Our goal in this work is to establish the existence and the uniqueness of a smooth solution to what we call in this paper the corner problem, that is to say, the wave equation together with absorbing conditions at two orthogonal boundaries. First we set the existence of a very smooth solution to this initial boundary value problem. Then we show the decay in time of energies of high order—higher...

For an optimal control problem with fixed initial state and constraints on admissible controls we propose new second-order necessary optimality conditions using second-order tangents to the set of controls. In the absence of constraints on controls, our conditions are stronger than those of Gilbert and Bernstein (1983). Then, we investigate optimal control problems with fixed initial state and ...

In this paper, we study the differentiability of the trajectories of the logarithmic barrier algorithm for a nonlinear program when the set Λ∗ of the Karush-Kuhn-Tucker multiplier vectors is empty owing to the fact that the constraint qualifications are not satisfied.

We propose an adaptive approach in picking the wave-number parameter of absorbing boundary conditions for Schrödinger-type equations. Based on the Gabor transform which captures local frequency information in the vicinity of artificial boundaries, the parameter is determined by an energy-weighted method and yields a quasi-optimal absorbing boundary conditions. It is shown that this approach can...

“Security” parallels “health” in that it is commonly defined as the absence of its negation, “illness”. In fact, the concept of security challenges any attempt to be objectively apprehended, except as an absence of insecurity. Illness, however, can be identified wherever and whenever by sets of visible symptoms that are indicators of regularities, usually bringing forth the same effects. This i...

The Yule-Nielsen modified spectral Neugebauer model enables predicting reflectance spectra from surface coverages. In order to provide high prediction accuracy, this model is enhanced with an ink spreading model accounting for physical dot gain. Traditionally, physical dot gain, also called mechanical dot gain, is modeled by one ink spreading curve per ink. An ink spreading curve represents the...

We define tropical Psi-classes on M 0,n (R 2 , d) and consider intersection products of Psi-classes and pull-backs of evaluations on this space. We show a certain WDVV equation which is sufficient to prove that tropical numbers of curves satisfying certain Psi-and evaluation conditions are equal to the corresponding classical numbers. We present an algorithm that generalizes Mikhalkin's lattice...

Positivity preserving properties have been conjectured for the bilaplace Dirichlet problem in many versions. In this note we show that in any dimension there exist bounded smooth domains Ω such that even the solution of ∆u = 1 in Ω with the homogeneous Dirichlet boundary conditions u = uν = 0 on ∂Ω is sign-changing. In two dimensions this corresponds to the Kirchhoff-Love model of a clamped pla...

Abstract. We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a known sufficient condition for exponential stability with respect to the H-norm is not sufficient for the exponential stability with respect to the C-norm. Hence, due to the nonlinearity, even in the case of classical solutions, the exponential stability depends strongly ...