MATHEMATICAL ANALYSIS OF WEST NILE VIRUS MODEL WITH DISCRETE DELAYS

The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics,...     

Mathematical Analysis of West Nile Virus Model with Discrete Delays

The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics, has a locally-asymptotically stable disease-free equilibrium whenever the associated reproduction number (?₀) is less than unity. As reveal in [3, 20], the analyses of the model show the existence of the phenomenon of backward bifurcation (where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the reproduction number of the disease is less than unity). It is shown, that the backward bifurcation phenomenon can be removed by substituting the associated standard incidence function with a mass action incidence. Analysis of the reproduction number of the model shows that, the disease will persist, whenever ?₀ > 1, and increase in the length of incubation period can help reduce WNV burden in the community if a certain threshold quantities, denoted by Δ_b and Δ_v are negative. On the other hand, increasing the length of the incubation period increases disease burden if Δ_b > 0 and Δ_v > 0. Furthermore, it is shown that adding time delay to the corresponding autonomous model with standard incidence (considered in [2]) does not alter the qualitative dynamics of the autonomous system (with respect to the elimination or persistence of the disease).     

Airport runway scheduling

Airport runway optimization is an ongoing challenge for air traffic controllers. Since demand for air-transportation is predicted to increase, there is a need to realize additional take-off and landing slots through better runway scheduling. In this paper, we review the techniques and tools of operational research and management science that are used for scheduling aircraft landings and take-offs. The main solution techniques include dynamic programming, branch and bound, heuristics and meta-heuristics.     

Associated Prime Submodules of Finitely Generated Modules

As generalizations of annihilators and associated primes, we introduce the notions of weak annihilators and weak associated primes, respectively. We first study the properties of the weak annihilator of a subset X in a ring R. We next investigate how the weak associated primes of a ring R behave under passage to the skew monoid ring R*M. Let R be a semicommutative ring, and M an ordered monoid and φ: M → Aut(R) a compatible monoid homomorphism. Then we can describe all weak associated primes of the skew monoid ring R*M in terms of the weak associated primes of R in a very straightforward way.     

Ultrasound promoted aminolysis of epoxides in aqueous media: a rapid procedure with no pH adjustment for additive-free synthesis of beta-aminoalcohols

An efficient and environmentally friendly procedure promoted by ultrasound irradiation is developed for stereoselective ring opening of various epoxides with aromatic and aliphatic amines under aqueous conditions in the presence of no catalyst or additive. Chemoselectivity of the protocol is shown by competition of piperidine and aniline to react with different epoxides resulting in exclusive formation of the respective products of piperidine.     

Influence of ultrasound on cadmium ion removal by sorption process

This study presents the removal of Cd(II) from aqueous solution by the sorption process in the presence (sono-sorption) and absence (conventional method) of ultrasound. Batch experiments were conducted to study the main parameters such as sorbate concentration, amount of sorbent, contact time, and ultrasound intensity. In addition, the sorbate/sorbent concentration ratios were studied in two different ways: (a) in a constant sorbate concentration and variable amount of sorbent, (b) in a constant amount of sorbent and variable sorbate concentration. The results indicated that under proper conditions, there was a possibility to remove cadmium ion very fast and efficiently from aqueous solution. In addition, the intensity of ultrasound and the sorbate/sorbent concentration ratio were two important factors for the removal of this pollutant and therefore, this study was focused mostly on these two variables.     

Effect of operational parameters on degradation of Malachite Green by ultrasonic irradiation

The aim of the present study was to apply ultrasonic technique to remove Malachite Oxalate Green (MG) from aqueous solution. An ultrasonic bath with frequency of 35 kHz was used to investigate the effect of different operational parameters such as MG concentration, power density, temperature, mechanical agitation and addition of EtOH, 2-PrOH and iso-BuOH. Decolorization of MG follows a first order kinetics and hydroxyl radicals have an important role in degradation of MG. The apparent reaction rate constant (k(ap)) was influenced by variation of operational parameters. The activation energy was 30.95 kJ/mol in temperature range of 21-34 degrees C, suggesting a diffusion-controlled reaction. Alcohols act as hydroxyl radicals scavengers having undesirable contribution. UV-vis spectral change of MG showed hypsochromic shift occurred with increasing sonication time, proposing N-demethylation process of MG.     

Fragmentation of chitosan by ultrasonic irradiation

Kinetics of chitosan fragmentation by ultrasonic irradiation at frequency of 20 kHz, and the effects of experimental variables (power of ultrasound, chitosan concentration and solution temperature) on fragmentation were investigated. The kinetics studies were followed by measuring solution viscosity of the original and its fragments, and determining average number of chain scission of the fragments. The effects of ultrasonic power, chitosan concentration and solution temperature on fragmentation process were followed by viscometry and size exclusion chromatography. The chemical structure of the original chitosan and its fragments were examined by (1)H NMR spectroscopy and elemental analysis. The experimental results showed that the rate of fragmentation increased with an increase in power of ultrasound. Chain scission increased with an increase in power of ultrasound; and solution temperature, but a decrease in chitosan concentration. The chemical structure and polydispersity of the original and the fragments were nearly identical. A model based on experimental data to describe the relationship between chain scission and experimental variables (power of ultrasound; irradiation time; reduced concentration, c[eta]; and solution temperature) was proposed. It was concluded that ultrasonic irradiation is a suitable method to perform partial depolymerization and to obtain moderate macromolecules from large ones.     

Highly efficient removal of toxic lead ions from aqueous solutions using a new magnetic metal‐organic framework nanocomposite

A magnetic metal‐organic framework (MOF) nanocomposite was successfully prepared by a new and green strategy through reasonable design. Magnetic MOF of Fe₃O₄‐NHSO₃H@HKUST‐1 nanocomposite use for removal of lead ions as an environmental pollutant. The experimental results indicated that the nano adsorbent of Fe₃O₄‐NHSO₃H@HKUST‐1 can removed lead ions under optimum operational conditions. The dosage of the nanocomposite, pH of the sample solution, and contact time were obtained to be 10 mg, 7.0, and 90 min, respectively, while the initial concentration of Pb(II) ions of 400 mg/L was used. A kinetic study indicated that a pseudo‐second‐order model agreed well with the experimental data. The isotherm experiments revealed that the Langmuir model attained better fits to the equilibrium data than the Freundlich model. The maximum adsorption capacity of the adsorbent for the removal of lead under the optimum operational conditions of pH 7.0 and temperature 25°C was found to be 384.6 mg/g. The thermodynamic parameters indicate that the adsorption of lead is spontaneous and endothermic. The magnetic MOF nanocomposite could be recovered easily and reused many times without significant loss of its nano‐adsorbent activity. The proposed method is simple, eco‐friendly, low cost, and efficient in the removal of lead ions from aqueous solutions.