Conservation of a resource based fishery through optimal taxation

In the present paper, we study a dynamic reaction model in which (i) the predator is provided with an alternative food in addition to the prey species, (ii) the predator is harvested, and (iii) a tax is imposed to regulate the system. The existence of possible steady states along with their local as well as global stability is discussed for both the exploited and unexploited systems. Boundedness of the system is also discussed. It is seen that the system undergoes a Hopf bifurcation by the addition of alternative prey and the criteria for the Hopf-bifurcation is also discussed. Optimal tax policy is discussed using Pontryagin’s maximal principle. Finally, some numerical simulations are given to show the consistency with theoretical analysis.     

Kerr metric,geodesic motion,and Flyby Anomaly in fourth-order Conformal Gravity

In this paper we analyze the Kerr geometry in the context of Conformal Gravity, an alternative theory of gravitation, which is a direct extension of General Relativity (GR). Following previous studies in the literature, we introduce an explicit expression of the Kerr metric in Conformal Gravity, which naturally reduces to the standard GR Kerr geometry in the absence of Conformal Gravity effects. As in the standard case, we show that the Hamilton–Jacobi equation governing geodesic motion in a space-time based on this geometry is indeed separable and that a fourth constant of motion—similar to Carter’s constant—can also be introduced in Conformal Gravity. Consequently, we derive the fundamental equations of geodesic motion and show that the problem of solving these equations can be reduced to one of quadratures. In particular, we study the resulting time-like geodesics in Conformal Gravity Kerr geometry by numerically integrating the equations of motion for Earth flyby trajectories of spacecraft. We then compare our results with the existing data of the Flyby Anomaly in order to ascertain whether Conformal Gravity corrections are possibly the origin of this gravitational anomaly. Although Conformal Gravity slightly affects the trajectories of geodesic motion around a rotating spherical object, we show that these corrections are minimal and are not expected to be the origin of the Flyby Anomaly, unless conformal parameters are drastically different from current estimates. Therefore, our results confirm previous analyses, showing that modifications due to Conformal Gravity are not likely to be detected at the Solar System level, but might affect gravity at the galactic or cosmological scale.     

Structural and some electrophysical properties of the solid solutions Si1 − x Sn x (0 ≤ x ≤ 0.04)

Films of the solid solutions Si_{1 ? x} Sn _x (0 ≤ x ≤ 0.04) on Si substrates have been grown by liquid phase epitaxy. The structural features of the films have been investigated using X-ray diffraction. The temperature behavior of current-voltage characteristics and the spectral dependence of the photocurrent for the heterostructures p-Si-n-Si_{1 ? x} Sn _x (0 ≤ x ≤ 0.04) have been analyzed. The grown epitaxial films of the solid solutions Si_{1 ? x} Sn _x (0 ≤ x ≤ 0.04) have a perfect single-crystal structure with a (111) orientation and a subgrain size of 60 nm. In the epitaxial films at the Si-SiO₂ interfaces between silicon subgrains and SiO₂ nanocrystals, where there are many sites with a high potential, the Sn ions with a high probability substitute for the Si ions and encourage the formation of Sn nanocrystals with different orientations and, as follows from the analysis of the X-ray diffraction patterns, with different sizes: 8 nm (for the (101) orientation) and 12 nm (for the (200) orientation). The current-voltage characteristics of the heterostructures p-Si-n-Si_{1 ? x} Sn _x (0 ≤ x ≤ 0.04) are described by the exponential law J = J ₀exp(qV/ckT) at low voltages (V < 0.2 V) and the square law J = (9qμ _p τ _p μ _n N _d /8d ³)V ² at high voltages (V > 1 V). These results have been explained by the drift mechanism of charge carrier transport in the electrical resistance relaxation mode.     

A Molibdenum(VI)–Gallein–Diphenhydramine Ion Associate and Its Application to the Extraction-Photometric Determination of Diphenhydramine

Optimum conditions for the formation and extraction of a slightly soluble ion associate of diphenhydramine with the anionic complex molibydenum–gallein were determined. The ternary complex was extracted with butanol at pH 4–7. In the presence of diphenhydramine, the color strength became stronger, which was manifested in the absorption spectra as hypsochromic and bathochromic shifts. Some physicochemical characteristics of the complex were determined, the specificity of the reaction with respect to diphenhydramine was studied, and the probable complexation scheme was proposed. It was found that the molybdenum–gallein–diphenhydramine complex forms at a component ratio of 1: 2: 2. A procedure for the extraction–photometric determination of diphenhydramine in injection solutions and tablets was developed (RSD = 15–20%). The linearity range of the calibration graph was 0.02–0.20 mg/mL.     

A Methodology for Temperature Correction When Using Two-Color Pyrometers - Compensation for Surface Topography and Material

In this investigation, the applicability of the two-color pyrometer technique for temperature measurements in dry hard turning of AISI 52100 steel was studied, where both machined surfaces as well as cutting tools were considered. The impacts of differing hard turned surface topography on the two-color pyrometer readings was studied by conducting temperature measurements on reference samples created using cutting tools with different degrees of tool flank wear. In order to conduct measurements in a controlled environment, a specially designed furnace was developed in which the samples were heated step-wise up to 1,000 °C in a protective atmosphere. At each testing temperature, the temperatures measured by the two-color pyrometer were compared with temperatures recorded by thermocouples. For all materials and surfaces as studied here, the two-color pyrometer generally recorded significantly lower temperatures than the thermocouples; for the hard turned surfaces, depending on the surface topography, the temperatures were as much as ~20 % lower and for the CBN cutting tools, ~13 % lower. To be able to use the two-color pyrometer technique for temperature measurements in hard turning of AISI 52100 steel, a linear approximation function was determined resulting in three unique equations, one for each of the studied materials and surfaces. By using the developed approximation function, the measured cutting temperatures can be adjusted to compensate for differing materials or surface topographies for comparable machining conditions. Even though the proposed equations are unique for the hard turning conditions as studied here, the proposed methodology can be applied to determine the temperature compensation required for other surface topographies, as well as other materials.     

An Unusual S-and N-Alkylation of Mercapto Substituted Heterocycles With O,O-Dialkyl Chlorophosphate/Thiophosphate

The reaction of different mercapto substituted heterocycles with o,o-dialkyl chlorphosphate or thiophosphates, gave the corresponding S- and N- alkylated derivatives instead of the expected phosphorylated products.     

Conductivity anomalies in Y–Ba–Cu–O at 40K and 100K under high quasihydrostatic pressures

Electrical resistance measurements at low temperatures and high quasihydrostatic pressures on superconducting and non-superconducting varieties of Y_0.8Ba_1.2Cu₂O₅ (obtained by annealing in oxygen and air respectively) show striking anomalies in the vicinity of 100K and 40K. Arguments are presented to show that these anomalies as also the occurrence of T 's in the oxide superconductors either in the vicinity of 100K or of 40K are connected with their layered structure containing planes of Cu-O otahedral complexes.