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     

On the diffusion field in the neighborhood of two identical spheres

Summary Under steady state conditions the reduction in the diffusive flux into a sphere due the presence of a neighboring, identical sphere is calculated. Taking the flux into a sphere as 1 when the particles are at infinite separation, the flux decreases to a minimum value of 0.693 when the spheres are touching.

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Zusammenfassung Unter stationären Bedingungen wird die Abnahme des Diffusionsflusses in eine Kugel, bedingt durch eine benachbarte identische Kugel, berechnet.Wird der Diffusionsfluß in eine Kugel gleich 1 gesetzt, wenn die Partikel unendlich weit voneinander entfernt sind, so nimmt der Diffusionsfluß auf einen Minimalwert von 0,693 ab, wenn sich die Kugeln berühren.

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With 2 figures     

Umsetzung von hydrobromiertem 1,4-Polybutadien mit lithiumorganischen Verbindungen

Ohne ZusammenfassungMit 1 Abbildung und 1 Tabelle     

Eine semiempirische Gleichung zur Beschreibung des Lösungsmitteleinflusses auf Statik und Kinetik chemischer Reaktionen. Teil I

A model has been developed for calculating the enthalpy, entropy and free energy change associated with the creation of cavities in a liquid the size of which corresponds to the volume occupied by a solvent molecule. The molar enthalpy change H _cav equals the molar enthalpy of vaporization of the liquid, the free energy change G _cav is given by G _cav=–RT ln (V _m ·p _eq /RT) (V _m =molar volume,p _eq =equilibrium vapor pressure) and is related to the standard free energy of vaporization. This relationship provides an estimate of the free energy of cavity formation required to accomodate a substrate in the liquid. It has been shown, that the free energy of solvation of a substrate can be dissected into different contributions accounting for (1) the concentration dependence of partial molar free energy quantities, (2) the formation of holes in the solvent, (3) the existence of specific, short range solute-solvent interactions and (4) the dielectric polarization of the medium. Application of this concept leads to an equation of the general form G ^S –G ^R =a(DN ^S –DN ^R )+b(AN ^S –AN ^R )+c(G _vp ^oS –G _vp ^oR ), where G represents the free energy of reaction or activation,DN the donor number,AN the acceptor number and G _vp ^o the standard free energy of vaporization of a solventS and a reference solventR, resp.

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Mit 3 Abbildungen     

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.     

Untersuchung der Temperaturabhängigkeit derg ik -Tensoren von Polyäthyleneinkristallen

Zusammenfassung Es wurden die Kristallitgröße und die Änderungen der parakristallinen Gitterstörungen aus den Linienbreiten des Röntgenweitwinkeldiagramms von lösungskristallisiertem linearem Polyäthylen bei den Temperaturen 15°K, 73°K, 173°K und Zimmertemperatur bestimmt. Es wurde eine Zunahme der Gitterstörungen mit fallender Temperatur gefunden.

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Summary The crystallite size and the paracrystalline distortions in polyethylene single crystals were evaluated by the measurement of the linewidth in the X-ray wide angle diagram at four different temperatures (15°K, 73°K, 173°K and 297°K). An increase of the lattice distortions with decreasing temperature was found.

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Mit 3 Abbildungen

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Vorgetragen auf der Arbeitssitzung des Fachausschusses Physik der Hochpolymeren in der Frühjahrstagung 1970 des Regionalverbandes Hessen-Mittelrhein-Saar der Deutschen Physikalischen Gesellschaft in Darmstadt, 10.–13. März 1970.     

Die Schmelzdiagramme der Systeme CsN3/Zn(N3)2 und KN3/Zn(N3)2

The phase diagrams of the systems CsN₃/Zn(N₃)₂ and KN₃/Zn(N₃)₂ have been obtained employing the microscopic technique ofL. Kofler andA. Kofler. Within the system CsN₃/Zn(N₃)₂ three eutectics at 148°C, 142°C, and 210°C were found. Besides Cs₂Zn(N₃)₄, melting incongruently in the interval 153°C to 170°C, there exist two further compounds of the most probable composition Cs₃Zn₂(N₃)₇ and CsZn₂(N₃)₅, melting congruently at 170°C and 210°C, resp. In the system KN₃/Zn(N₃)₂ there exist two eutectics at 203°C and 172°C and two compounds, one of them, i.e. K₂Zn(N₃)₄, melting congruently at 206°C, the other one, with composition KZn₃(N₃)₇ or KZn₄(N₃)₉, melting incongruently at 210°C.

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Mit 8 Abbildungen

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Herrn Professor Dr.Heribert Grubitsch zum 70. Geburtstag gewidmet.