Volume 17 – Issue 3

In this work, improved modified Exp-function method is used to obtain the exact solution for (1+1)-dimensional Benjamin-Bona Mahony equation of fractional order. This differential equation arises in modeling of long surface gravity waves of small amplitude. It is appropriate to use a generalized fractional complex transformation to convert this equation to ordinary differential equation which further resulted into number of exact solutions

This paper presents the theory of Interpolation and its applications in numerical analysis. It specially focuses on cubic spline interpolation. Data interpolation is useful for scientific visualization for data interpretation. One of the efficient methods for data interpolation is cubic spline function. Cubic splines are the most popular. They produce an interpolated function that is continuous through to the second derivative; Splines tend to be stabler than fitting a polynomial through the N +1 points, with less possibility of wild oscillations between the tabulated points.

The concept of fuzzy differential superordination was introduced by Waggas Galib Atshan and Khudair O. Hussain in [5] as a dual concept of fuzzy differential subordination [3]. Let Ω be a set in C^2 and ϕ: C^2 x U → Cℂbe an analytic function in Ω and let the function p be an analytic in the unit open disk U such that ϕ(p(z), zp'(z)) is univalent in U and satisfies F_h(U) (h(z)) ≤ F_ϕ(C^2xU) (ϕ(p(z), zp'(z)). In this article, we have identified the conditions on functions θ,w,µ and h so that F_h(U) (h(z)) ≤ F_ϕ(C^2xU) (ϕ(p(z), zp'(z)), implies F_q(U) (q(z) ≤ F_p(U) (p(z)).

In the present paper, we obtain some classes of gcd – closed sets with 9 elements on which LCM matrices are singular by adding an element to a gcd – closed set with 8 elements on which the LCM matrix is also singular. Finally, examining these examples we present two new conjectures.

In this article, we introduce modular A-metric spaces. Also, we give topology induced by this metric and some results obtained from this. As an application, we prove the uniqueness and existence of fixed point of Banach contraction mapping in modular A-metric spaces.

Nonlinear mathematical problems and their solutions attain many attentions. In soliton theory an efficient tool to attain various types of soliton solutions is the improved modified Exp-function technique. Under study article is devoted to find soliton wave solutions of modified KdV equation of fractional-order via a reliable mathematical technique. By use of proposed technique we attain soliton wave solution of various types. The regulation of proposed algorithm is demonstrated by consequent results and computational work. It is concluded that under discussion technique is user friendly with minimum computational work; also we can extend it for physical problems of different nature.

In this paper, we apply a modified version of the variational iteration method (MVIM) for solving K–S equation. The proposed modification is made by introducing He’s polynomials in the correction functional of the variational iteration method (VIM). The nonlinear term can be easily handled by the use of He’s Polynomials. The use of Lagrange multiplier coupled with He’s polynomials are the clear advantages of this technique over the decomposition method.

In [3] the author introduced such definition ( Definition 1.6.1 ) p.25, for some weak 𝜔 −open sets in the subspace topology. And prove some properties and theorems for them. In this paper we shall improve the definition mentioned above and answer the question: Are these properties and theorems satisfied for this improving definition?

This paper applies homotopy analysis method (HAM) to obtain analytical solutions of system of fractional order DEs, which arises very frequently in mechanical engineering, control theory, solid mechanics and applied sciences. Analytical results reveal the complete compatibility of proposed algorithm for such problems. Some mathematical problems are presented to show the efficiency and simplicity of the method.

In this paper, we generalize Jacobsthal and Jacobsthal- Lucas quaternions to k- Jacobsthal and k- Jacobsthal-Lucas quaternions. We give Binet- like formulas, generating functions and matrix representation of k- Jacobsthal quaternions and kJacobsthal-Lucas quaternions.

This document is to present a improved collocation method based on Chelyshkov polynomials to solve the functional integro-differential equations with mixed delays under the initial-boundary conditions. An efficient error estimation for the Chelyshkov collocation method is also introduced. Some examples from quite different fields of pure and applied mathematics are given to demonstrate the validation and application of the method and a comparison is made between obtained and existing results.

Today, digital has invaded all areas and the sectors of the economy of information and communication contributes to the largest share of wealth. The trend accelerated during the last 15 years of the digital economy and the new Information and Communication Technology (NICT) diffusion affect the enterprise competitiveness and the country level on the international market also. This work aims briefly the theoretical competitiveness concept and NICT impact under the development and innovation of a country competitiveness process. Secondly, this paper aims the empirical findings within a data analysis for the 35 countries sample during 2012-2015 years in order to examine the relationship between NICT development and the global competitiveness of the Euro-Mediterranean region, issues related in the productivity evolution and enabling innovation as key indicators of the overall countries competitiveness of this area.

Globalization, liberalization of markets, internationalization and Internet has led to new open visions and business opportunities. Now, large and small businesses may have business relationships all over the world and obtain many important advantages such as: rapid transfer of information, rapid connectivity, diversity, interculturality, finding new knowledge, experiences, and values, and lower costs for communication and collaboration, anytime, anywhere. In a world where many activities are now online, why not the commercial activity to not be online? The Internet, as the newest direct marketing technique, has led to increased sales made online.The customers and the organizations, make purchase and sale online, known as e-commerce. In this article we analyse the role played by the Internet in commerce actvities, implementing mathematical modeling and simulation to show their implication in commercial activities and to show there is a direct and positive relation between the Internet and the commercial activities.

