Coupling of the relaxation and resonant elements in the autonomous chaotic relaxation oscillator (ACRO)

If a harmonic oscillator is embedded in a relaxation oscillator, the resulting system may behave like an autonomous chaotic relaxation oscillator (ACRO). The discharge transient of the relaxation oscillator excites sinusoidal oscillations in the harmonic oscillator and these sinusoids affect when the next discharge occurs. This can lead to chaotic intervals in the oscillator periods. A simple electronic model of the ACRO is studied over a wide range of parameters using numerical, analytic, and experimental techniques. The dynamics of the ACRO is found to be determined by three parameters: (1) tuning, (2) coupling, and (3) damping. Complex, intermittent outputs can always be inhibited by increasing the damping of the harmonic oscillator. For weak damping, strong coupling yields chaotic periods. With weak damping and weak coupling, complex behavior only occurs if the relaxation oscillator is tuned near a resonance of the harmonic oscillator. A new path to chaos, called a disruption bifurcation, is the source for intermittency in the ACRO. This bifurcation occurs when the amplitude of internal resonances is excited to the degree that existing limit cycles are disrupted.     

Enhancement of the solubilities of polycyclic aromatic hydrocarbons by weak hydrogen bonds with water

Summary The thermodynamics of mobile order is applied to predict the aqueous solubility of liquid and solid aliphatic and polycyclic aromatic hydrocarbons. The solubility values are mainly determined by the magnitude of the hydrophobic effect. However, contrary to the solubilities of the alkanes, the solubilities of polycyclic aromatic hydrocarbons in water predicted in absence of solute-solvent hydrogen (H) bonds are systematically too low. This shows the contribution of weak specific interactions between the OH groups and the electrons of the aromatic substances. According to the theory, these interactions are characterized by a stability bility constant K_o which can be derived from solubility data. At 25°C, this constant amounts to 80 cm³/mol, the order of magnitude of which can be explained by the competition of these intermolecular bonds with the rather weak self-association bonds in the secondary chains of water.     

Signatures andS-discrete lattice-ordered groups

The central theme of this article is the approximation of lattice-ordered groups (l-groups) first by Specker groups and, subsequently, by the so-calledS-discretel-groups. The sense of these approximations is made precise via the notion of a signature, defined below, and by that ofa ^*-subgroups. Sample result: ifG is a projectablel-group then it has anl-subgroupH which is Specker and for which the mapPPH defines a boolean isomorphism between the algebras of polars ofG andH.Presented by L. Fuchs.This article was written while this author was a Stouffer Visiting Professor at the University of Kansas. He wishes to thank the members of the Mathematics Department of that institution for their hospitality.     

The dispersion of the Hammersley Sequence in the unit square

The notion of dispersion, a measure of denseness of sequences, plays an important role in quasi-Monte Carlo optimization. In this paper, we obtain an explicit formula for the dispersion of an important low dispersion sequence, namely the Hammersley Sequence in the unit square. The dispersiond _M of theM points of this sequence, whereM=2^N withN a positive integer is given by $$d_M = \frac{{\sqrt {2M - 2\sqrt M + 1} }}{M},if N is even, d_M = \frac{{\sqrt {\left( {5/2} \right)M - \sqrt {8M} + 1} }}{M},if N is odd.$$ .     

Photochemistry of artificial photosynthetic reaction centers in liquid crystals probed by multifrequency EPR (9.5 and 95 GHz)

