On 0-distance-preserving permutations of affine and projective quadrics

Two pointsX, Y of a quadricF in an affine or projective space are called 0-distant, writtenX Y, if they coincide or if their connecting line is a subset ofF. In this paper, answers are given to the question under which conditions an arbitrary permutation ofF satisfyingX Y X Y X,Y F can be extended to a collineation of the given space.Dedicated to Rafael Artzy on the occasion of his 80th birthday     

NUMERICAL CALCULATION OF LONDON-VAN DER WAALS ADHESION FORCE DISTRIBUTIONS FOR DIFFERENT SHAPED PARTICLES

A basic method to calculate van der Waals dispersion force distributions for submicron superquadric particles in particle-wall systems is presented. The force distribution is achieved by rotating particles through a large number of arbitrary spatial orientations, each time keeping constant the contact distance to the wall surface while calculating the dispersion force. To accomplish this, the use of 2D particle shape suffices, that is, through using an inter-dimensional function, which has been determined previously. A further development of the method within digital image analysis may lead to possible applications to forecasting the macroscopic properties of particle systems, for example, flowability, agglomeration behavior or dispersibility. For small ranges of superquadric particle shapes, each with a different size, the way from determining the inter-dimensional function up to applying image analysis is shown in an example.     

Second Order Cones for Maximal Monotone Operators via Representative Functions

It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T, in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the Graph T. In particular we obtain formula for the proto-derivative, as well as its polar, the normal cone to the graph of T. First order derivatives are shown to be useful in recognising points of single-valuedness of T. We show that a strong form of proto-differentiability to the graph of T, is often associated with single valuedness of T. The second author’s research was funded by NSERC and the Canada Research Chair programme, and the first author’s by ARC grant number DP0664423. This study was commenced between August and December 2005 while the first author was visiting Dalhousie University.     

A topological Paley-Wiener property for locally compact groups

We investigate a certain topological Paley-Wiener property and show, for instance, that compact-free nilpotent groups and simply connected solvable groups share this property.

     

Modelling of particle layer detachment—Role of transient kinetic effects

Particle layers tend to build up on walls in many filtration and separation processes, calling for periodic removal in order to keep the apparatus running. Important factors are the adhesion of the layer on the substrate and the cohesion of the particles in the layer. Models describing such layer detachment generally assume constant and homogeneous conditions for the forces acting on the layer. But in reality detachment is extremely non-stationary concerning place and time, primarily due to changing conditi...