OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

1H NMR Studies on the Methylation,Protonation, and Hydration Sites in Some Benzo[b]Naphthyridines (Azaacridines)

Abstract

The 300.13 MHz ¹H NMR spectra of the methylated and protonated 6(9)-methylbenzo[b][1,x] naphthyridines (x=5, 6, 7, 8) (5-methylazaacridines) were collected at 298 K in deuterated dimethyl sulfoxide and chloroform, respectively. The methylation and protonation sites were assigned by comparisons of these data with those of the free bases. The results were compared with similar data for related heterocycles and showed that both methylation and protonation occur at the nitrogen in the outer pyrido ring in all four series.

The hydration site in some 2-and 3-azaacridines was determined by specific line broadening in their ¹H NMR spectra to be the same nitrogen as that involved in methylation and protonation. Variable temperature ¹H NMR demonstrated that the specific line broadening results from some changes of ¹⁴N quadrupolar relaxation produced by the slow chemical exchange between unhydrated and hydrated species. Deuterium exchange experiments indicated that the direct spin-spin interaction of a water proton and the protons alpha to the hydrated nitrogen may also have some contribution.     

Finite time blowup of the <Emphasis Type="Italic">n</Emphasis>-harmonic flow on <Emphasis Type="Italic">n</Emphasis>-manifolds

In this paper, we generalize the no-neck result of Qing and Tian (in Commun Pure Appl Math 50:295–310, 1997) to show that there is no neck during blowing up for the n-harmonic flow as \(t\rightarrow \infty \). As an application of the no-neck result, we settle a conjecture of Hungerbühler (in Ann Scuola Norm Sup Pisa Cl Sci 4:593–631, 1997) by constructing an example to show that the n-harmonic map flow on an n-dimensional Riemannian manifold blows up in finite time for \(n\ge 3\).     

Electrochemical and Spectroscopic Properties of Fly Ash–Polyaniline Matrix Nanorod Composites

Polyaniline (PANI) nanocomposites were prepared with fly ash (FA) either by aging the starting materials (aniline and FA) before oxidative polymerisation or by including poly(styrene sulphonic acid) (PSSA) eliminating the aging step. The aging procedure formed polymer nanotubes that have cross-sectional diameters of 50–110 nm. The procedure involving PSSA produced nanorods and nanofibres composites that have diameters of 100–500 nm and length of up to 10 μm attributed to the presence of metal oxides and silica in FA. The electrochemical analysis of the PANI–PSSA–FA nanorod composites shows three redox couples with formal potentials, , values of 105 mV, 455 mV and 670 mV, and conductance, C, value of 1.21 × 10⁻² S. The UV-Vis spectroscopy of the polymeric nanorod shows absorption maxima at 340 and 370 nm (due to π–π^* transition of the benzoid rings), and 600–650 nm (due to charge transfer excitons of the quinoid structure), which are characteristic of emeraldine base.     

Single-ion heat capacities, C(p)(298)ion, of solids: with a novel route to heat-capacity estimation of complex anions

Single-ion heat capacities, C(p)(298)(ion), are additive values for the estimation of room-temperature (298 K) heat capacities of ionic solids. They may be used for inferring the heat capacities of ionic solids for which values are unavailable and for checking reported values, thus complementing our independent method of estimation from formula unit volumes (termed volume-based thermodynamics, VBT). Analysis of the reported heat-capacity data presented here provides a new self-consistent set of heat capacities for both cations and anions that is compatible (and thus may be combined) with an extensive set developed by Spencer. The addition of a large range of silicate species permits the estimation of the heat capacities of many silicate minerals. The single-ion heat capacities of individual silicate anions are observed to be strictly proportional to the total number of atoms (Si plus O), n, contained within the silicate anion complex itself (e.g., for the anion Si(2)O(7)(2-), n = 9, for SiO(4)(2-), n = 5), C(p)(silicate anion)/J K(-1) mol(-1) = 13.8n, in a new rule that is an extension of the Neumann-Kopp relationship. The same linear relationship applies to other homologous anion series (for example, oxygenated heavy-metal anion complexes such as niobates, bismuthates, and tantalates), although with a different proportionality constant. A similar proportionality, C(p)(complex anion)/J K(-1) mol(-1) ≈ 17.5n, which may be regarded as a convenient "rule of thumb", also applies, although less strictly, to complex anions in general. The proportionality constants reflect the rigidity of the complex anion, being always less than the Dulong-Petit value of 25 J K(-1) mol(-1). An emergent feature of our VBT and single-ion approaches to an estimation of the thermodynamic properties is the identification of anomalies in measured values, as is illustrated in this paper.     

Hydrogen-bonding contributions to the lattice energy of salts for second harmonic generation

The lattice energies of a series of organic dihydrogenphosphate salts capable of second harmonic generation (SHG) have been calculated. These calculations, coupled with empirical data, indicate that a minimum of 20–25% of the lattice energy arises from hydrogen-bond interactions. Hydrogen bonding is shown to be a strong enough force to have a profound effect on the overall packing and crystal geometry of such ionic materials, and is thus an important factor to consider for crystal engineering.     

Synthesis of the insecticidal 1′-acetoxy-mammeins and surangin b

Methods are examined for the synthesis of 4-(1′-acetoxy) alkylcoumarins having hexasubstituted aromatic rings. This has led to synthesis of the three insecticidal coumarins mammea E/BB, mammea E/BA and surangin B.