We construct and analyze a family of well-conditioned boundary integral equations for the Krylov iterative solution of three-dimensional elastic scattering problems by a bounded rigid obstacle. We develop a new potential theory using a rewriting of the Somigliana integral representation formula. From these results, we generalize to linear elasticity the well-known Brakhage-Werner and Combined F...

Derivatives of a solution of an ODE Cauchy problem can be computed inductively using the Faà di Bruno formula. In this paper, we exhibit a noninductive formula for these derivatives. At the heart of this formula is a combinatorial problem, which is solved in this paper. We also give a more tractable form of the Magnus expansion for the solution of a homogeneous linear ODE.

We evaluate the tachyon potential in the Schnabl gauge through off-shell computations in the sliver frame. As an application of the results of our computations, we provide a strong evidence that Schnabl’s analytic solution for tachyon condensation in open string field theory represents a saddle point configuration of the full tachyon potential. Additionally we verify that Schnabl’s analytic sol...

We study the asymptotic behavior of the solutions related to a singularly perturbed q-differencedifferential problem in the complex domain. The analytic solution can be splitted according to the nature of the equation and its geometry so that both, Gevrey and q−Gevrey asymptotic phenomena are observed and can be distinguished, relating the analytic and the formal solution. The proof leans on a ...

We show the existence of a global unique and analytic solution for the mean curvature flow and the Willmore flow of entire graphs for Lipschitz initial data with small Lipschitz norm. We also show the existence of a global unique and analytic solution to the Ricci-DeTurck flow on euclidean space for bounded initial metrics which are close to the euclidean metric in L∞ and to the harmonic map fl...

We study the satisfiability of random Boolean expressions built from many clauses with K variables per clause (K-satisfiability). Expressions with a ratio alpha of clauses to variables less than a threshold alphac are almost always satisfiable, whereas those with a ratio above this threshold are almost always unsatisfiable. We show the existence of an intermediate phase below alphac, where the ...

We obtain an extension of Bjorken’s 1+1 dimensional scaling relativistic flow solution to relativistic transverse velocities with cylindrical symmetry in 1+3 dimension at constant, homogeneous pressure (vanishing sound velocity). This can be the situation during a first order phase transition converting quark matter into hadron matter in relativistic heavy ion collisions. Hydrodynamics often al...