A scheme for automatic generation of boundary-fitted depth- and depth-gradient- dependent grids in arbitrary two-dimensional regions

In this paper we present a scheme for the numerical generation of boundary-fitted grids that adapt to both water depth and depth gradient. The scheme can be used in arbitrary two-dimensional regions and is based on the application of the well-known control function approach to generate adaptive grids. The method includes the evaluation of water depths at the grid points from a known distribution of depth points and their associated depths plus a procedure for the numerical evaluation of depth gradients. It is demonstrated that the smoothness of the grid can be enhanced by introducing a suitable filtering technique.     

On the determination of an orthogonal transformation

Let A and B be n × m-matrices with m >- n. An iterative algorithm for the determination of the orthogonal P minimizing /vbPA - B /vb_F² is suggested and analyzed. Convergence is proved under natural assumptions.     

Gluino pair production in electron-positron annihilation

We summarize the effects of some unknown supersymmetry breaking mechanism by the addition to the super-QCD lagrangian of explicit, and different, mass terms for the scalar superpartners of quarks and antiquarks. Allowing also a possible Majorana mass for the gluino, we then calculate cross sections for e⁺e^? → two gluinos, a process which may be observable if the gluino is sufficiently long-lived.     

On the absence of a density effect for inner shell ionization

It is shown that the observed absence of a density effect in inner shell ionization in solids is due to the fact that the required momentum transfer has a wavelength of the order of, or smaller than, the lattice constant, and thus cannot be transmitted to the lattice. This leads to a cut-off in the dielectric function corresponding to electronic binding energies above 1—1.5 keV, depending on the lattice constant. For more strongly bound electrons there shoul be no density effect.     

On the double layer of mercury in contact with potassium fluoride/potassium hydroxide solutions

Differential capacities of the dropping mercury electrode in contact with KF+KOH solutions were measured by a differential chronopotentiometric method. Adsorption of anions at positive polarisation was confirmed.     

Grafting of monodisperse low-molecular-weight polystyrene onto cellulose acetate

Well-defined low-molecular-weight polystyrene was grafted onto cellulose acetate in a homogeneous solution. The grafting was performed by esterifying the free hydroxyls in the cellulose acetate (acetyl DS 2.5) with anionically prepared polystyrene having a carboxylic acid group at one end of the chain. The carboxylic acid end group of the polystyrene was activated by either conversion to the corresponding acid chloride, or by reaction with trifluoroacetic anhydride. Pyridine and the more active 4-dimethylaminopyridine were used as catalysts in the esterifications. The polystyrene contents of the copolymers varied between 10 and 80% and the molecular weights of the polystyrene grafts were 2500, 12,100 and 17,100 (M?_w/M?_n = 1.1).     

On Montgomery's conjecture and the distribution of Dirichlet sums

A new version of Montgomery's conjecture (1971) on the estimation of Dirichlet sums is disproved by means of a modification of the idea of “short sums” (due to Bourgain, 1991). We also study the distribution of the values of Dirichlet's “long sums”.     

Robust registration of point sets using iteratively reweighted least squares

Registration of point sets is done by finding a rotation and translation that produces a best fit between a set of data points and a set of model points. We use robust M-estimation techniques to limit the influence of outliers, more specifically a modified version of the iterative closest point algorithm where we use iteratively re-weighed least squares to incorporate the robustness. We prove convergence with respect to the value of the objective function for this algorithm. A comparison is also done of different criterion functions to figure out their abilities to do appropriate point set fits, when the sets of data points contains outliers. The robust methods prove to be superior to least squares minimization in this setting.