Graphical representation of DNA sequence provides a simple way of viewing, sorting and comparing various gene structures. A new two-dimensional graphical representation method using a two- quadrant Cartesian coordinates system has been derived for mathematical denotation of DNA sequence. The two-dimensional graphic representation resolves sequences' degeneracy and is mathematically proven to el...

The classical Thom–Porteous formula expresses the homology class of the degeneracy locus of a generic map between two vector bundles as an alternating sum of Schur polynomials. A proof of this formula was given by Pragacz by expressing this alternating sum as the Euler characteristic of a Schur complex, which gives an explanation for the signs. Fulton later generalized this formula to the situa...

Aims. In the present work, the effect of near-degeneracy on rotational Petersen diagrams (RPD) is analysed. Methods. Seismic models are computed considering rotation effects on both equilibrium models and adiabatic oscillation frequencies (including second-order near-degeneracy effects). Contamination of coupled modes and coupling strength on the first radial modes are studied in detail. Result...

We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro [KT06] and prove a sharp Hölder regularity result. The central difficulty is that there is no a priori non-degeneracy in the free boundary condition. Thus we must establish non-degeneracy by means of monotonicity formulae.

We show non solvability results in Gevrey spaces Gs for a linear partial differential operator with a single real characteristic of constant multiplicity m, m ≥ 3, provided s > m/(m−2)+δ, where δ > 0 depends on the order of the degeneracy of a suitable lower order term. In particular, δ → 0 as the order of the degeneracy tends to +∞.