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     

Selection theorems,based on generalized variation and oscillation

In this paper we prove selection theorems for everywhere and almost everywhere convergent subsequences, based on the notion of uniformly limited oscillation, ofA, Λ-oscillation and ofA, Λ-variation, whereA is a system of intervals and Λ a sequence of reals. By this, we generalize and strengthen the selection theorems of Schrader (for oscillation) and of Waterman (for Λ-variation).     

Synthetic erythropoietic proteins: tuning biological performance by site-specific polymer attachment

Chemical synthesis in combination with precision polymer modification allows the systematic exploration of the effect of protein properties, such as charge and hydrodynamic radius, on potency using defined, homogeneous conjugates. A series of polymer-modified synthetic erythropoiesis proteins were constructed that had a polypeptide chain similar to the amino acid sequence of human erythropoietin but differed significantly in the number and type of attached polymers. The analogs differed in charge from +5 to -26 at neutral pH and varied in molecular weight from 30 to 54 kDa. All were active in an in vitro cell proliferation assay. However, in vivo potency was found to be strongly dependent on overall charge and size. The trends observed in this study may serve as starting points for the construction of more potent synthetic EPO analogs in the future.     

Reversible immobilization of engineered molecules by Ni-NTA chelators

Electrochemical synthesis of nickel-nitrilotriacetic acid (Ni-NTA) chelators, for subsequent immobilization of (His)(6)-tagged proteins (Photosystem II (PSII) as model molecule), on Au or Au-graphite electrodes is compared to chemical synthesis. Results show: (i) higher Ni-NTA surface density, (ii) shorter treatment time (1-12 min vs. 16 h normally needed for self-assembled monolayer (SAM)), (iii) possibility of addressing the chelator to only one Au electrode, in a sensor micro-array.     

DNA-mediated coordinative assembly of upconversion hetero-nanostructures for targeted dual-modality imaging of cancer cells

We reported a simple and universal strategy for DNA-mediated assembly of CdTe quantum dots (QDs) and lanthanide-doped upconversion nanoparticles (UCNPs). Such DNA-QD/UCNPs heterostructures not only maintains both fluorescent properties of QDs and upconversion luminescence behaviors of UCNPs, but also offers a polyvalent DNA surface, allowing for targeted dual-modality imaging of cancer cells using an aptamer     

Supramolecular helical mesomorphic polymers. Chiral induction through H-bonding

The work described here concerns a challenge of general interest in supramolecular chemistry: the achievement of chiral helical organizations with controlled structures. This work provides a strategy to obtain supramolecular polymers in which a chiral helical conformation has been induced by a noncovalent association, that is, through hydrogen bonding. Polycatenar 2,4,6-triarylamino-1,3,5-triazines, which organize into columnar mesophases and are susceptible to H-bonding interactions, were chosen as a starting point to build up the chiral supramolecular structure. The stacking of these mesogens has been forced to wind in a helical way by means of H-bond association with (R)-3-methyladipic acid, within the mesophase. The optically active columnar organization has been studied in depth by optical microscopy, differential scanning calorimetry (DSC), X-ray diffraction, and circular dichroism. Formation of stable complexes between the triazine units and (R)-3-methyladipic acid has also been investigated by means of NMR diffusion-ordered spectroscopy (DOSY) experiments in chloroform.     

Phase transition and mixed oxide-proton conductivity in germanium oxy-apatites

La_9.75□_0.25(Ge₆O₂₄)O_2.62 oxy-apatite shows a phase transition from triclinic to hexagonal symmetry at approximately 1020 K that has been characterised by high-temperature synchrotron X-ray and neutron powder diffraction, and ionic conductivity measurements. The crystal structure at 1073 K has been determined from joint Rietveld refinements of synchrotron X-ray and neutron powder diffraction data. The study shows that hexagonal-La_9.75□_0.25(Ge₆O₂₄)O_2.62 contains interstitial oxygen at the position previously reported for other oxy-germanates. Changes in the oxide conductivity associated with this structural transition are discussed. The thermal analyses showed a weight loss on heating close to 600 K very likely due to water release. The synchrotron thermodiffractometric study shows an anomaly in the cell parameters evolution at that temperature, which indicates that this residual water is located into the apatite channels. The electrical characterisation under different atmospheres (dry and wet synthetic air) indicates that there is a significant proton contribution to the overall conductivity below 600 K, mainly under wet atmosphere.     

Electronic spectral and photophysical properties of some p-phenylenevinylene oligomers in solution and thin films

A comprehensive photophysical and spectroscopic study of a new class of p-phenylenevinylene oligomers (PPV-trimers) possessing different alkyl and alkyloxy sidechain substituents and different end groups (aldehyde, CC, phenylene and anthracene units) was undertaken in solution at room temperature (293 K), low temperature (77 K) and in thin films. The study comprises absorption, emission and triplet–triplet absorption spectra, together with quantitative measurements of quantum yields (fluorescence, intersystem crossing, internal conversion and singlet oxygen formation) and lifetimes. The data allow the determination of rate constants for all decay processes. From these, several conclusions could be drawn. Changing from alkyl to alkyloxy substituents does not change fluorescence and internal conversion yields but decreases the (already small) intersystem crossing yield. The introduction of anthracene at the terminal ends of the PPV-trimers leads to the lowest fluorescence yield reported in this study. Of particular importance is the fact that the fluorescence quantum yields in films are of the same order of magnitude as those in solution, which suggests the potential for use of these oligomers for light-emitting device applications. With one of the alkyloxy derivatives, a more detailed study of the early part of the fluorescence decay was made, and it was found that upon excitation a fast conformational relaxation process of the initially excited oligomer occurs, leading to a more planar conjugation segment.     

A Formal Total Synthesis of (+)-Methyl Trachyloban-18-oate and (+)-Methyl 16-Oxo-17-norkauran-18-oate: Regio- and Diastereoselective Preparation of Methyl (13S)-13-Hydroxyisoatisiren-18-oate from (−)-Abietic Acid

A novel preparation of methyl (13S)-13-hydroxyisoatisiren-18-oate ( 4 ), a key-intermediate in a synthesis of (+)-methyl trachyloban-18-oate ((+)- 1 ), from (?)-abietic acid, is described. Since (?)- 1 has been previously converted into (?)-methyl 16-oxo-17-norkauran-18-oate ((?)- 16 ), our preparation of 4 constitutes also a formal total synthesis, from (?)-abietic acid, of (+)- 16 . Key steps in this approach were the allene photoaddition to podocarp-8(14)-en-13-one ( 5 ) and the conversion of the endo-toluene-4-sulfonate 11 into the exo-benzoate 12b .     

Synthesis of 2-amino-3-hydroxy- and of 2,3-diamino-3H-1,4-benzodiazepines

A new synthesis of 7-chloro-2,3-diamino-5-phenyl-3H-1,4-benzodiazepines is described, which allows for the preparation of compounds bearing the same or different substituents at the 2 and 3 positions, starting from 2-amino-7-chloro-3-hydroxy-5-phenyl-3H-1,4-benzodiazepines.