On some new analytical solutions for the nonlinear long–short wave interaction system

This paper deals with exact soliton solutions of the nonlinear long–short wave interaction system, utilizing two analytical methods. The system of coupled long–short wave interaction equations is investigated with the help of two analytical methods, namely, the generalized \(\tan (\phi /2)\)-expansion method and He’s semi-inverse variational method. Moreover, in this paper we generalize two aforementioned methods which give new soliton wave solutions. As a consequence, solutions are including solitons, kink, periodic and rational solutions. Moreover, dark, bright and singular solition solutions of the coupled long–short wave interaction equations have been found. All solutions have been verified back into its corresponding equation with the aid of maple package program. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. Finally, we believe that the executed methods are robust and efficient than other methods and the obtained solutions in this paper can help us to understand the soliton waves in the fields of physics and mechanics.     

Biopreservation of hamburgers by essential oil of Zataria multiflora

Hamburgers with high nutrient supply and a loosely-packed structure present favourable conditions for microbial growth. In this study, the chemical composition and antimicrobial activity of the essential oil of Zataria multiflora and its potential application as a natural preservative in reducing the indigenous microbial population of hamburgers were investigated. Carvacrol, thymol and linalool were found to be the most abundant constituents of the essential oil using GC-MS analysis. The essential oil exhibited strong antibacterial activity against Gram-positive and Gram-negative bacteria. Addition of Z. multiflora essential oil in concentrations higher than MIC values influenced the microbial population of hamburgers stored at 25°C, 4°C and -12°C. The significant results of this study are our observations that the use of Z. multiflora essential oil at 0.05% v/w increases the time needed for the natural microflora of hamburgers to reach concentrations able to produce a perceivable spoilage at refrigerator and room temperatures without any inverse effect on their sensory attributes. Freezing of essential oil-treated hamburgers may also reduce the risk of diseases associated with consumption of under-cooked hamburgers through significant microbial reduction by more than 3 log.     

A numerical method for solving linear integral equations of the second kind on the non-rectangular domains based on the meshless method

The main purpose of this article is to describe a numerical scheme for solving two-dimensional linear Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on radial basis functions (RBFs) constructed on a set of disordered data. The proposed method does not require any background mesh or cell structures, so it is meshless and consequently independent of the geometry of domain. This approach reduces the solution of the two-dimensional integral equation to the solution of a linear system of algebraic equations. The error analysis of the method is provided. The proposed scheme is also extended to linear mixed Volterra–Fredholm integral equations. Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the new technique.     

Enantioselective addition of diethylzinc to aryl aldehydes catalyzed by novel chiral imino alcohol ligands

The enantioselective alkylation of aryl aldehydes by diethylzinc in the presence of catalytic amounts of several novel chiral imino alcohol ligands, synthesized from the reaction of (R)-2-amino-1-butanol with aromatic aldehydes, was studied. The influence of temperature and ligand structure was investigated and enantioselectivity up to 81% was obtained.     

A method based on meshless approach for the numerical solution of the two‐space dimensional hyperbolic telegraph equation

In the current article, we investigate the RBF solution of second‐order two‐space dimensional linear hyperbolic telegraph equation. For this purpose, we use a combination of boundary knot method (BKM) and analog equation method (AEM). The BKM is a meshfree, boundary‐only and integration‐free technique. The BKM is an alternative to the method of fundamental solution to avoid the fictitious boundary and to deal with low accuracy, singular integration and mesh generation. Also, on the basis of the AEM, the governing operator is substituted by an equivalent nonhomogeneous linear one with known fundamental solution under the same boundary conditions. Finally, several numerical results and discussions are demonstrated to show the accuracy and efficiency of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation

In this paper, we employ the boundary-only meshfree method to find out numerical solution of the classical Boussinesq equation in one dimension. The proposed method in the current paper is a combination of boundary knot method and meshless analog equation method. The boundary knot technique is an integration free, boundary-only, meshless method which is used to avoid the known disadvantages of the method of fundamental solution. Also, we use the meshless analog equation method to replace the nonlinear governing equation with an equivalent nonhomogeneous linear equation. A predictor-corrector scheme is proposed to solve the resulted differential equation of the collocation. The numerical results and conclusions are obtained for both the ‘good’ and the ‘bad’ Boussinesq equations.     

Minimum flow problem on network flows with time-varying bounds

In this paper, we consider the minimum flow problem on network flows in which the lower arc capacities vary with time. We will show that this problem for set {0, 1, … , T} of time points can be solved by at most n minimum flow computations, by combining of preflow-pull algorithm and reoptimization techniques (no matter how many values of T are given). Running time of the presented algorithm is O(n²m).     

The numerical solution of the non-linear integro-differential equations based on the meshless method

This article investigates the numerical solution of the nonlinear integro-differential equations. The numerical scheme developed in the current paper is based on the moving least square method. The moving least square methodology is an effective technique for the approximation of an unknown function by using a set of disordered data. It consists of a local weighted least square fitting, valid on a small neighborhood of a point and only based on the information provided by its n closet points. Hence the method is a meshless method and does not need any background mesh or cell structures. The error analysis of the proposed method is provided. The validity and efficiency of the new method are demonstrated through several tests.     

Growth of tin oxide nanotubes by aerial carbothermal evaporation

One-dimensional nanostructures of tin oxide nanotubes were fabricated by carbothermal evaporation at 900°C in air. The synthesized film was grown on Au-coated (100) Si substrate. Heterogeneous catalysis by Au/Sn droplets assisted the formation of the tin oxide nanotubes of less than 40 nm diameter at Sn vapor pressures around 1.4×10⁻⁷ Pa. In order to reduce the nanotube diameter further, an increase in the Sn vapor pressure by changing the source materials’ ratio seemed viable.