Various scenarios of the initial inflation of the universe are distinguished by the choice of a scalar field potential U(φ) which simulates a temporarily non–vanishing cosmological term. Our new method, which involves a reparametrization in terms of the Hubble expansion parameter H, provides a classification of allowed inflationary potentials and of the stability of the critical points. It is b...

It is well-known that Γ-convergence of functionals provides a tool for studying global and local minimizers. Here we present a general result establishing the existence of critical points of a Γ-converging sequence of functionals provided the associated Γ-limit possesses a nondegenerate critical point, subject to certain mild additional hypotheses. We then go on to prove a theorem that describe...

We discuss the local behaviour of vector elds in the plane R 2 around a singular point (i.e. a zero), on the basis of standard (Poincar e-Dulac) normal forms theory, and from the point of view of Poincar e renormalized forms 28]. We give a complete classiication for regular singular points and provide explicit formulas for non-degenerate cases. A computational error for a degenerate case of cod...

We discuss the local behaviour of vector fields in the plane R around a singular point (i.e. a zero), on the basis of standard (PoincaréDulac) normal forms theory, and from the point of view of Poincaré renormalized forms [28]. We give a complete classification for regular singular points and provide explicit formulas for non-degenerate cases. A computational error for a degenerate case of codi...

An infinite plane problem with a circular boundary under the screw dislocation is solved by using a new method. The angle-based fundamental solution for screw dislocation is expanded into degenerate kernel. Our method can explain why the image screw dislocation is required. Besides, the location of the image point can be obtained easily by using degenerate kernel after satisfying boundary condi...

It is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎Also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

We construct an approximate renormalization transformation that combines Kolmogorov-Arnol'd-Moser and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of t...