Solutions of the SIR models of epidemics using HAM

In this paper, we investigate the accuracy of the Homotopy Analysis Method (HAM) for solving the problem of the spread of a non-fatal disease in a population. The advantage of this method is that it provides a direct scheme for solving the problem, i.e., without the need for linearization, perturbation, massive computation and any transformation. Mathematical modeling of the problem leads to a system of nonlinear ODEs. MATLAB 7 is used to carry out the computations. Graphical results are presented and discussed quantitatively to illustrate the solution.     

On new iterative method for solving systems of nonlinear equations

Solving systems of nonlinear equations is a relatively complicated problem for which a number of different approaches have been proposed. In this paper, we employ the Homotopy Analysis Method (HAM) to derive a family of iterative methods for solving systems of nonlinear algebraic equations. Our approach yields second and third order iterative methods which are more efficient than their classical counterparts such as Newton’s, Chebychev’s and Halley’s methods.     

Bound-exciton emission bands in ZnSe single crystals and mixed plasmon-phonon modes

The paper reports a cathodoluminescence study of ZnSe single crystals annealed in a Bi melt at 1200 K for 120 h. It is found that the distance between the phonon structure satellites in the bound-exciton series I ₁ ^s -nLO and I ₁ ^d -nLO and the relative satellite intensity are different in samples with different conduction electron concentrations. It is shown that this difference is due to the mixing of the plasmon and phonon modes. The shape of the bound-exciton emission spectrum in ZnSe crystals in the 450–470 nm region is calculated, and a satisfactory agreement with the experiment calculations is obtained.     

A de Vries (SmC*) Phase in a Novel Series of Chiral Fluorinated Organosiloxane Liquid Crystals

The synthesis and characterization of a series of five chiral fluorinated low molar mass (bifurcated tail) organosiloxane materials is presented. The mesogenic moiety is similar to that in the TSiKN65F mesogen reported by Naciri et al., which displays a de Vries-type SmA* phase. The one parameter varied across the series reported herein is the length of the alkyl chain linking the mesogen's core to the bifurcated siloxane tail. One of the five materials displays a de Vries SmC* phase upon cooling from SmA*.     

Assessment of Immune Response and Efficacy of Essential Oils Application on Controlling Necrotic Enteritis Induced by Clostridium perfringens in Broiler Chickens

Necrotic enteritis (NE) caused by Clostridium perfringens is one of the most important enteric diseases in poultry. The antibacterial activity of two different essential oil (EO) blends against C. perfringens was investigated both in vitro and in vivo. Additionally, the immunological response to EO treatment was assessed. In the in vitro study, the antibacterial activity of EO formulas and commonly used antibiotics was evaluated against C. perfringens using disk diffusion assay, minimum inhibitory concentration (MIC) assay, and minimum bactericidal concentration (MBC) assay. In the in vivo study, NE experimental infection was performed on 440 Ross broiler chicks at 19 days of age for 4 continuous days. The chicks were treated with either EOs or amoxicillin at 22 days of age for 5 continuous days. One day after the end of treatment, the birds’ performance was evaluated by calculating the feed conversion ratio. Serum samples from 120 birds were collected to measure the levels of IL-1β, IFN-γ, IL-8, IL-10, and IL-17. After that, all birds were slaughtered, and their small intestines were subjected to gross and histopathological evaluation. In addition, bacterial counts in the small intestines were evaluated. In the in vitro study, EOs showed higher antimicrobial activities in comparison with antibiotics against C. perfringens. In the in vivo study, birds treated with EOs showed a significant decrease in bacterial counts, a significant decrease in intestinal lesions, and a significant improvement in performance compared with untreated birds (p < 0.05). Moreover, treating birds with EOs directed the immune system toward an anti-inflammatory pathway. None of the treated birds died due to NE compared with the 10% mortality rate in untreated birds. In conclusion, EOs might be an effective and safe alternative to antibiotics in the treatment of chicken NE.     

Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma

In this paper, we propose a computational method for nonlinear partial differential equations modeling ion-acoustic waves as well as dusty plasmas in laboratory and space sciences. Many types of solitary waves including soliton solutions, N-soliton solutions and singular N-soliton solutions are derived. The characteristic line method and graphical analysis are applied to discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Furthermore, the effects of inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed.     

Dynamics of non-autonomous difference equation

In this paper we study the asymptotic behavior and periodicity of the equation \(x_{n+1}=p_{n}+\frac{x_{n}}{x_{n-1}}\), where \(x_{0}\ge 0, x_{-1}>0\) and \(p_{n}\) is a positive bounded sequence.     

Toward a New Algorithm for Nonlinear Fractional Differential Equations

This paper is concerned with the development of an efficient algorithm for the analytic solutions of nonlinear fractional differential equations. The proposed algorithm Laplace homotopy analysis method (LHAM) is a combined form of the Laplace transform method with the homotopy analysis method. The biggest advantage the LHAM has over the existing standard analytical techniques is that it overcomes the difficulty arising in calculating complicated terms. Moreover, the solution procedure is easier, more effective and straightforward. Numerical examples are examined to demonstrate the accuracy and efficiency of the proposed algorithm.