Related papers: Oscillatory Integral Decay, Sublevel Set Growth, a…
We consider a degenerate wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a boundary…
In this paper, we study the symmetry properties of nondegenerate critical points of shape functionals using the implicit function theorem. We show that, if a shape functional is invariant with respect to some continuous group of rotations,…
Whether in the Standard Model or beyond it, neutrinos contribute to the invisible decay mode of orthopositronium but practically not at all to that of parapositronium. Although this remark does not resolve the orthopositronium decay puzzle,…
We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in $n=3$ dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping…
An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to…
Neutrino decay in vacuum has often been considered as an alternative to neutrino oscillations. Because non-zero neutrino masses imply the possibility of both neutrino decay and neutrino oscillations, we present a model-independent formal…
We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. We argue that the answer is negative. We describe a method to make functions non-degenerate after…
We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and…
Quantum phase transition in the spin-boson model was claimed on the basis of various numerical studies, but not strictly proven. Here by using a unitary transformation to decompose the Hamiltonian into two branches of odd and even parity we…
We study the classical decay of unstable scalar solitons in noncommutative field theory in 2+1 dimensions. This can, but does not have to, be viewed as a toy model for the decay of D-branes in string theory. In the limit that the…
In this paper, we first generalize the Fresnel integrals by changing of a path for integration in the proof of the Fresnel integrals by Cauchy's integral theorem. Next, according to oscillatory integral, we also obtain further…
We consider different notions of non-degeneracy, as introduced by Kouchnirenko (NND), Wall (INND) and Beelen-Pellikaan (WNND) for plane curve singularities $\{f(x,y) = 0\}$ and introduce the new notion of weighted homogeneous Newton…
Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence…
Degeneracies of the neutrino oscillation parameters are explained using the $\sin^22\theta_{13}$--$s^2_{23}$ plane. Measurements of $\sin^22\theta_{13}$ by reactor experiments are free from the parameter degeneracies which occur in…
The stability under phase perturbations of the decay rate of local scalar oscillatory integrals in two dimensions is analyzed. For a smooth phase S(x,y) and a smooth perturbation function f(x,y), the decay rate for phase S(x,y) + tf(x,y) is…
Recent work has proposed that the interaction between ordinary matter and a stochastic gravitational background can lead to the decoherence of large aggregates of ordinary matter. In this work we point out that these arguments can be…
We apply Noether's theorem to show how the invariances of conservative systems are broken for nonconservative systems, in the variational formulation of Galley. This formulation considers a conservative action, extended by the inclusion of…
The neutrino oscillation patterns can be modified by neutrino interactions with external environments including electromagnetic fields that can influence on neutrinos in the case neutrinos have nonzero electromagnetic properties [1]. The…
In systems subject to periodic boundary conditions, Haldane has shown that states at arbitrary filling fraction possess a degeneracy with respect to center of mass translations. An analysis is carried out for multi-component electron…
Recently, it was observed that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In particular, under mild assumptions on the…