Sentence examples for valid for the generalized from inspiring English sources

This factorization algorithm is valid for the generalized s-fold CBIJM of order p s over finite field with a suitable matrix unit α of size p×p.

This is due to the simple geometrical ideas and the fact that this result, despite several efforts, is in most cases no more valid for the generalized Liénard equation x ¨ + f ( x ) x ˙ + g ( x ) = 0.

Thus, not all of the properties of the generalized Neumann kernel which have been studied in [3] are valid for the generalized Neumann kernel which will be studied in this paper.

By using the same approach used in [3] for unbounded multiply connected regions, we can prove that the properties of the generalized Neumann kernel proved in [3], except Theorem 8, Theorem 10 and Corollary 2, are still valid for the generalized Neumann kernel formed with the function A ( t ) in (10) above (see [5]).

This paper studies the selection of valid and relevant moments for the generalized method of moments (GMM) estimation.

Then, by considering disturbance effects, a universally valid uncertainty relation is investigated for the generalized equation of motion with a certain boundary condition.

Moreover, since Q can take non-integer values, this model is also valid for the representation of non-orthogonal or generalized MC signals.

In this paper, a new formula for the generalized twist is presented which is valid for linearly elastic, nonhomogeneous and anisotropic beams of solid cross section.

Although Eq. (2) is obtained for a highly idealized geometry, this relationship is valid for slightly more generalized cases as shown in Fig. 2, in which the relationship between the aspect ratio, plate size and the toroidal/poloidal spectra has been calculated and plotted.

In this paper, we are going to prove that these results are valid for the rough fractional multilinear integral operator (T_{Omega,alpha }^{A,m}) on generalized Morrey spaces.

Therefore Hypothesis 1 is true for the generalized version.