Photoinduced charge separation and recombination in a carotenoid-porphyrin-fullerene triad C-P-C(60)(1) have been followed by multifrequency time-resolved electron paramagnetic resonance (TREPR) at intermediate magnetic field and microwave frequency (X-band) and high field and frequency (W-band). The electron-transfer process has been characterized in the different phases of two uniaxial liquid crystals (E-7 and ZLI-1167). The triad undergoes photoinduced electron transfer, with the generation of a long-lived charge-separated state, and charge recombination to the triplet state, localized in the carotene moiety, mimicking different aspects of the photosynthetic electron-transfer process. Both the photoinduced spin-correlated radical pair and the spin-polarized recombination triplet are observed starting from the crystalline up to the isotropic phase of the liquid crystals. The W-band TREPR radical pair spectrum has allowed unambiguous assignment of the spin-correlated radical pair spectrum to the charge-separated state C(.+)-P-C(60)(.-). The magnetic interaction parameters have been evaluated by simulation of the spin-polarized radical pair spectrum and the spin-selective recombination rates have been derived from the time dependence of the spectrum. The weak exchange interaction parameter (J = +0.5 +/- 0.2 G) provides a direct measure of the dominant electronic coupling matrix element V between the C(.+)-P-C(60)(.-) radical pair state and the recombination triplet state (3)C-P-C(60). The kinetic parameters have been analyzed in terms of the effect of the liquid crystal medium on the electron-transfer process. Effects of orientation of the molecular triad in the liquid crystal are evidenced by simulations of the carotenoid triplet state EPR spectra at different orientations of the external magnetic field with respect to the director of the mesophase. The order parameter (S = 0.5 +/- 0.05) has been evaluated.     

FORTY YEARS OF BLUE-LIGHT RESEARCH AND NO ANNIVERSARY

The status of near- UV/blue-light research is described and critically assessed. It is argued that the generally accepted proposition of flavins acting as near- UV/blue-light photoreceptors is reasonable, but that also other pigments, specifically pteridines and pterins, should be considered. In view of the fact that a receptor assay, applicable to any organism and near-UV/blue-light reaction, is not yet at hand, caution appears to be indicated as to what one can accept as a reasonable “criterion” for the involvement of any proposed photoreceptor pigment.     

Conotoxins as research tools and drug leads

The complex mixture of biologically active peptides that constitute the venom of Conus species provides a rich source of ion channel neurotoxins. These peptides, commonly known as conotoxins, exhibit a high degree of selectivity and potency for different ion channels and their subtypes making them invaluable tools for unravelling the secrets of the nervous system. Furthermore, several conotoxin molecules have profound applications in drug discovery, with some examples currently undergoing clinical trials. Despite their relatively easy access by chemical synthesis, rapid access to libraries of conotoxin analogues for use in structure-activity relationship studies still poses a significant limitation. This is exacerbated in conotoxins containing multiple disulfide bonds, which often require synthetic strategies utilising several steps. This review will examine the structure and activity of some of the known classes of conotoxins and will highlight their potential as neuropharmacological tools and as drug leads. Some of the classical and more recent approaches to the chemical synthesis of conotoxins, particularly with respect to the controlled formation of disulfide bonds will be discussed in detail. Finally, some examples of structure-activity relationship studies will be discussed, as well as some novel approaches for designing conotoxin analogues.     

Synthesis of a Tetracyclo [4.4.0.02,4.03,8]decanone via Intramolecular Reductive Coupling

The reduction of cis-4 a-methyl-1,2,4a,7,8,8 a-hexahydronaphthalene-2,7-dione ( 1 ) was studied by cyclic voltammetry and product analysis. On a preparative scale, 6-hydroxy-3-methyltetracyclo[4.4.0.0^2,4.0^3,8]decan-10-one ( 2 ) was obtained in 22% yield via an intramolecular hydrodimerization/aldol reaction sequence. The CV. results (Hg, DMF) suggest that the cyclopropane ring is formed after the first electron transfer by coupling of the anion radical with the second C. C-double bond.     

