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     

Improved limits on the mass of the tau neutrino

Several methods to determine (or set an upper bound on) the mass of the tau neutrino are described. The decay spectrum of \(\tau \to e\bar \nu _e \nu _\tau \) near the high center-of-mass electron-energy end is particularly sensitive to the tau-neutrino mass. It is shown that an upper bound of 20 MeV or lower may be feasible. In addition, improved limits on the mass and mixing angle of a heavy component of the tau-neutrino may be readily obtained. We also discuss the purely leptonic decays of theD andF mesons, and show how measurements of the ratiosB(D→τν_τ/B(D→μν_μ,B(F→τν_τ/B(D→μν_μ can be sensitive to tau-neutrino masses of 30 MeV or greater.     

An Asymmetric Edge-Sharing Bioctahedral Complex: (η2-DAniF)MoIII(μ-DAniF)2(μ-O,Cl)MoVCl2 (DAniF=N,N′-di-p-anisylformamidinate)

A novel asymmetric, edge-sharing bioctahedral complex with formamidinato ligands ( ²-DAniF)Mo(-DAniF)₂(-O,Cl)MoCl₂, 1, (DAniF=N,N-di-p-anisylformamidinate) has been isolated as a byproduct from the preparation of the dimolybdenum(II,III) compound Mo₂(DAniF)₃Cl₂. An X-ray crystallographic study shows that the structure consists of edge-sharing bioctahedra, with the shared edge defined by the vector joining the: -O and -Cl ligands. Compound 1 is best formulated as a mixed-valent Mo^IIIMo^V compound, the Mo(V) ion being that with the two terminal Cl^– ligands. The cyclic voltammogram of 1 shows a reversible reduction at –0.472 V and a reversible oxidation at 1.028 V vs. the Ag/AgCl reference electrode, while the absorption spectrum of 1 reveals an intense low energy absorption at 523 nm ( _max=12 500) which is attributed to an intervalence charge transfer transition. Crystallographic data for 1 are as follows: a=13.387(1) Å, b=15.500(2) Å, c=21.855(2) Å, =98.786(2)°, V=4481.8(8) ų, P2₁/c, R1 (wR2)=0.082 (0.177).     

Donor—acceptor interactions of substituted benzenes with molecular chlorine and carbon disulfide

CNDO molecular orbital calculations have been performed to analyze donor—acceptor interactions between molecular chlorine and benzene, toluene, mesitylene and hexamethylbenzene and the, as yet, unreported chlorine—hexafluorobenzene and carbon disulfide—benzene pairs. The stabilization energy and the dipole moment and its derivative (?p/?R_CICI) calculated for the benzene—chlorine complex are in good agreement with the estimated experimental values. The trends in the experimental stabilization energies and the Cl-Cl vibrational frequencies with increasing methyl substitution appear to be well reproduced by the calculations. The charge transferred from the benzene donor is polarized toward the outer chlorine atom or sulfur atom. For hexafluorobenzene-chlorine the direction of electronic charge polarization is reversed from that of the benzene and methylbenzene complexes. The calculated results are discussed within the framework of Muliiken's simplified resonance theory for complexes.     

Synthesis of 1,2-dihydroindolo [1,7-AB] [1,5] benzodiazepines and related structures. A new heterocyclic ring system

The synthesis of the novel 1,2-dihydroindolo [1,7-ab][1,5]benzodiazepine ring system 4 is described. Condensation of 2-fluoronitrobenzene with indoline provided the starting material for the synthesis, 1-(2-nitrophenyl)indoline (1a) in high yield. The nitro group was reduced catalytically and the resulting amino function was acylated to afford the heterocycle percursor amide 3. Refluxing this amide in phosphorus oxychloride brought about a Bischler-Napieralski type cyclodehydration to form the target 1,2-dihydroindolo[1,7-ab][1,5]benzodiazepine ring system. Dehydrogenation of the latter led to the fully aromatic indolo[1,7-ab][1,5]benzodiazepine structure 5, while reduction with sodium borohydride provided the 1,2,6,7-tetrahydroindolo[1,7-ab]-[1,5]benzodiazepine tetracycle 6.     

Liquid–solid disk extraction followed by supercritical fluid elution and gas chromatography of phenols from water

A method combining the techniques of liquid – solid disk extraction (LSDE) and supercritical fluid elution (SFE) has been developed for the phenols regulated by the Clean Water Act. LSDE uses a disk or membrane made of polytetrafluoroethylene (PTFE) fibrils impregnated with small particles, e.g. styrene divinylbenzene (SDB) resin, to extract phenols from water. After disk extraction the retained analytes are eluted from the disk using SFE. SFE is used as an alternative to liquid solvent elution with an organic solvent. Analytes are separated, identified, and quantified using gas chromatography – ion trap detector mass spectrometry (GC-ITDMS). The method is capable of sub parts per billion detection limits, and precision of 5–28% RSD. Evaluation of various disks or membranes, such as C₁₈-silica disks, SDB disks, and ion exchange membranes, has also been performed for the extraction of phenols from water. The results obtained from the in-situ aqueous acetylation of phenols and extraction of their acetates are quantitative. The utilization of LSDE and SFE techniques has proven to be a more effective approach than liquid – liquid extraction in minimizing air pollution and solvent waste.     

High ionization potential conjugated polymers

We report the synthesis of a series of poly(p-phenylene ethynylene)s (PPEs) with high ionization potentials and associated high excited-state electron affinities. Their photophysical properties were investigated using steady-state and time-resolved fluorescence techniques. The ionization potentials of the polymer thin films were determined using ultraviolet photoelectron spectroscopy (UPS), and those with the highest ionization potentials displayed high sensitivity for the detection of electron-donating aromatic compounds. The effects of sterics, chemical structure, and electronic properties on the polymers' sensory responses were investigated by fluorescence quenching experiments in both solution and solid thin films. In addition, we report that in some cases the excited-state charge-transfer complexes (exciplexes) of the PPEs with analytes were observed. These latter effects provide promising opportunities for the formation of sensitive and selective chemical sensors.     

Diode or tunnel-diode characteristics? Resolving the catalytic consequences of proton coupled electron transfer in a multi-centered oxidoreductase

Protein film voltammetry has been employed to define multiple catalytic consequences of proton coupled electron transfer (PCET) in a cytochrome c nitrite reductase. Current-potential profiles reflecting the steady-state rate of nitrite-limited reduction have been defined from pH 4 to 8. Lowering the electrode potential at pH 8 causes the catalytic current to increase and then decrease before it takes a value independent of any further lowering of electrode potential. By comparison, at pH 4, catalysis is initiated at more positive electrode potentials in an approximately sigmoidal fashion with no attenuation of the catalytic rate evident at more negative electrode potentials. The results show that activity is turned on by the coupled transfer of two electrons and one proton to the enzyme. The decreased rate of catalysis at lower electrode potentials under more alkaline conditions shows that this rate attenuation occurs only when reduction is not coupled to compensating protonation(s) of the enzyme. Sites within the enzyme whose reduction and/or protonation may contribute to the definition of these activities are discussed.