Optimal Harvesting in an Age-Structured Predator–Prey Model

We investigate optimal harvesting control in a predator–prey model in which the prey population is represented by a first-order partial differential equation with age-structure and the predator population is represented by an ordinary differential equation in time. The controls are the proportions of the populations to be harvested, and the objective functional represents the profit from harvesting. The existence and uniqueness of the optimal control pair are established.     

Decay of solutions of ordinary differential equations

We investigate the rate of decay of eigenfunctions of Schrödinger equations using a perturbation method which consists of making a perturbation B of the operator L of the form B[y]=L[y]−(g⁻¹Lg)[y], where g is an appropriately chosen function. In our theory we allow B to be either relatively compact or satisfy a certain boundedness condition. We give some examples which apply the results of our main theorems coupled with recent work on the relative boundedness and compactness of differential operators.     

Radiotracer studies of the antitumor metallocene molybdocene dichloride with biomolecules

Neutron irradiation of Cp₂MoCl₂ for 24 h afforded the radiotracer Cp₂⁹⁹MoCl₂ which was characterised by UV–Vis spectroscopy and thin layer chromatography. Binding experiments with the thiol containing protein human serum albumin (HSA) or calf thymus DNA, were monitored for ⁹⁹Mo using a gamma counter. Under the conditions investigated, molar ratios of binding of 0.2:1 (Cp₂MoCl₂:DNA) and 9.4:1 (Cp₂MoCl₂:HSA) were calculated. The results are consistent with in vitro coordination studies that have shown strong preferential interaction of Cp₂MoCl₂ with thiols versus other donor sites in biomolecules including DNA.     

Permeability of N2, Ar,He, O2, and CO2 through as‐extruded amorphous and biaxially oriented polyester films: Dependence on chain mobility

For as‐extruded amorphous and biaxially orientated polyester films based on poly(ethylene terephthalate), poly(ethylene naphthalate), and copolymers containing poly(ethylene terephthalate) and poly(ethylene naphthalate) moieties, permeability, diffusion, and solubility coefficients are interpreted in terms of chain mobility. The influence of polymer morphology is determined by comparison of the data for as‐extruded amorphous sheets and materials produced with different biaxial draw ratios. The crystallinities of the samples were assessed using differential scanning calorimetry and density measurements. Changes in mobility at a molecular level were investigated using dielectric spectroscopy and dynamic mechanical thermal analysis. The study, in conjunction with our earlier work, leads to the conclusion that the key to understanding differences in gas transport is the difference in local chain motions rather than in free volume. This was illustrated by the permeability results for He, Ar, N₂, and O₂ in the range of polyesters. However, the permeability of CO₂ was found to require alternative explanations because of polymer–penetrant interactions. For biaxially oriented samples, the differences in diffusivity are not only due to differences in local chain motions, but also additional constraints resulting from the increased crystallinity and chain rigidity—which also act to hinder segmental mobility. The effectiveness of the reduction in permeability in the biaxially oriented films is consequently determined by the ability of the polymer chains to effectively align and form crystalline structures. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2916–2929, 2004     

Solving a class of multiplicative programming problems via c-programming

In this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the minimization of the product of several convex functions on a convex set which was studied recently by Kunoet al. [3]. It is shown that these problems are typical composite concave programming problems and thus can be handled elegantly by c-programming [4]–[8] and its techniques.     

Practical syntheses of [1,3,5]‐triazine dendritic molecules on solid supports

A practical and divergent synthesis of supported [1,3,5]‐triazine dendritic molecules on Wang resin, PEGA resin, SynPhase? Lanterns, and silica gel is described. The alkylamine linkers used allow derivatization with functionality for both synthetic (e.g., supported reagent and scavenger activity) and chemical biology applications. The use of supported intermediates allows differentiation of symmetric linkers without the need for protecting group chemistry. The synthetic route uses inexpensive, readily available starting materials in a straightforward and scaleable strategy. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2248–2259, 2006     

Synthesis of some substituted 3-alkenyl-1-phenylpyrazoles

The regioselective synthesis of new 3-alkenyl-1-phenylpyrazoles 4 from the reaction of phenylhydrazine with 2,3-dihydro-4H-pyran-4-ones 1 is described.     

Synthesis of 3-formyltetronic acid and enamine derivatives

The first reported synthesis of 3-formyltetronic acid and its conversion to enamine derivatives is described. 3-Dimethylaminomethylene-2,4-dioxotetrahydrofuran derivatives were also prepared by treatment of tetronic acids with dimethylformamide diethyl acetal. Nmr spectral studies are included.     

Direct optical emission spectroscopy of liquid analytes using an electrolyte as a cathode discharge source (ELCAD) integrated on a micro-fluidic chip

Atomic emission detection of metallic species in aqueous solutions has been performed using a miniaturised plasma created within a planar, glass micro-fluidic chip. Detection was achieved using an Electrolyte as a Cathode Discharge source (ELCAD) in which the sample solution itself is used as the cathode for the discharge. To realise the ELCAD technique within a micro-fluidic device, a parallel liquid-gas flow was set up in a micro-channel and a glow discharge ignited between the flowing liquid sample surface and a metal wire anode. The detection of copper and sodium was achieved, using atmospheric pressure air as a carrier gas, by observation of atomic emission lines of copper at 324 nm, 327 nm, 511 nm, 515 nm and 522 nm and an atomic emission line of sodium at 589 nm using a commercially available miniaturised spectrometer. A total electrical power of less than 70 mW was required to sustain the discharge. A semi-quantitative, absolute detection limit of 17 nmol s(-1) was obtained for sodium with a sample flow rate of 100 microL min(-1) and an integration time of 100 ms in air at atmospheric pressure. The volume required for such detection is approximately 170 nL. Further analysis was performed with an Echelle spectrometer using both argon and air as a carrier gas. The geometry and flow rates used demonstrate the feasibility of integrating such micro-plasmas into other micro-fluidic devices, such as miniaturised CE devices, as a method of detection. The potential for using such micro-plasmas within highly portable miniaturised systems and mu-TAS devices is presented and discussed.     

The initiation of polymerization by organoaluminium amides

Two organoaluminium amides have been used to initiate the polymerizations of methyl methacrylate, acetaldehyde and n-butyraldehyde. Methyl methacrylate polymerized through the vinyl function to give amorphous products. The aldehydes reacted through the carbonyl group at low temperatures with high degrees of stereospecificity to give polymers with substantial crystallinity. The molecular weight of the polyacetaldehyde is very high.