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.     

Resolving Component Overlap in Multiwavelength Kinetic Spectroscopy: Application to Raman Scattering from Intermediates in Triplet-State Photoreactions

Abstract— Understanding of reaction mechanisms in photochemistry is advanced both by kinetic measurements to determine rates of reaction and by spectroscopic studies of the structures of precursors and photoproducts. When kinetics and spectroscopy are combined in a time-resolved, multiwavelength spectroscopic measurement on a reacting system, spectra and structures of intermediates can also be determined. In this paper, the application of multidimensional least-squares and factor analysis techniques for resolving overlapped spectra from intermediates in photochemical kinetics are discussed. The methods are employed specifically to resolve Raman spectra of intermediates in triplet-state photoreactions. By varying excitation intensity, spectra of excited-triplet states are resolved from ground states and solvent. By varying the concentration of a triplet quencher in the sample, the Raman spectrum of a sensitizer excited state (benzophe-none) can be resolved from those of acceptor-triplet states or radical photoproducts. Applications of these concepts in other areas of photochemical kinetics are addressed.     

Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm

This paper proposes a hybrid self-adaptive evolutionary algorithm for graph coloring that is hybridized with the following novel elements: heuristic genotype-phenotype mapping, a swap local search heuristic, and a neutral survivor selection operator. This algorithm was compared with the evolutionary algorithm with the SAW method of Eiben et al., the Tabucol algorithm of Hertz and de Werra, and the hybrid evolutionary algorithm of Galinier and Hao. The performance of these algorithms were tested on a test suite consisting of randomly generated 3-colorable graphs of various structural features, such as graph size, type, edge density, and variability in sizes of color classes. Furthermore, the test graphs were generated including the phase transition where the graphs are hard to color. The purpose of the extensive experimental work was threefold: to investigate the behavior of the tested algorithms in the phase transition, to identify what impact hybridization with the DSatur traditional heuristic has on the evolutionary algorithm, and to show how graph structural features influence the performance of the graph-coloring algorithms. The results indicate that the performance of the hybrid self-adaptive evolutionary algorithm is comparable with, or better than, the performance of the hybrid evolutionary algorithm which is one of the best graph-coloring algorithms today. Moreover, the fact that all the considered algorithms performed poorly on flat graphs confirms that graphs of this type are really the hardest to color.     

Optimal control of harvesting coupled with boundary control in a predator—prey system

We consider boundary control and control via harvesting in a parabolic predator—prey system for a bounded region. The boundary control depicts the relationship between the boundary environment and the possibly harmful species. In addition, a proportion of the predator is harvested for profit. We choose to maximize the objective functional which incorporates the amount of the prey and the revenue of harvesting of the predator less the economic cost of sustaining a satisfactory boundary habitat and the cost due to the harvesting component. Moreover, we characterize the unique optimal control in terms of the solution to the optimality system, which is the state system coupled with the adjoint system.     

Equilibrium polarization of ultrathin PbTiO3 with surface compensation controlled by oxygen partial pressure

We present a synchrotron x-ray study of the equilibrium polarization structure of ultrathin PbTiO(3) films on SrRuO(3) electrodes epitaxially grown on SrTiO(3) (001) substrates, as a function of temperature and the external oxygen partial pressure (pO(2)) controlling their surface charge compensation. We find that the ferroelectric Curie temperature (T(C)) varies with pO(2) and has a minimum at the intermediate pO(2), where the polarization below T(C) changes sign. The experiments are in qualitative agreement with a model based on Landau theory that takes into account the interaction of the phase transition with the electrochemical equilibria for charged surface species. The paraelectric phase is stabilized at intermediate pO(2) when the concentrations of surface species are insufficient to compensate either polar orientation.     