Analysis of conformational equilibria in aplidine using selective excitation 2D NMR spectroscopy and molecular mechanics/dynamics calculations

Aplidine (dehydrodidemnin B), a natural product with potent antitumor activity currently in multicenter phase II clinical trials, exists in DMSO as a mixture of four slowly interconverting conformations in a ratio of 47:33:13:7. NMR spectroscopy shows that these arise as a consequence of cis/trans isomerization about the NMe-Leu(7)-Pro(8) and Pro(8)-Pyr amide bonds of the molecule's side chain. Two major conformations account for 47% and 33% of the total population, a ratio of 60:40 between the two. They correspond to the cis- and trans-isomers, respectively, about the Pro(8)-Pyr amide bond. Two minor conformers arise as a consequence of similar isomerism about the Pro(8)-Pyr amide bond, but in structures in which the NMe-Leu(7)-Pro(8) amide bond is cis rather than trans. These account for approximately 13% and 7% of the total population, corresponding to a ratio of 65:35 cis/trans, respectively. Molecular dynamics simulations show that the three-dimensional structures of all four conformational isomers are similar in the macrocycle and that all are essentially unchanged with respect to the macrocycle of didemnin B. Significant differences in the conformation of the molecule's side chain are, however, observed between major and minor pairs. Analysis of hydrogen-bonding patterns shows that each major conformer exhibits a beta-turn like structure and is stabilized by hydrogen bonding between a different carbonyl group of the pyruvyl unit of the molecule's side chain and the NH of the Thr(6) residue. The minor isomers have a cis-amide bond between the NMe-Leu(7) and Pro(8) residues that obliges the side chain to adopt an extended disposition where hydrogen bonding to the macrocycle is absent. These results suggest that the ability of the molecule's side chain to adopt a beta-turn-like conformation may not be a prerequisite for biological activity in the didemnins and that conformations having an extended side-chain may play a role in the biological activity of aplidine.     

Programmable gate delayed ion mobility spectrometry-mass spectrometry: a study with low concentrations of dipropylene-glycol-monomethyl-ether in air

The concept of using a short ionisation event, in this case a pulsed corona discharge, in conjunction with programmed gate delay is described. This technique is proposed for the selective study of different ionisation processes within the reaction region of an ion mobility spectrometer. The utility of such an approach was tested in a study of the ionisation of dipropylene-glycol-monomethyl-ether (DPM); a compound commonly used to test the operation of ion mobility spectrometers. Dipropylene-glycol-monomethyl-ether at a concentration of 113 microg m(-3) in air, with a water level of 75 mg m(-3) in air, was analysed using a switchable, high resolution ion mobility spectrometer, operating in the positive mode at 40 degrees C at ambient pressure. The ion mobility spectrometer was fitted with a pulsed corona discharge ionisation source, doped with ammonia at a concentration of 1.3 mg m(-3) in the reaction region, and interfaced to a mass spectrometer. Synchronisation of the ionisation event to the operation of the shutter grids for the drift region enabled different parts of the product ion population to be injected into the drift tube, and programming the gate delays produced a map of the gate delay verses drift time response surface. Ammonium bound dipropylene-glycol-monomethyl-ether was observed, [(DPM)NH4]+ (m/z 166) as well as the ammonium bound dimer [(DPM)2NH4]+ (m/z 314), the same as those observed with a 63Ni source. Two other species were also observed, but their molecular identity was not elucidated. One of them m/z 146, also observed with 63Ni, formed ammonium bound ions [(m/z 146)NH4]+ (K0= 1.49 cm2 V(-1) s(-1)), ammonium bound dimer ions [(m/z 146)2NH4]+(K0= 1.18 cm2 V(-1) s(-1)) and a mixed cluster ion with DPM [(m/z 146)(DPM)NH4]+(K0= 1.18 cm2 V(-1) s(-1)); while the other, m/z 88 a decomposition product, formed ammonium bound monomer [(m/z 88)NH4]+(K0= 1.68 cm2 V(-1) s(-1)), dimer ions [(m/z 88)2NH4]+(K0= 1.40 cm2 V(-1) s(-1)) and a mixed cluster ion containing DPM and ammonium, [(DPM)(m/z 88)2NH4]+(K0= 1.40 cm2 V(-1) s(-1)). The assignment of responses to these ions required the additional dimensionality in the data provided from the gate delay studies. The relationships evident in the programmable gate delay data enabled these ions to be differentiated from alternative assignments of possible nitrogen clusters, formed at the interface of the mass spectrometer.