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.     

Duplex oligomers defined via covalent casting of a one-dimensional hydrogen-bonding motif

Hydrogen-bonded tapes comprised of monomeric molecular precursors are used to define structural parameters for the design of related oligomers encoded with predetermined modes of assembly. Application of this "covalent casting" strategy vis-à-vis the one-dimensional H-bonding motif expressed by 2-amino-4,6-dichlorotriazine has enabled the design of high-affinity duplex molecular strands. Dimeric, trimeric, and tetrameric duplex oligomers are prepared through an iterative synthetic protocol involving sequential homologation of the oligo(aminotriazine). The mode of assembly and interstrand affinity of homologous oligomers are established in solution by (1)H NMR dilution experiments, isothermal titration calorimetry (ITC), vapor pressure osmometry (VPO), cross-hybridization experiments involving the analysis of dye-labeled strands via thin-layer chromatography (TLC), and in the solid state by X-ray crystallographic analysis. Binding free energy per unimer (-Delta G degrees/n) increases significantly upon extension from monomer to dimer to trimer, signifying a strong positive cooperative effect. Nanomolar binding affinity (K(d) = 1.44 +/- 0.50 nM) was determined for the duplex trimer by ITC in 1,2-dichloroethane at 20 degrees C. In-register duplex formation is not observed for the tetramer, which appears to adopt an alternative binding mode. These data give insight into the structural and interactional features of the oligomers required for high-affinity, high-specificity binding and define a platform for the design of second-generation systems and related duplex strands for use in nanoscale assembly.     

Nonlinear rheology of highly entangled polymer solutions in start‐up and steady shear flow

Orientation angle and stress‐relaxation dynamics of entangled polystyrene (PS)/diethyl phthalate solutions were investigated in steady and step shear flows. Concentrated (19 vol %) solutions of 0.995, 1.81, and 3.84 million molecular weight (MW) PS and a semidilute (6.4 vol %) solution of 20.6 million MW PS were used to study the effects of entanglement loss on dynamics. A phase‐modulated flow birefringence apparatus was developed to facilitate measurements of time‐dependent changes in optical equivalents of shear stress (n₁₂ ≈ Cσ) and first normal stress differences (n₁ = n₁₁ ? n₂₂ ≈ CN₁) in a planar‐Couette shear‐flow geometry. Flow birefringence results were supplemented with cone‐and‐plate mechanical rheometry measurements to extend the range of shear rates over which entangled polymer dynamics are studied. In slow (τ > ) steady shear‐flow experiments using the ultrahigh MW polymer sample (20.6 × 10⁶ MW PS), steady‐state n₁₂ and n₁ results manifest unusual power‐law dependencies on shear rate [n_12,ss ～ ^0.4 and n_1,ss ～ ^0.8]. At shear rates in the range τ < < τ, steady‐state orientation angles χ_SS are found to be nearly independent of shear rate for all but the most weakly entangled materials investigated. For solutions containing the highest MW PS, an approximate plateau orientation angle χ_p in the range 20–24° is observed; χ_p values ranging from 14 to 16° are found for the other materials. In the start‐up of fast steady shear flow (γ˙ ≥ τ), transient undershoots in orientation angle are also reported. The molecular origins of these observations were examined with the help of a tube model theory that accommodates changes in polymer entanglement density during flow. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2275–2289, 2001     

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.     

Bis(N,N′-disalicylidene-3,4-phenylenediamine-1-ethylbenzoato)zirconium(IV), an eight-coordinate chelate with linear polymerization possibilities

Synthesis of the Schiff-base complex bis(N,N′-disalicylidene-3,4-phenylenediamine-1-ethylbenzoato)zirconium(IV), which has two, linearly disposed, uncoordinated ester groups, has been accomplished from the reaction of a zirconium alkoxide with the new Schiff ligand N,N′-disalicylidene-3,4-phenylenediamine-1-ethylbenzoate. The ligand itself was isolated in two forms, yellow and orange, which are believed to be tautomers based on infrared data. Elemental analyses, IR, NMR, and UV-Visible data are included for all new compounds, as well as mass spectral data for the complex. Broadening of ¹H NMR resonances in the complex spectrum, relative to TMS and ethanol of solvation resonances, may be indicative of a slow molecular motion. Preliminary attempts to polymerize the complex with aromatic amines failed, however, due to decomposition of the metal chelate unit at the high temperatures (300°C) required.     

Alkaloid studies—XXX Isolation and constitution of three new Aspidosperma alkaloids: Cylindrocarpine, cylindrocarpidine and pyrifolidine

The isolation and structure elucidation of three new Aspidosperma alkaloids is reported. Cylindrocarpine (II) and cylindrocarpidine (XI) are noteworthy in that they represent analogs of aspidospermine (I) in which the latter's angular ethyl group has been replaced by an angular acetic acid methyl ester function. Furthermore, cylindrocarpine (II) represents the first naturally occurring dihydroindole with a N-cinnamoyl residue. Pyrifolidine (XII) has been shown to be the antipode of O-methylaspidocarpine (XV) and thus bears an enantiomeric relationship at all four asymmetric centers to (-)-aspidospermine (I). Attention is drawn to the possible biogenetic implications of this observation.     

The boat conformation of α-parachloral. Notes on the revised structures of α- andβ-parachloral

The boat conformation of-parachloral [2,4,6-tris(trichloromethyl)-1,3,5-trioxane] has been confirmed by X-ray crystallography. Evidence for a chair conformation based upon calculations of dipole moments has been shown to be unreliable, but the possibility of this existing in solution has been studied by¹H and¹³C NMR spectroscopy. The X-ray structures of both- and-parachloral have been redetermined.