ON THE OPTIMAL POLICY FOR COMBINED HARVESTING OF INDEPENDENT SPECIES

By a combination of analytical reasoning and numerical experiment it is demonstrated that, for the combined harvesting of two ecologically independent species which grow logistically and are harvested at a rate proportional to both stock level and effort, there is a unique attainable equilibrium which yields positive revenue and to which the approach path satisfies all of Pontryagin's necessary conditions for maximizing the harvest's present value. A simple feedback law governs this approach and is conjectured to be the optimal policy. On that basis, criteria are found for the survival of the less productive species, as a function of the system parameters and initial stocks. An economic interpretation of the equilibrium is also given.     

Periodic behavior of the stochastic Brusselator in the mean-field limit

Summary We prove a propagation of chaos result for the mean-field limit of a model for a trimolecular chemical reaction called Brusselator. Then we show that the pair of nonlinear (i.e. law-dependent) stochastic differential equations describing the evolution of the concentration of the molecules at a given site in the mean field limit has a solution with a periodic law (in t). Finally we identify the limit and establish a central limit theorem for the periodic law in the case where the noise tends to zero.Part of this work was performed while on leave at the Department of Mathematics and Statistics, Carleton University, Ottawa, Canada and supported by NSERC operating grants of M. Csörgö and D. Dawson     

Liposomes as signal amplification reagents for bioassays in microfluidic channels

Liposomes with encapsulated carboxyfluorescein were used in an affinity-based assay to provide signal amplification for small-volume fluorescence measurements. Microfluidic channels were fabricated by imprinting in a plastic substrate material, poly(ethylene terephthalate glycol) (PETG), using a silicon template imprinting tool. Streptavidin was linked to the surface through biotinylated-protein for effective immobilization with minimal nonspecific adsorption of the liposome reagent. Lipids derivatized with biotin were incorporated into the liposome membrane to make the liposomes reactive for affinity assays. Specific binding of the liposomes to microchannel walls, dependence of binding on incubation time, and nonspecific adsorption of the liposome reagent were evaluated. The results of a competitive assay employing liposomes in the microchannels are presented.     

Substitution and condensation reactions with poly(anilineboronic acid): reactivity and characterization of thin films

Poly(anilineboronic acid) thin films are treated under various conditions to achieve substitution or condensation reactions involving the boronic acid moiety. These reactions are studied with polarization modulated infrared reflection absorption spectroscopy, cyclic voltammetry, and UV-vis spectroscopy. The results suggest the single-step formation of substituted polyanilines, such as poly(hydroxyaniline), halogenated polyanilines, and mercury chloride-substituted polyaniline. A condensation reaction of poly(anilineboronic acid) with cis-diol compounds in aqueous solution, as well as with phenylenebisboronic acid and salycilamide in THF, indicates the formation of boronic esters. The latter reactions appear to be a good entry point for the formation of complex or supramolecular polymer structures.     

A novel synthetic route to substituted pyranoanthocyanins with unique colour properties

Anthocyanins, isolated from natural sources by countercurrent chromatography, were reacted with cinnamic acids bearing at least one electron-donating substituent at the para-position. The resulting pyranoanthocyanins obtained by this simple one-step reaction were much less susceptible to pH shifts and retained their original colour over a wide pH-range. Through reaction with p-dimethylamino cinnamic acid, synthetic malvidin- and cyanidin-based anthocyanins with a unique violet hue were prepared.     

CHEMISTRY OF SINGLET OXYGEN—XXVI. PHOTOOXYGENATION OF PHENOLSy†

Abstract— The aerobic dye-sensitized photooxygenation of monohydric phenols proceeds by way of singlet oxygen under the conditions studied. Various phenols give different proportions of reaction with and quenching of singlet oxygen. Para-substituted 2,6-di-t-butylphenols show a linear correlation between the log of the total rate of singlet oxygen removal and their halfwave oxidation potentials; the same correlation is given for certain phenol methyl ethers. A Hammett plot using s?⁺ gives ρ - 1.72 ± 0.12, consistent with development of some charge in the quenching step. Reaction of photo-chemically generated singlet oxygen with 2,4,6-triphenylphenol gives 2,4,6-triphenylphenoxy radical as an intermediate in singlet oxygen quenching, although no overall reaction occurs. Kinetic analysis indicates that the radical is derived exclusively from the interaction of 2,4,6-triphenylphenol with singlet oxygen. A charge-transfer mechanism for quenching of singlet oxygen by phenols is proposed.     

A CNDO/INDO crystal orbital model for transition metal polymers of the 3d series—basis equations

The crystal orbital formalism in the tight-binding approximation is combined with a recently developed CNDO/INDO model for transition metal species of the 3d series in order to allow band structure calculations on the Hartree-Fock (HF) SCF level for one-dimensional (1D) chains with organometallic unit cells. The band structure approach based on the CNDO and INDO approximation can be used for any atom combination up to bromine under the inclusion of the 3d series. The matrix elements for the tight-binding Hamiltonian are derived for an improved CNDO and INDO framework. The total energy of the 1D chain is partitioned into one-center contributions and into two-center increments of the intracell and intercell type. Semiempirical band structure calculations on simple model systems are compared with available ab initio data of high quality.     

Field desorption mass spectrometry of quaternary ammonium salts: Cluster ion formation

The field desorption mass spectra of salts such as quaternary ammonium and carbenium salts with organic cations in addition to high cation intensities show signals for cluster ions composed of the salt cation + salt molecule, i.e. [C + nM]⁺, n = 1–5, thus allowing determination of the molecular weights of salts. In some cases cluster ions of the type [nM – 1]⁺ are detected. Conditions for the formation of cluster ions are discussed.     

Solution structure of a beta-peptide ligand for hDM2

We recently reported a beta-peptide foldamer, beta53-1, that folds into a 14-helix in aqueous solution, binds the oncoprotein hDM2 with submicromolar affinity, and potently inhibits the interaction of hDM2 with a peptide derived from the activation domain of p53 (p53AD). Here, we present the solution structure of beta53-1 in methanol. Details of the structure illustrate fundamental and novel elements of beta-peptide folding and recognition. These elements include the detailed arrangement of a complex, 14-helix-stabilizing salt bridge on one helical face, and a unique "wedge into cleft" packing interaction along a second. The structure also reveals how a subtle distortion in the beta53-1 14-helix geometry alters the presentation of its recognition epitope, rendering it particularly well suited for alpha-helix mimicry. The solution structure of beta53-1 demonstrates that well folded beta-peptide oligomers can effectively present an extended, highly variable surface that could be used as a general platform for targeting critical protein-protein interfaces.     

Sizes and interfacial free energies of crystallites formed from fractionated linear polyethylene

Replicas of fracture surfaces of fractions of linear polyethylene, which were crystallized at elevated temperatures for extended time periods, were examined by electron microscopy. Striated. lamella-type crystallites were observed for all molecular weights over the range 3.2 × 10³?5.7 × 10⁵. In agreement with Anderson's previous report, for molecular weights of 12,000 or less, the crystallite thicknesses were comparable to the extended chain length. As the molecular weight increased above this level, however, the crystallite sizes increased only slightly and hence at high molecular weights were very much smaller than the extended chain length. From the measured melting temperatures, crystallite interfacial free energies were calculated from the theory for the melting of finite size crystals comprised of chains of finite length. The crystallite interfacial free energy was found to increase with molecular weight. Based on these results, a crystallization process is outlined which allows for the formation of either extended chain crystallites, or crystallites whose size is much smaller than the extended chain length without any change in nucleation mechanism or arbitrary adjustment in growth mechanism with molecular weight.