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.     

Growth of masking as a measure of response growth in hearing-impaired listeners

Growth-of-masking functions were obtained from 19 normal and 5 hearing-impaired listeners using a simultaneous-masking paradigm. When masker and probe frequency are identical, the slope of masking approximates 1.0 for both normal-hearing and impaired listeners. For masker frequencies less than or greater than probe frequency, the slopes for impaired listeners are shallower than those of normals. These findings are consistent with previously reported physiological data (single-fiber rate versus level and AP masking functions) for animals with induced cochlear lesions. Results are discussed in terms of a potential masking technique to estimate the growth of response in normal and impaired ears.     

Temperature Dependence of the Threshold Current and the Lasing Wavelength in 1.3-μm GalnNAs/GaAs Single Quantum Well Laser Diode

Temperature stability of the threshold current and the lasing wavelength is investigated in a 1.3-μm GaInNAs/ GaAs single quantum-well laser. The measured characteristic-temperature was 88 K. The small wavelength shift per change in temperature of 0.35 nm/°C was obtained, indicating the superior lasing-wavelength stability. Therefore, it is shown experimentally that GaInNAs is very promising material for the fabrication of light source with excellent high-temperature performance for optical fiber communications.     

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.