How often do simple dynamical processes have infinitely many coexisting sinks?

This work concerns the nature of chaotic dynamical processes. Sheldon Newhouse wrote on dynamical processes (depending on a parameter )x _x+1=T(x _n ; ), wherex is in the plane, such as might arise when studying Poincaré return maps for autonomous differential equations in IR³. He proved that if the system is chaotic there will very often be existing parameter values for which there are infinitely many periodic attractors coexisting in a bounded region of the plane, and that such parameter values would be dense in some interval. The fact that infinitely many coexisting sinks can occur brings into question the very nature of the foundations of chaotic dynamical processes. We prove, for an apparently typical situation, that Newhouse's construction yields only a set of parameter values of measure zero.This research was supported in part by grants from the Air Force Office of Scientific Research AFOSR 81-0217, the Consiglio Nazionale delle Ricerche-Comitato per le Matematiche, and the National Science Foundation DMS 84-19110On leave from: Dipartimento di Matematica G. Castel nuovo Universita di Roma La Sapienza P. le Aldo Moro 5, I-00185 Rome, Italy     

Single-step preparation and catalytic activity of mesoporous MCM-41 and SBA-15 silicas functionalized with perfluoroalkylsulfonic acid groups analogous to Nafion

Preparation of hybrid organic-inorganic MCM-41 and SBA-15 silicas functionalized with perfluoroalkylsulfonic acid groups has been achieved in a single step by reacting the mesoporous silicas with 1,2,2-trifluoro-2-hydroxy-1-trifluoromethylethane sulfonic acid beta-sultone; the catalysts showed higher activity than commercial Nafion-silica composite for the esterification of long chain fatty acids with ethanol.     

Studies on the metal-nuclotide (Co-5′IMP,Co-5′GMP) interaction via mössbauer emission spectroscopy and magnetic susceptibility measurements

By means of⁵⁷Co Mössbauer emission spectroscopy and magnetic susceptibility measurements, the local symmetries and electronic structure of the Co(II) ions in the Co-5IMO and Co-5GMP complexes in the hydrated and dehydrated forms have been determined.     

Phase Diagram and Properties of Glasses of the System Sb<Subscript>2</Subscript>S<Subscript>3</Subscript>-AgI

The phase diagram of the system Sb₂S₃-AgI was constructed from data of the differential thermal and X-ray phase analyses. The physicochemical properties of glassy and crystalline alloys were studied.     

An electrochemical investigation on (MoO<Subscript>3</Subscript>+PVP+PVA) nanobelts for lithium batteries

Molybdenum trioxide (MoO₃) xerogel films modified with poly(vinyl alcohol)+poly(vinyl pyrrolidone) (PVP+PVA) polyblends were obtained by ion-exchange method with sol-gel technique. Investigations were conducted using X-ray “diffractometry”, Fourier transform infrared spectroscopy, and cyclic voltammetry. The results show that the H atoms in polyblend are H-bonded with the O atoms in the Mo=O bonds of MoO₃ xerogel, which effectively shield the electrostatic interaction between MoO₃ interlayer and Li⁺ ions when MoO₃ xerogel is modified by the intercalation of (PVP+PVA). The reversibility of the insertion/extraction of Li⁺ ions is greatly improved by the modification with polyblend of MoO₃ nanocomposite films. MoO₃ and (PVP+PVA) _x MoO₃ (x = 0, 0.5) nanobelts were obtained by a simple hydrothermal process from MoO₃ sol. The electrochemical cells with configuration Li/(LiPF₆+EC+DMC)/MoO₃ modified by (PVP+PVA) were fabricated and their discharge profiles studied.     

Mössbauer studies on one-dimensional iron phthalocyanines

Summary Magnetic moments and⁵⁷Fe Mössbauer spectra at room temperature and at liquid nitrogen temperature of polynuclear ligand-bridged iron phthalocyanines, FePcL (L = pyrazine and 4,4-bipyridyl), are reported. The experimental data are in agreement with a pseudo-octahedral environment around the iron(II) cation. Partially oxidized derivatives, FePc(pz)I_0.26 and FePc(bipy)I_1.06 have been synthesized and their⁵⁷Fe Mössbauer spectra and magnetic moments within the same temperature range obtained. Oxidation is shown to be metal centred and the iodine is found to be in I^– form for FePc(pz)_0.26 and as both I^– and I ₃ ^– species for FePc(bipy)I_1.06. While the magnetic moment of FePc(pz) increases upon oxidation, the opposite occurs for FePc(bipy).     

Development of a capillary electrophoretic method for the separation of diastereoisomers of a new human immunodeficiency virus protease inhibitor

A capillary electrophoretic (CE) method was developed for the separation of diastereoisomers of a new human immunodeficiency virus (HIV) protease inhibitor TMC114. In total 16 isomers of this drug have been synthesized (eight pairs of enantiomers). We succeeded in the separation of the eight diastereoisomers, but no enantiomers could be separated. Because of the high similarity and water-insolubility of these isomers, the separation is a real challenge. Different CE modes were tried out: capillary zone electrophoresis (CZE), nonaqueous capillary electrophoresis (NACE), micellar electrokinetic capillary chromatography (MEKC), and microemulsion electrokinetic capillary chromatography (MEEKC). Only MEEKC offered resolution of these compounds.