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.     

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.     

Effect of gamma irradiation with or without hot water dip and transportation from Thailand to Canada on nutritional qualities, ripening index and sensorial characteristics of Thai mangoes (Nahng Glahng Wahn variety)

Two lots of mangoes of the Nahng Glahng Wahn variety from Thailand were irradiated at the Thai Irradiation Center (TIC) at 0.49 to 0.77 kGy. Following this, one batch was retained in Thailand while the other was shipped to the Canadian Irradiation Center (CIC) for investigation of the same variables during storage. This way, it was hoped to compare the effects of gamma radiation with hot water dip (HWI) or without (I) before and after transportation on the ripening, vitamin C and vitamin A content and sensory qualities of mangoes. The results indicate that the I and HWI treatments delayed the ripening of the mangoes. The irradiated groups appeared to have a slightly higher content of ascorbic acid on the first day after irradiation than their corresponding controls. The sensory evaluation indicates that the panelists mostly favoured the I and HWI irradiated groups for the overall appearance and texture of whole mangoes and pulp and in taste and palatability of the pulp alone. Transportation stress did not appear to have much of an effect on the ascorbic acid and dehydroascorbic acid levels and the sensorial tests. The mangoes stored and studied in Canada appeared to have a lower vitamin A content.     

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.     

Tetronic acids and derivatives. Part XI . Structure of coupling products of tetronic acids with benzenediazonium sulfate

¹³C Nmr, ¹H nmr and ir parameters of coupling products of tetronic acids (4-hydroxy-5H-furan-2-ones) with benzene diazonium sulfate are only consistent with a phenylhydrazone formulation with an almost equal ratio of the syn and anti configurations. These results contrast with those of coupling products of acyclic 3-ketoesters, existing mainly as anti tautomers, and more sharply with the 3-parabromophenylhydrazone of L-dehydro ascorbic acid, which is exclusively syn.