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.     

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.     

Hypericin-Induced Phototoxicity in Cultured Fibroblasts and Swine Erythrocytes

Hypericin is a naturally occurring photosensitizer, whose presence in plants has been responsible for cutaneous phototoxicity in grazing animals. The photosensitizing properties of this agent have recently been exploited in models for anti-tumor and anti-viral activity. The cytotoxicity of hypericin and light was assessed in 3T3 mouse fibroblasts using the MTT [3-(4, 5-dimethylthiazol-2-yl)-2, 5-diphenyl tetrazolium bromide)] assay and the lactate dehydrogenase (LDH) leakage assay. Membrane damage was assessed in swine erythrocytes using hemolysis, potassium (K⁺) leakage and formation of lipid hydroperoxides. Concentration- and light-dependent decreases in fibroblast viability were seen starting at hypericin concentrations of 1.25 μM and light power flux levels of 24 J/cm² using a visible light source and at 0.417 μM hypericin and a similar light dose using a solar simulator, No LDH leakage was observed at hypericin concentrations up to 30 μM and visible light up to 144 J/cm². Light-and/or concentration-dependent increases in hemolysis, K⁺ leakage and formation of lipid hydroperoxides in red blood cell (RBC) membranes were observed, but at concentrations and light doses much greater than those required to induce cytotoxicity in fibroblasts. Lipid peroxidation and hemolysis occurred at 15 μM hypericin and 24 J/cm² (visible light source). Potassium ion leakage occurred at concentrations and light levels as low as 5 μM and 12 J/cm² or 15 μM and 4.8 J/cm² (visible light source) but was still a less sensitive indicator than fibroblast cytotoxicity. Evidence for both type I and type II reactions was shown in RBC membranes by TLC analysis of cholesterol products. In the absence of light, hypericin appears to be relatively nontoxic in the models tested.     

Nitrile ylide dimerization: investigation of the carbene reactivity of nitrile ylides

A series of novel hexaaryl diazatrienes 5 ("nitrile ylide dimers") were synthesized directly from the corresponding diaryl ketimines 12 and dichlorotoluenes 13 in a facile one-pot synthesis. The carbene character of the nitrile ylides was investigated by varying the substituents on the aromatic ring adjacent to the carbene center. The isolation of the corresponding carbene dimers as stable crystalline materials with absorption maxima (lambda(max)) from 363 to 422 nm was shown to be promoted by the absence of strongly electron-withdrawing substituents. The crystal structures indicate that the E-isomers were isolated when phenyl, 3-methylphenyl, and 3-chlorophenyl substituents are present at the carbene carbon; the Z-isomer was isolated when the more sterically hindered 2,4,6-trimethylphenyl substituent (Mes) is present. The (1)H NMR spectra of the E-isomers demonstrate the nonequivalence of the aromatic rings, in which two of the aromatic rings of the imine moiety are pseudoaxial and the remaining aromatic rings are pseudoequatorial. The reactions proceed via the intermediate nitrile ylides 1 generated by the base-promoted 1,1-elimination of HCl from the intermediate chloroimine 14. The nitrile ylide was also generated by 1,3-elimination of HCl from the imidoyl chloride 18, confirming common pathways via the nitrile ylide as the dimer products obtained from these different routes were identical. The strongly electron-withdrawing 4-nitrophenyl substituent promotes the linear carbanion character of the 1,3-dipole and no dimer is formed.