An analytic families index is defined for (cusp) pseudodifferential operators on a fibration with fibres which are compact manifolds with boundaries. This provides an extension to the boundary case of the setting of the (pseudodifferential) Atiyah-Singer theorem and to the pseudodifferential case of the families Atiyah-Patodi-Singer index theorem for Dirac operators due to Bismut and Cheeger an...

This paper examines a voxel (N-dimensional pixel) based representation for shape optimisation problems, and shows that although a basic genetic algorithm performed poorly on a simplified beam design problem, the use of three domain specific operators improved performance greatly. Additionally, the use of a ‘directed smoothing’ operator that preferentially adds material to high stress areas was ...

Associated to each set S of simple roots for SL(n, C) is an equivariant fibration X → XS of the space X of complete flags of C n. To each such fi-bration we associate an algebra JS of operators on L 2 (X) which contains, in particular, the longitudinal pseudodifferential operators of negative order tangent to the fibres. These form a lattice of operator ideals whose common intersection is the c...

Associated to each set S of simple roots for SL(n, C) is an equivariant fibration X → XS of the space X of complete flags of C n. To each such fi-bration we associate an algebra JS of operators on L 2 (X) which contains, in particular, the longitudinal pseudodifferential operators of negative order tangent to the fibres. These form a lattice of operator ideals whose common intersection is the c...

Abstract: For n > 3, we study the Cauchy problem for the fourth order nonlinear Schrödinger equations, for which the existence of the scattering operators and the global well-posedness of solutions with small data in Besov spaces Bs 2,1(R n) are obtained. In one spatial dimension, we get the global well-posedness result with small data in the critical homogeneous Besov spaces Ḃs 2,1. As a by-pr...

A recent area of interest is the development and study eigenvalue problems arising in scattering theory that may provide potential target signatures for use nondestructive testing materials. We consider a generalization electromagnetic Stekloff problem depends upon smoothing parameter, which we establish two main results were previously unavailable this type problem...

One component in Additive Schwarz Method (ASM) Domain Decomposition (DD) preconditioners BPS89, SBG96] using inexact subdomain solvers Boe89, HLM91] consists of an operator extending the boundary data into the interior of each subdomain, i.e., a homogeneous extension with respect to the diierential operator given in that subdomain. This paper is concerned with the construction of cheap extensio...

Dispersive characters are studied for waves on the one-dimensional free surface of an infinitely deep perfect fluid under the influence of gravity and surface tension. The hydrodynamic problem for surface water-waves is discussed with emphasis on the effects of surface tension. A new formulation is developed as a second-order in time quasilinear dispersive equation for a dynamic variable define...

Managers engage in income smoothing either to communicate private information about future earnings to investors (informativeness hypothesis) or to distort financial performance for opportunistic purposes (opportunism hypothesis). Business cycles and the monitoring role of institutional ownership may affect the earnings informativeness of income smoothing. The purpose of this research is to exa...

Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in the non-parametric model will have two different non-parametric regression functions. Therefore, we...