Computing hysteresis points of nonlinear equations depending on two parameters

A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system ofn nonlinear equations inn variables depending on two parameters. By addition of two equations a minimally extended system ofn+2 nonlinear equations is constructed for which the hysteresis point is an isolated solution. An efficient implementation of Newton's method is presented not requiring evaluations of second derivatives of the original problem. Two numerical examples show the efficiency of theQ-quadratically convergent method.     

Investigation of the action of flame retardants in cellulose. I. Investigation of the flame retardant action of 2,2′-oxybis(5,5-dimethyl-1,3,2-dioxaphosphorinane-2,2′-disulfide) in cellulose

Pyrolysis experiments were performed in high vacuum and under reduced air pressure (100 Pa). The volatile products of pure cellulose and cellulose containing various amounts of flame retardant 2,2′-oxybis (5,5-dimethyl-1,3,2-dioxaphosphorinane-2,2′-disulfide), i.e., Sandoflam 5060 of Sandoz AG, were studied by means of gas chromatography in combination with mass spectroscopy. The volatile products were characterized with infrared spectroscopy. The studied revealed that the incorporation of the flame retardant enhanced the water release and shifted the onset of this reaction to lower temperature. On the basis of these findings an explanation for the mechanism of flame retardancy in generated cellulose fibers modified with this particular flame retardant is attempted. From experiments with different residual air pressure the influence of oxygen on the primary processes of the pyrolytic degradation of cellulose is being discussed.     

A personal computer based system used in electromyography for interpretation and reporting

Programs for rule based electromyography (EMG) interpretation and reporting are described. A number of parameters are obtained during an EMG investigation. The combination of these data leads to a neurophysiological conclusion. Knowledge from the literature, research and experience is the basis for rule development. Rules have been developed for 14 of the most commonly used classifications of an EMG. The syntax is relatively easy and the user may change the rules, add rules or apply the system for other types of data. The results are displayed in a new graphical way. The system presented here is part of an integrated EMG laboratory with administrative routines, distributed databases for storage of results and routines for automatic report generation.     

High yield formation of carbon nanotubes using a rotating cathode in open air

Carbon nanotubes (CNTs) have been synthesized using the arc discharge method with a rotating graphite disc as the cathode. Arcing was carried out in open air and without the use of catalysts. The current density was maintained constant through out the experiment, while, the rate of rotation of the cathode and atmosphere under which arcing was carried out were changed during experimentation. Characterization of the samples produced indicates that rotation of the cathode has a significant impact on the quality and yield of the process. It is proposed that rotation of the cathode drags plasma formed between two electrodes away from high temperature region. This results in a sudden quenching of the reactive plasma. The time available for nucleation and growth phenomena is significantly reduced and thus leads to the formation of highly graphitic multi walled CNTs (yield 60%) and traces of double walled CNTs.     

Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

Computing Minimal Multi-Homogeneous Bezout Numbers Is Hard

The multi-homogeneous Bezout number is a bound for the number of solutions of a system of multi-homogeneous polynomial equations, in a suitable product of projective spaces. Given an arbitrary, not necessarily multi-homogeneous, system, one can ask for the optimal multi-homogenization that would minimize the Bezout number. In this paper it is proved that the problem of computing, or even estimating, the optimal multi-homogeneous Bezout number is actually NP-hard. In terms of approximation theory for combinatorial optimization, the problem of computing the best multi-homogeneous structure does not belong to APX, unless P = NP. Moreover, polynomial-time algorithms for estimating the minimal multi-homogeneous Bezout number up to a fixed factor cannot exist even in a randomized setting, unless BPP ⫆ NP.     

Characterization and optimization of linearly tapered slot antenna pattern

A parametric study of linearly tapered slot antenna (LTSA) in air and a method for optimization of its pattern are presented. A method of moments code is utilized to investigate the behavior of LTSA’s as the length, height and the taper angle varies. It is shown that the antenna pattern can be improved using a top layer of dielectric material with varying permittivity.