Sentence examples for hierarchy of evolution from inspiring English sources

It follows that a type of new integrable hierarchy of evolution equations, possessing bi-Hamiltonian structure, is obtained.

Under an isospectral Lax pair, a new integrable hierarchy of evolution equations is obtained by starting from a given Lie algebra T, which can be reduce to a new coupled integrable equation similar to the long wave equation, but it is not the standard long wave equation.

The problem remains that we now need to close the infinite hierarchy of evolution equations of the alignment tensors.

"We're told that there's this hierarchy of evolution, in which vertebrates evolved from some worm-like creature to fish, amphibians, reptiles, birds, mammals, and so forth, and that living vertebrates represent these stages in both body plan and brain intelligence.

In order to generate a hierarchy of evolution equations associated with the spectral problem (2.1), we solve the stationary zero-curvature equation V x − [ U, V ] = 0, V = ( V i j ) 3 × 3, (2.4).

Hochrainer (2015) derives the hierarchy of evolution equations for dislocation density alignment tensors by first generalizing the CCT dislocation density tensor to a higher dimensional space which is the direct product of the 3D Euclidean space and the space of line directions (second-order dislocation density tensor, SODT).

Again utilizing Tu-pattern obtains two types of various integrable Hamiltonian hierarchies of evolution equations.

The reason why we adopt equation (3) to investigate discrete integrable hierarchies aims at applying the Tu scheme [33] to generate lattice integrable hierarchies, which has been a current way for generating integrable hierarchies of evolution equations.

Aim of this paper is to provide preliminary elements for discussion about the implications of the Hierarchy Theory of Evolution on the design and evolution of artificial systems and socio-technical organizations.

Hierarchy of lncRNA evolution linked to increase complexity of gene regulation.

From which, corresponding hierarchy of nonlinear evolution equation is derived and the integrable couplings of AKNS, D-AKNS, TD, Levi, Li, Ma and Fan hierarchies are deduced, and they are integrable in sense of Liouville.