Total-reflection inelastic X-ray scattering from a 10-nm thick La0.6Sr0.4CoO3 thin film

To study equilibrium changes in composition, valence, and electronic structure near the surface and into the bulk, we demonstrate the use of a new approach, total-reflection inelastic x-ray scattering, as a sub-keV spectroscopy capable of depth profiling chemical changes in thin films with nanometer resolution. By comparing data acquired under total x-ray reflection and penetrating conditions, we are able to separate the O K-edge spectra from a 10 nm La0.6Sr0.4CoO3 thin film from that of the underlying SrTiO3 substrate. With a smaller wavelength probe than comparable soft x-ray absorption measurements, we also describe the ability to easily access dipole-forbidden final states, using the dramatic evolution of the La N4,5 edge with momentum transfer as an example.     

Mathematics instruction and the tablet PC

The use of tablet PCs in teaching is a relatively new phenomenon. A cross between a notebook computer and a personal digital assistant (PDA), the tablet PC has all of the features of a notebook with the additional capability that the screen can also be used for input. Tablet PCs are usually equipped with a stylus that allows the user to write on the screen. Handwriting recognition software converts this input into text for use with software such as internet browsers and email programs. As an educational tool, two of the most important features of the tablet PC are annotation and wireless communication. The annotation feature allows the user to write on almost any document much as one would annotate a printout of the same document. The wireless communication feature allows tablet PCs to share information with one another. The advantages of these features and their impact on the Murray State University (MSU) classroom will be discussed in the evaluation section.     

Polarization switching without domain formation at the intrinsic coercive field in ultrathin ferroelectric PbTiO₃

Polarization switching in ferroelectrics has been thought to occur only through the nucleation and growth of new domains. Here we use in situ synchrotron x-ray scattering to monitor switching controlled by applied chemical potential. In sufficiently thin PbTiO? films, nucleation is suppressed and switching occurs by a continuous mechanism, i.e., by uniform decrease and inversion of the polarization without domain formation. The observed lattice parameter shows that the electric field in the film during switching reaches the theoretical intrinsic coercive field.     

Local electronic structure of dicarba-closo-dodecarboranes C2B10H12

We report nonresonant inelastic X-ray scattering (NRIXS) measurement of core-shell excitations from both B 1s and C 1s initial states in all three isomers of the dicarba-closo-dodecarboranes C2B10H12. First, these data yield an experimental determination of the angular-momentum-projected final local density of states (l-DOS). We find low-energy resonances with distinctive local s- or p-type character, providing a more complete experimental characterization of bond hybridization than is available from dipole-transition limited techniques, such as X-ray absorption spectroscopies. This analysis is supported by independent density functional theory and real-space full multiple scattering calculation of the l-DOS which yield a clear distinction between tangential and radial contributions. Second, we investigate the isomer sensitivity of the NRIXS signal and compare and contrast these results with prior electron energy loss spectroscopy measurements. This work establishes NRIXS as a valuable tool for borane chemistry, not only for the unique spectroscopic capabilities of the technique but also through its compatibility with future studies in solution or in high-pressure environments. In addition, this work also establishes the real-space full multiple scattering approach as a useful alternative to traditional approaches for excited states calculations of aromatic polyhedral boranes and related systems.     

Electronic structure of lithium battery interphase compounds: comparison between inelastic x-ray scattering measurements and theory

In lithium ion batteries, decomposition of the electrolyte and its associated passivation of the electrode surface occurs at low potentials, resulting in an electronically insulating, but Li-ion conducting, solid electrolyte interphase (SEI). The products of the SEI and their chemical constituents/properties play an important role in the long-term stability and performance of the battery. Reactivity and the sub-keV core binding energies of lithium, carbon, oxygen, and fluorine species in the SEI present technical challenges in the spectroscopy of these compounds. Using an alternative approach, nonresonant inelastic x-ray scattering, we examine the near-edge spectra of bulk specimens of common SEI compounds, including LiF, Li(2)CO(3), LiOH, LiOH·H(2)O, and Li(2)O. By working at hard x-ray energies, we also experimentally differentiate the s- and p-symmetry components of lithium's unoccupied states using the evolution of its K edge with momentum transfer. We find good agreement with theoretical spectra calculated using a Bethe-Salpeter approach in all cases. These results provide an analytical and diagnostic foundation for better understanding of the makeup of SEIs and the mechanism of their formation.