) ) satisfies the form (g=yb_{0} x,y) ).
If { x i } i = 1 ∞ Open image in new window is dense on [ 0, 1 ] Open image in new window and the solution of Equation 2.1 is unique, then the solution of Equation 2.1 satisfies the form u ( x ) = L − 1 f ( x, u ( x ) ) = ∑ i = 1 ∞ k = 1 i ik f ( x k, u ( x k ) ) ψ ¯ i ( x ).
We note that since f ( 1 ) given in (24) satisfies the form (26), we are allowed to assume all higher order terms to be taken zero, i.e., f ( j ) = 0, j ⩾ 2. Thus, hereafter as a generalization of this fact, one can assume in deriving i-q-soliton solution, f ( j ) = 0 for all j ⩾ i + 1.
The functions ( psi (z) in mathcal {A}(m)) are said to be the starlike functions of order ( lambda, 0 le lambda <1)) in ( {mathbb {U}}), if it satisfies the form begin{aligned} {mathfrak {R}}left{ frac{z psi ^{prime } z)}{psi (z)}right} > lambda quad ( z in mathbb {U}), end{aligned} (2 we note that ( mathcal {S}_{lambda }^(m) subseteq mathcal {S}_{0}^(m)equiv mathcal {S}^(m)subseteq mathcal {S}(m)).
If so, the differential equation can be solved simply as a quadratic equation as demonstrated by the subsequent steps: Check to see if the differential equation satisfies the form shown in equation (1) in Figure 6.
If so, the differential equation can be solved as follows: To solve a more general nth-order linear differential equation, check to see if the differential equation satisfies the form shown in equation (1) in Figure 10.
If so, simply follow the steps outlined in Figure 8. Solving nth order linear differential equations with constant coefficients: Check to see if the differential equation satisfies the form shown in equation (1) in Figure 9.
Check to see if the differential equation satisfies the form shown in equation (1) in Figure 5, where f(x) is a function of x alone, or a constant.
If so, simply follow the steps outlined in Figure 5. Solving second order linear differential equations with constant coefficients: Check to see if the differential equation satisfies the form shown in equation (1) in Figure 6.
Check to see if the differential equation satisfies the form shown in equation (1) in Figure 5, where f y) is a function of y alone, or a constant.
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The phrase "satisfy the form " functions as a verb phrase, where 'satisfy' acts as a transitive verb requiring a direct object ('the form'). Ludwig AI confirms its usability. It indicates that certain criteria or requirements are fulfilled by the form, ensuring its acceptance or validity.
Expression frequency: Uncommon
