Motivated by the work of Colin de Verdière and Saint-Raymond on spectral theory for zeroth-order pseudodifferential operators tori, we consider viscosity limits in which operators, P, are replaced P + iν Δ, ν > 0. By adapting Helffer–Sjöstrand scattering resonances, show that, a complex neighbourhood continuous spectrum, eigenvalues Δ have as goes to In simplified setting this justifies claims ...

We study the zeroth law for Killing horizon in scalar-hairy Lovelock gravity, and show that surface gravity of a general is constant, provided dominant energy condition obeyed by matter field.

We propose and analyze a randomized zeroth-order optimization method based on approximating the exact gradient by finite differences computed in set of orthogonal random directions that changes with each iteration. A number previously proposed methods are recovered as special cases including spherical smoothing, coordinate descent, well discretized descent. Our main contribution is proving conv...

The mathematical representation of chemical bonds in molecules is discussed. The molecule is viewed as a system of weakly interacting chemical bonds. The intrabond problems and the averaged electrostatic interbond interactions are handled at the . zeroth order, while the small interbond delocalization and dispersion effects are taken into account on the basis of the perturbation theory. A speci...

This work investigates the approximate verification of probabilistic specifications expressed as any non-nested PCTL formula over Markov processes on general state spaces. The contribution puts forward new algorithms, based on higher-order function approximation, for the efficient computation of approximate solutions with explicit bounds on the error. Approximation error related to higher-order...

The Prandtl number dependence of unsteady laminar natural convection along an infinite vertical plate in a thermally stratified fluid is investigated. Flows are induced by an impulsive (step) change in plate temperature and by a suddenly imposed plate heat flux. Analytical solutions of the viscous equations of motion and thermodynamic energy are obtained for Prandtl numbers near unity by the me...

4 Estimates 9 4.1 The zeroth order and volume estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.2 A partial second order estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.3 Gradient estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.4 The second order estimates . . . . ....