Sentence examples for irreducible case from inspiring English sources

The general complex characteristic equation is solved by using irreducible case of Cardano's method with the help of DeMoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation of various modes.

Several consequences of this notion are established, such as Perron– Frobenius type theorems, independence on p of the spectral radius in Lpp, continuity of spectral radius, and especially the existence of spectral gap in the irreducible case.

Thus the reducible case is converted into the irreducible case.

Only by adopting a mind-set of mindlessness, so to speak, can scientists produce accurate evolutionary explanations that disprove "irreducible complexity" case by case.

Irreducible casing pressure, also known as Sustained Casing Pressure (SCP), cannot be bled off as it is caused by late gas migration in the annular fluid column above the top of leaking cement.

A closed path d is irreducible in case d cannot be written as e j for any closed path e and j > 1.

Case 2. | G / G ′ | = p. Let χ be a non-principle irreducible character of G and θ an irreducible constituent of χ G ′.

Case 1. | G / G ′ | > p. Let φ be a non-linear irreducible character of G ′.

As we shall see, in the Euclidean case, irreducible representations enter the picture through the existence of a dominant wavelength in the correlation spectrum; our recent paper in this journal [34] focuses on the role of this monochromaticity condition in getting a precise pinwheel density and quasiperiodicity.

Nevertheless, a small, apparently irreducible number of cases remains in which overlapping cytological details make definitive diagnosis impossible.

It leads in the case of irreducible subalgebras to the following maximality result: Corollary 8 Let denote an irreducible subalgebra of su ( k ), i.e. cent su ( k ) ( g ) = { 0 }.