A comparison of the efficiency of techniques for digital encoding of contour maps

There are two digitizing techniques which are operable without human interpretation of contour-mapped data and which thus may be performed semi-automatically; line following and raster scanning. After a comparison of these techniques the author concentrates on raster scanning, as this technique facilitates creation of matrix data, the data structure most widely used in spatial analysis performed by digital computers. The author proposes the quantization method of computing matrix data and shows that quantized data may be used not only for overall computations but also to determine geometrical properties of surfaces - giving the possibility of error estimation-shown by the contour map. In particular such an approach enables pre-determination of a scanning parameter track spacing before digitizing to satisfy the required accuracy of analysis. The different aspects of utilising data obtained by raster scanning are discussed; storage, display in contour map form - the algorithm to produce the type of map where the contour lines pass exactly through the sample points taken during scanning is included

High-order adaptive methods for computing invariant manifolds of maps

The author presents efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric modeling. He uses B´ezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of B´ezier curves/triangles. The author develops and tests the methods for an ordinary parametric curve; then he adapts these methods to invariant manifolds of planar maps. Next, he develops and tests the method for parametric surfaces and then he adapts this method to invariant manifolds of three-dimensional maps

Collective magnetization dynamics in ferromagnetic (Ga,Mn)As mediated by photo-excited carriers

We present a study of photo-excited magnetization dynamics in ferromagnetic (Ga,Mn)As films observed by time-resolved magneto-optical measurements. The magnetization precession triggered by linearly polarized optical pulses in the absence of an external field shows a strong dependence on photon frequency when the photo-excitation energy approaches the band-edge of (Ga,Mn)As. This can be understood in terms of magnetic anisotropy modulation by both laser heating of the sample and by hole-induced non-thermal paths. Our findings provide a means for identifying the transition of laser-triggered magnetization dynamics from thermal to non-thermal mechanisms, a result that is of importance for ultrafast optical spin manipulation in ferromagnetic materials via non-thermal paths.Comment: 11 pages, 9 figure

Use of bernstein moments in QCD tests

It is pointed out that when comparing QCD predictions with experimental data for deep inelastic structure functions it is advisable to use Bernstein moments

Analytic solution of the QCD evolution equation for the non-siglet structure functions

The solution of the leading log QCD evolution equation for the non-singlet evolution function is given in the form of a convergent series. The convergence is rapid for small values of x. An asymptotic expansion in powers of (1 - x) is also obtained. Its first few terms reproduce within about one per cent all the moments of the evolution function in the kinematical range of present and near future interest. Using simultaneously the two expansions it is easy to calculate structure functions in all the region 0 < x $\leq$ with an accuracy of the order of one per cent

On the master equations for patron distributions

The evolution equations derived for parton distributions by Altarelli and Parisi are reformulated so, as to include explicit loss terms. This gives equations closer to master equations from statistical physics and supplies the necessary regularization of divergences without involving arguments foreign to the parton model. Relations with other approaches are also discussed

on hardy and bmo spaces for grushin operator

We study Hardy and BMO spaces associated with the Grushin operator. We first prove atomic and maximal functions characterizations of the Hardy space. Further we establish a version of Fefferman–Stein decomposition of BMO functions associated with the Grushin operator and then obtain a Riesz transforms characterization of the Hardy space