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.     

Fabrication and transport properties of multiwall carbon nanotube crossroads

A multiwall carbon nanotube crossroads has been fabricated by a manipulation technique using a glass microcapillary, and the low temperature transport properties investigated. The two-terminal conductance of an individual tube shows Tomonaga–Luttinger liquid behavior G∝T^α at high temperature and dI/dV ∝V ^α at low temperature. However, no evidence of such a power-law behavior is obtained in the four-terminal conductance at the junction, where the conductance shows an almost metallic behavior ‘corrected’ by weak localization. Weak localization would essentially appear in electron states at the junctions of MWNTs.     

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.