Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Ultrastructural analysis of Wuchereria bancrofti (Nematoda: Filarioidea) body wall

Bancroftian filariasis constitutes the principal mosquito-borne nematode infection of humans and the surface of adult of Wuchereria bancrofti seems to be especially important in the intricate interplay between host and parasite. The study of the parasite's surface structure might help to understand the localization and function of various organelles. W. bancrofti adult worms were recovered from untreated patients during hydrocele repair surgery and studied by transmission electron microscopy. The body wall of adult parasite is composed of cuticle, hypodermis and muscular layer. Cuticle is the external layer and shows transverse cuticular striation. It is composed by an epicuticle, cortical layers, median layer, fibrous layers and basal layer. The epicuticle is the most external cuticular layer and appears as a single laminar electron-dense layer. The cortical external region is more electron-dense and granular in appearance than the inner cortical layer. Electron-dense structures, called bosses are randomly distributed filling the cuticular striation. The median layer is formed by an electron-dense and continuous thick line. The fibrous layer is subdivided in inner and external layers connected by projections. The basal layer includes a large quantity of membranous projections directed toward the hypodermis. The hypodermis is a syncytium where some cellular organelles are observed. The somatic musculature is meromyarian. The muscle fibers consist of contractile and non-contractile regions and the contractile region is composed of myofilaments separated by dense body. This is the first study of W. bancrofti adult worms obtained from untreated patients and studied by transmission electron microscopy.     

Analogy between unconventional superconductivity and unconventional states of liquid crystals

An analogy is stressed between the order-parameter symmetries of the two-dimensional d-pairing wave superconductors and of liquid-crystal mesophases formed from achiral bent-shaped molecules. It leads to a definition of a class of liquid-crystal states which are the analogs of the unconventional superconducting states, and are characterized by a loss of discrete symmetry operations of the parent state.     

Deriving the magnitude of niobium off-center displacement in ferroelectric niobates from infrared spectroscopy

A KSr₂Nb₅O₁₅ nanopowder was synthesized by a chemical route based on a modified polyol method. The nanopowder exhibits the space group P4bm (ferroelectric) ascribed to the displacement of Nb from the central position of an [NbO₆] octahedron, parallel to the c-axis (polarization axis). The magnitude of the niobium off-center, ∆z, was determined by X-ray diffraction and mid-infrared spectroscopy (FTIR). Analysis of the infrared spectrum carried out using curve fitting based on Gaussian functions has revealed a very strong vibration at 413 cm^–1, ascribed to a bond of the Nb off-center with apical oxygen. A classical molecular theory was applied to derive the force constant of this bond from the vibrational frequency. Using the calculus of energies for the wavelength and the harmonic oscillator, we alternatively derived the ∆z parameter.     

Tin-doped indium oxide nanobelts grown by carbothermal reduction method

This communication discusses the formation of doped nanobelts produced by a simple route. Tin-doped indium oxide (ITO) nanobelts were obtained by a carbothermal reduction method. The nanostructures were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDX) and wavelength-dispersive X-ray spectroscopy (WDX). The results show that the nanobelts have a cubic structure, are single crystalline and doped with tin and grow in the [400] direction. PACS 81.07.-b; 61.46.+w; 68.37.Hk; 68.37.Lp