A classification result for the quasi-linear Liouville equation

Entire solutions of the n-Laplace Liouville equation in ${\mathbb{R}}^n$ with finite mass are completely classified.     

Resonance at two consecutive eigenvalues for semilinear elliptic equations

The solvability of the Dirichlet problem for a semilinear elliptic equation is studied in some situations where the classical resonance conditions of Landesman and Lazer may fail.     

A note on nonlinear oscillations at resonance

Existence of 2π-periodic solutions to the equation \(\ddot x + g(x) = p(t)\) is proved, under sharp nonresonance conditions on the interaction, ofg(x)/x with two consecutive eigenvaluesm ² and(m+1) ²: touch with the eigenvalues is allowed.     

Unitarity-Cuts and Berry’s Phase

Elaborating on the observation that two-particle unitarity-cuts of scattering amplitudes can be computed by applying Stokes’ theorem, we relate the optical theorem to the Berry phase, showing how the imaginary part of arbitrary one-loop Feynman amplitudes can be interpreted as the flux of a complex 2-form.     

The Dirichlet problem for the Laplace equation in a starlike domain of a Riemann surface

We consider the Dirichlet problem for the Laplace equation in a starlike domain, i.e. a domain which is normal with respect to a suitable polar co-ordinates system. Such a domain can be interpreted as a non-isotropically stretched unit circle. We write down the explicit solution in terms of a Fourier series whose coefficients are determined by solving an infinite system of linear equations depending on the boundary data. Numerical experiments show that the same method works even if the considered starlike domain belongs to a two-fold Riemann surface.     

Double-cut of scattering amplitudes and Stokes' Theorem

We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions in two complex-conjugated variables, which are simply computed by an indefinite integration in a single variable, followed by Cauchy's Residue integration in the conjugated one. The method is suitable for the cut-construction of the coefficients of 2-point functions entering the decomposition of one-loop amplitudes in terms of scalar master integrals.     

Sharp non-resonance conditions for periodically perturbed Liénard systems

Archiv der Mathematik -     

Quantitative prediction of protein folding behaviors from a simple statistical model

The statistical nature of the protein folding process requires the use of equally detailed yet simple models that lend themselves to characterize experiments. One such model is the Wako-Saito?-Mun?oz-Eaton model, that we extend here to include solvation effects (WSME-S), introduced via empirical terms. We employ the novel version to analyze the folding of two proteins, gpW and SH3, that have similar size and thermodynamic stability but with the former folding 3 orders of magnitude faster than SH3. A quantitative analysis reveals that gpW presents at most marginal barriers, in contrast to SH3 that folds following a simple two-state approximation. We reproduce the observed experimental differences in melting temperature in gpW as seen by different experimental spectroscopic probes and the shape of the rate-temperature plot. In parallel, we predict the folding complexity expected in gpW from the analysis of both the residue-level thermodynamics and kinetics. SH3 serves as a stringent control with neither folding complexity nor dispersion in melting temperatures being observed. The extended model presented here serves as an ideal tool not only to characterize folding data but also to make experimentally testable predictions.