Turing instability for a ratio-dependent predator-prey model with diffusion

Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation search. In this paper we study the conditions of the existence and stability properties of the equilibrium solutions in a reaction-diffusion model in which predator mortality is neither a constant nor an unbounded function, but it is increasing with the predator abundance. We show that analytically at a certain critical value a diffusion driven (Turing type) instability occurs, i.e. the stationary solution stays stable with respect to the kinetic system (the system without diffusion). We also show that the stationary solution becomes unstable with respect to the system with diffusion and that Turing bifurcation takes place: a spatially non-homogenous (non-constant) solution (structure or pattern) arises. A numerical scheme that preserve the positivity of the numerical solutions and the boundedness of prey solution will be presented. Numerical examples are also included.     

Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials

In this paper, we state and prove a new formula expressing explicitly the integratives of Bernstein polynomials (or B‐polynomials) of any degree and for any fractional‐order in terms of B‐polynomials themselves. We derive the transformation matrices that map the Bernstein and Legendre forms of a degree‐n polynomial on [0,1] into each other. By using their transformation matrices, we derive the operational matrices of integration and product of the Bernstein polynomials. These matrices together with the Tau method are then utilized to reduce the solution of this problem to the solution of a system of algebraic equations. The method is applied to solve linear and nonlinear fractional differential equations. Copyright © 2013 John Wiley & Sons, Ltd.     

Simulation of Multiphase Flows with Strong Shocks and Density Variations

The system of extended Euler type hyperbolic equations is considered to describe a two-phase compressible flow. A numerical scheme for computing multi-component flows is then examined. The numerical approach is based on the mathematical model that considers interfaces between fluids as numerically diffused zones. The hyperbolic problem is tackled using a high resolution HLLC scheme on a fixed Eulerian mesh. The global set of conservative equations (mass, momentum and energy) for each phase is closed with a general two parameters equation of state for each constituent. The performance of various variants of a diffuse interface method is carefully verified against a comprehensive suite of numerical benchmark test cases in one and two space dimensions. The studied benchmark cases are divided into two categories: idealized tests for which exact solutions can be generated and tests for which the equivalent numerical results could be obtained using different approaches. The ability to simulate the Richtmyer-Meshkov instabilities, which are generated when a shock wave impacts an interface between two different fluids, is considered as a major challenge for the present numerical techniques. The study presents the effect of density ratio of constituent fluids on the resolution of an interface and the ability to simulate Richtmyer-Meshkov instabilities by various variants of diffuse interface methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of catalytic, surface and magnetic properties of nanocrystalline manganese ferrite

Single-domain manganese ferrite nanoparticles have been synthesized with narrow particle size distribution using the combustion technique. Influence of fuel ratios on the as-prepared powders were characterized by XRD, SEM, VSM, N₂ adsorption at −196 °C and conversion of cyclohexene at 200–400 °C. Ratios of fuel to cations were maintained variously at 0.0, 0.67, 1.33 and 2.67.The fuel to cations ratio of 2.67 gives better yield in the formation of nanocrystalline Mn ferrite and single-domain particles with a narrow range of size distribution. Maximum magnetization and coercivity values of the investigated ferrite are also greater for the ratio of 2.67. These values measured at room temperature are found to be 68.58 emu/g and 62.57 Oe, respectively. The BET surface area of the investigated solids was found to decrease by increasing the ratio between fuel and cations due to increasing the flame temperature. However, this treatment resulted in a significant increase in catalytic activity of the as-synthesized solids. All solids investigated behaved as dehydrogenation catalysts. The change in fuel/cations ratios did not alter the mechanism of dehydrogenation of cyclohexene, but increased the concentration of active sites involved in the catalyzed reaction.     

Low lying energy levels of56Fe from γ-γ coincidences

The level scheme of⁵⁶Fe was built up from γ-γ coincidence measurements using Ge(Li) detectors and a Dual Parameter data collection system. The previously suggested γ-transitions [8] of 263.3, 410.9, 485.2, 674.7 and 1,462.3 keV were confirmed and evidence found for a new 655.0 keV γ-transition between the levels at 4,100.32 and 3,445.32 keV. No evidence was found for the transition of 2,657.4 keV and the previously proposed β⁺-feeding of the level at 3,600.3 keV is ruled out, while the existence of a level at 4,447.5 keV is suggested. The relative intensities and branching ratios of 44 transitions were determined. A calculation of experimentalK-shell internal conversion coefficients α(K) showed large discrepancies from previous studies for the 3,009.6 and 3,451.2 keV transitions, the latter being assigned a different multipolarity. Logft values were calculated and spins and parities of the levels deduced. In particular the assignment of 3⁺ is verified for the level at 4,297.97 keV.     

