A theorem on the existence of symmetries of fractional PDEs

We propose a theorem that extends the classical Lie approach to the case of fractional partial differential equations (fPDEs) of the Riemann–Liouville type in (1+1$1+1$) dimensions.     

Solid-State and Solution FT-Raman Spectra of the Tetraiodine Dication I4 2+

Abstract

I₄ ²⁺ is the only known cyclic homopolyatomic cation or anion of iodine. It has a rectangular planar structure which may be thought of as containing two I₂ ⁺ units joined by a weak π?-π? 4 centre 2 electron bond.¹ In this paper we report our FT-Raman spectra of I₄ ²⁺, which conflict with those published by Gillespie et al. ¹ and present evidence that the peaks attributed to a species containing iodine in the +1 oxidation state are in fact due to I₄ ²⁺.     

Comparison results for oscillation of nonlinear differential equations

((without abstract.))     

Multiple-instrument analyses of single micron-size particles.

Physical, chemical, and isotopic analyses of individual radioactive and other particles in the micron-size range, key tools in environmental research and in nuclear forensics, require the ability to precisely relocate particles of interest (POIs) in the secondary ion mass spectrometer (SIMS) or in another instrument, after having been located, identified, and characterized in the scanning electron microscope (SEM). This article describes the implementation, testing, and evaluation of the triangulation POIs re-location method, based on microscopic reference marks imprinted on or attached to the sample holder, serving as an inherent coordinate system. In SEM-to-SEM and SEM-to-SIMS experiments re-location precision better than 10 microm and 20 microm, respectively, is readily attainable for instruments using standard specimen stages. The method is fast, easy to apply, and facilitates repeated analyses of individual particles in different instruments and laboratories.     

Recent developments in the synthesis of heterocyclic derivatives by PdI2-catalyzed oxidative carbonylation reactions

A simple catalytic system, consisting of PdI₂ in conjunction with an excess of KI, has proven to be very valuable for the direct one-step synthesis of a variety of heterocyclic derivatives by oxidative carbonylation of suitably functionalized alkynes. The same catalyst also promoted the oxidative carbonylation of β-amino alcohols to oxazolidin-2-ones with unprecedented catalytic efficiencies for this kind of reaction.     

A continuation theorem with applications to periodically forced Liénard equations in the presence of a separatrix

In this paper we prove a result on the existence of periodic motions for the periodically forced Liénard differential equation x ^″+f(x)x ^′+g(x)=e(t) in a situation where the phase portrait of the associated autonomous equation is similar to that of a centre limited by an unbounded separatrix. The existence result, which is based on a degree theoretic continuation theorem, enables us to treat some interesting cases not previously considered in the literature. Received: April 27, 2000 Published online: December 19, 2001     

Biogas production fromJatropha curcas press-cake

Applied Biochemistry and Biotechnology - Seeds of the tropical plantJatropha curcas (purge nut, physic nut) are used for the production of oil. Several methods for oil extraction have been...     

Asymptotic behaviour of solutions for second order nonlinear autonomous differential equations

For a class of second order nonlinear autonomous differential equations asymptotic properties of the solutions as are studied. The investigation is done in the phase plane and the phase portrait of the equivalent system is obtained by using the zero-isocline function. Some suffcient conditions are presented which for the case of Liénard equation become also necessary. Received December 21, 1995