Passages through resonance in weakly nonlinear systems

A method of determining asymptotic expansions for weakly couplednonlinearly perturbed systems of harmonic oscillators with slowlyvarying frequencies is presented. In an example with two oscillators,each one experiences a separate resonance passage that producesa first-order amplitude change. Simultaneously, second-orderadjustments occur to both oscillators. The determination isachieved by carrying the calculations to third order.     

ON THE IMPULSIVE BEVERTON–HOLT EQUATION AND EXTINCTION CONDITIONS IN POPULATION DYNAMICS

Abstract This paper is devoted to investigate extinction and nonextinction conditions of the extended Beverton–Holt equation (BHE) for dynamics of populations in Ecology when potential discontinuities at sampling points are included in the model. The proposed model is described by means of four sequences of parameters. Two of them are the intrinsic growth rate and the carrying capacity sequences which are included in the basic BHE model. The other two ones, namely, the harvesting (i.e., the hunting or fishing quota) and the internal consumption (which can include positive and negative migrations in the considered population habitat) sequences are included to parameterize the model discontinuities. Such discontinuities are related to impulses in the corresponding continuous‐time logistic equation. The obtained results establish how the harvesting quota and/or the internal consumption has to be fixed to guarantee the population nonextinction or, eventually, its extinction. Finally, some controllability results related to the search of a carrying capacity sequence such that the solution of the proposed impulsive BHE tracks a reference one are obtained.     

磺基水杨酸修饰电极联吡啶钌电化学发光体系测定可待因的研究

基于磷酸可待因对联吡啶钌在该电极上的电化学及其发光行为的增敏作用,建立了一种直接测定磷酸可待因的电化学发光新方法。在最佳实验条件下,磷酸可待因在1.0×10-4～4.0×10-6mol/L和4.0×10-6～2.0×10-7mol/L与相对发光强度呈线性关系,检出限为1.0×10-7mol/L(S/N=3)。连续测定4.0×10-7mol/l磷酸可待因5次,发光强度的RSD为2.7%。方法用于模拟尿样中磷酸可待因的测定,结果满意。     

Reduction of oxygen and hydrogen peroxide on electrodes with adsorbed monolayer of aliphatic compounds

Cathodic reduction of oxygen and hydrogen peroxide on amalgamated platinum electrodes, which are coated with monolayers of long-chain aliphatic compounds cetyl alcohol (CA) and stearic acid (SA), is retarded as compared with the same reactions on clean mercury (or amalgam) surface. The oxygen reduction kinetics differ from that on mercury. The difference is explained by that oxygen diffuses into the monolayer and is reduced in it at a certain distance from the metal surface and only at the limiting current the reaction is forced onto the monolayer surface. In contrast to the oxygen reduction, the hydrogen peroxide reduction kinetics on electrodes with SA and CA monolayers is much closer to that on mercury, but with some quantitative distinctions. All results favor the H₂O₂ reduction at the monolayer/solution interface. The difference in the behavior of O₂ and H₂O₂ is explained by different polarity of these molecules: it is significantly more difficult to penetrate the hydrocarbon monolayer for polar H₂O₂ molecule than for nonpolar O₂ molecule.     

An updated search of steady TeV γ-ray point sources in northern hemisphere using the Tibet air shower array

Using the data taken from Tibet Ⅱ High Density (HD) Array (1997 February--1999 September) and Tibet-Ⅲ array (1999 November--2005 November), our previous northern sky survey for TeV γ-ray point sources has now been updated by a factor of 2.8 improved statistics. From 0.0° to 60.0° in declination (Dec) range, no new TeV γ-ray point sources with sufficiently high significance were identified while the well-known Crab Nebula and Mrk421 remain to be the brightest TeV T-ray sources within the field of view of the Tibet air shower array. Based on the currently available data and at the 90% confidence level (C.L.), the flux upper limits for different power law index assumption are re-derived, which are approximately improved by 1.7 times as compared with our previous reported limits.     

Effect of the Length of the Hydrocarbon Chain of Adsorbed Aliphatic Acids and Alcohols on the Electron Transfer Probability

The kinetics of redox reactions of hemin adsorbed over a monolayer of long-chain aliphatic alcohols, such as cetyl alcohol (C₁₆) and stearyl alcohol (C₁₈), and stearic (C₁₈), behenic (C₂₂), and melissic (C₃₀) acids is studied. The reaction inhibition on an alcohol monolayer (0.34 orders of magnitude per methylene group) is close to that reported in the literature. The inhibition on an acid monolayer is substantially smaller (0.2 to 0.07 orders), which is attributed to irregularity of the structure of the monolayer of carboxylic acids caused by the dissociation of carboxyl groups, especially in alkaline solutions. Violation of a regular structure of an acid monolayer is confirmed by a considerable irreversible increase in the electrode capacitance in alkaline solutions and by a decrease in the ohmic resistance of a monolayer of the longest saturated acid, i.e. triacontanoic acid. For a regular monolayer structure, when the length of an extended hydrocarbon chain defines the barrier thickness (alcohols), experimental data accord with predictions of the superexchange theory, which holds that the probability of a long-distance electron transfer depends on the length of the chain of covalent bonds over which the superexchange occurs. If the film structure is irregular (film thickness decreases with increasing hydrocarbon chain length (acids)), the packing of these bonds becomes essential, which allows the electron not to pass over all the bonds but to hop onto a nonbonded chain link nearby. The obtained data indicate that the electron transfer probability is defined by the electron's path, rather than by the barrier's geometrical thickness.     

Effect of the aqueous–organic solvent structure on the cobalticenium–cobaltocene redox potential: The redox couple as a basis for determination of the single ion transfer energies

The redox potentials of the cobalticenium–cobaltocene couple have been determined voltammetrically in several aqueous–organic mixed solvents. The cosolvents studied were dimethylformamide, acetone, 1,4-dioxane (all three disrupting the 3D network of the water’s hydrogen bonds), propylenecarbonate (at low content structure-making, at higher – structure-breaking), and glycerol that incorporates into the 3D network. Cobalticenium spectra demonstrate the absence of ion pairs and solute–cosolvent complexes. The liquid junction potentials water-mixed solvent in the range of the cosolvent concentrations studied are small. At equal volume fractions of structure-breaking cosolvents the shifts of redox potential relative to water are similar. The potential shifts are more than by order of magnitude higher than those corresponding to the change of the mixed solvent’s dielectric constant. This is explained as due to disruption of the water hydrogen bonded structure, and disappearance therefore of the water anomalous dielectric response. The cobalticenium redox potential in the hypothetic “structureless” water was estimated as being ∼70 mV more positive than in real water. This is the potential that should be compared directly with the data for practically unstructured aprotic solvents.     

Hydrogen peroxide reduction on amalgamated platinum electrodes covered with a monolayer of stearic acid

The reduction of hydrogen peroxide and, for comparison, oxygen on an amalgamated platinum electrode covered with a monolayer of stearic acid is studied by methods of polarization curves and impedance spectroscopy. In contrast with the oxygen reduction, the reduction of dissolved hydrogen peroxide occurs predominantly on the monolayer surface, rather than inside it. This is explained by the difficulty of penetration of the polar molecule of hydrogen peroxide into hydrocarbon environment.