Synthesis of derivatives of dihydro-1,2-oxazine and tetrahydro-1,2-diazine from (4-chlorobutanoyl)-alkoxybenzenes

The reaction of (4-chlorobutanoyl)alkoxybenzenes with hydroxylamine and 2,4-dinitrophenylhydrazine gave dihydro-1,2-oxazines and tetrahydro-1,2-diazines, respectively.Institute of Petrochemical Processes, Academy of Sciences of the Republic of Azerbaijan, 370025 Baku. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 7, pp. 1685–1687, July, 1992.     

Synthesis and Anticancer Activity of New Pyrimidine and Oxadiazole Acyclic Nucleoside Analogs and Thiazolopyrimidine Derivatives

Russian Journal of General Chemistry - A group of new substituted pyrimidine compounds, and their thiazolopyrimidines and 1,3,4-oxadiazolyl acyclic sugar derivatives have been synthesized as...     

Synthesis of Novel Pyridothienopyrimidines,Pyridothienopyrimidothiazines, Pyridothienopyrimidobenzthiazoles and Triazolopyridothienopyrimidines

The reaction of 3‐amino‐4,6‐dimethylthieno[2,3‐b]pyridine‐2‐carboxamide (1a) or its N‐aryl derivatives 1b‐d with carbon disulphide gave the pyridothienopyrimidines 2a‐d , whilst when the same reaction was carried out using N¹‐arylidene‐3‐amino‐4,6‐dimethylthieno[2,3‐b]pyridine‐2‐carbohydrazides (1e‐h) , pyridothienothiazine 3 was obtained. Also, refluxing of 1b‐d with acetic anhydride afforded oxazinone derivative 4 . Compounds 2a and 2b‐d were also obtained by the treatment of thiazine 3 with ammonium acetate or aromatic amines, respectively. When compound 2a was allowed to react with arylidene malononitriles or ethyl α‐cyanocinnamate, novel pyrido[3″,2″:4′,5′]thieno[3′,2′:4,5]pyrimido[2,1‐b][1,3] thiazines 5a‐c were obtained. Treatment of 2b‐d with bromine in acetic acid furnished the disulphide derivatives 6a‐c . U.V. irradiation of 2b‐d resulted in the formation of pyrido[3″,2″:4′,5′]thieno[3′,2′:4,5]pyrimido[2,1‐b]benzthiazoles 7a‐c . The reaction of 2a‐d with some halocarbonyl compounds afforded the corresponding S‐substituted thiopyrido thienopyrimidines 8a‐j . Compound 8b was readily cyclized into the corresponding thiazolo[3″,2″‐a]‐pyrido[3′,2′:4,5]thieno[3,2‐d]pyrimidine 9 upon treatment with conc. sulphuric acid. Heating of 2a,b with hydrazine hydrate in pyridine afforded the hydrazino derivatives 11a,b . Reaction of ester 8c with hydrazine hydrate in ethanol gave acethydrazide 10 . Compounds 10 and 11a,b were used as versatile synthons for other new pyridothienopyrimidines 12–15 as well as [1,2,4] triazolopyridothienopyrimidines 16–19.     

Facile Synthesis and Antimicrobial Activity of 5‐Amino‐3‐methyl‐1‐phenyl‐1H‐thieno[3,2‐c]pyrazole‐6‐carbonitrile and Their Derivatives

5‐Amino‐thieno[3,2‐c]pyrazole derivative 2 was prepared by Gewald reaction in a one‐pot procedure. The amino group of compound 2 like primary aromatic amine formed the diazonium salt when treated with NaNO₂/HCl, followed by coupling with different nucleophiles to yield the azo coupling products 3a – d . The reactivity of 5‐amino‐thienopyrazole 2 has been investigated towards different electrophilic reagents such as aromatic aldehydes, alkyl halide, acid chloride, acid anhydride, phenyl isothiocyanate, carbon disulfide, ethyl glycinate, and thioacetamide, which afforded the reaction products 4 – 14 , respectively.