In order to master and improve the quality and properties of the final products, the major industrial challenge lies in the possibility of controlling the morphology, size of microstructures that reside within the molded pieces, as well as their defects; this is the fundamental reason according to which we are more and more interested in mastering the growth and germination of such alloys, as well as the developing structures, at the time of solidification process. On the one hand, the whole work focuses upon the modeling of the homogenization effect according to the three parameters: time, temperature and composition, and seeing each one influence upon the silicon concentration according to the distance between the surface and the core of the ingot, on the other hand, the purpose of this work is to model the influence of silicon addition upon the cooling process and various mechanical properties of aluminum. Usually, the microstructure and mechanical behavior of such alloys as Al-Si are directly influenced by some parameters such as composition, cooling velocity and homogenization process.

Seaweed are known and used from the most ancient times in food, in medicine and soil fertilization. Today the researchers from all over the world seek to solve the problems related to the exploration and exploitation of this precious marine flora. The studies regarding the chemistry and the biology of the kelp, or those focused on optimizing the processes of existing technology for recouping actually represents the measure the value for the use of these plants in the various fields of activity. The work presents the data on the distribution of algae biomass from new sources. Useful information on the composition in bioactive compounds in this algae biomass is highlighted. The chemical composition of the kelp is varied: terpenele, polysaccharides; alacaloids, halogenated compounds, phenolic compounds, vitamins, minerals.

The present paper describes the important components of the Autumn crocus (Colchicum autumnale) plant studied. The aim of our study was to characterize antioxidant activity, protein, carbohydrate and phytochemical compounds determinations (polyphenols, tannins, flavonoids, terpenoids) of the hidroalcoolic extract obtained using autumn crocus (Colchicum autumnale) plant. The samples (flowers and roots) were analyzed by UV–VIS, FTIR and RAMAN spectroscopy. Antioxidant activity of the extracts was evaluated using DPPH method.

Refining processes of rapeseed oil generate lechitins, gums or soapstocks. These secondary products have a major valorification potential and could contribute to elaboration of effective management systems for plant growth. Tagetes and Lobelia species need an extra phosphorus contribution and prefere alcaline solutions. In order to ensure the necessary nutritional components and to improve the growth and development conditions of medicinal herbs Tagetes patula L. and Lobelia erinus, it has been applied soapstock treatments in four different preparation forms (wet natural form, 1% (w/w) and 10% (w/w) mixtures with water and dried at 105° C, for 5 hours. The experimental study lasted 21 days. The final evaluation of plant growth has highlighted that Tagetes patula L. treatment with soapstock 10% (w/w) has led to important improvements: increasing with 200 % of buds number, with 200% of ramifications and with 30% of plant height than the start of the experimental study. Lobelia erinus plants from the soil treated with 10 g dry soapstock recorded an increase with 1144% of flowers number, with 457% of buds number and no modification of ramification’s plants. The most important increase in Lobelia erinus plant height (117%) was observed in those treated with 1% soapstock/water mixture.

Morocco has vast resources in marine renewable energy to be used to offset the energy requirements because marine energy is one of many kinds of interesting emerging renewable energy. In this research a numerical and analytical investigation we will use with two types of technologies, which is based on the recovery of the kinetic energy of the marine current to generate electricity. The aim is to demonstrate the energy extraction potential of a hydrogenerator with oscillating wing compared to the tidal turbine to the horizontal axis and to validate some numerical predictions.

The present study is carried out to examine the effects of radiation and chemical reaction on unsteady flow of a viscous, incompressible and electrically conducting fluid past an exponentially accelerated inclined plate with variable wall temperature and mass diffusion in the presence of transversely applied uniform magnetic field and Hall current. The plate temperature and the concentration level near the plate increase linearly with time. The flow model under consideration has been solved by Laplace transform technique. The model contains equations of motion, diffusion equation and equation of energy. To analyze the solution of the model, desirable sets of the values of the parameters have been considered. The numerical data obtained is discussed with the help of graphs and tables. The numerical values obtained for skin-friction, Sherwood number and Nusselt number have been tabulated. We found that the values obtained for velocity, concentration and temperature are in concurrence with the actual flow of the fluid

The paper examines the effects of thin flame velocity and other sensitive factors on the maximum temperature of the reaction during gravitational differentiation (GD) and radioactive decay (RD) processes in the interior of the earth.The partial differential equation governing the model together with the boundary conditions is transformed into ordinary differential equation by thin flame technique. The resulting equation is investigated for the effects of some sensitive factors such as activation energies ratio, flame velocity, gravitational differentiation and radioactive decay parameters, on maximum temperature of the reaction. We establish the criteria for the existence of unique solution of the resulting equations. Numerical results were obtained by shooting method.The results show that flame velocity, and other sensitive factors have appreciable effects on maximum temperature of the reaction. In particular, regulating the flame velocity has appreciable impact on the reactions in terms of heat release

. Transparent conducting materials (or Transparent conducting oxides, TCO) are essential elements in the construction of dye-sensitized solar cells (DSSC). They must have a small electrical resistance and a good optical transmittance. By electrical characterization of these materials, it can identify the possible structural defects that can adversely affect the yield of sunlight conversion into electricity in dye-sensitized solar cells (DSSC).

The concurrent engineering is a modern design concept through which the product manufacture is safety accomplished. The flow chart illustrates the essential contributions which avoid the start mistakes and correct connection with market. The application of this design procedure brings important advantages: the primary manufacturing stages are fully automated, a unitary approach of item production, a minimal spent design time, a real-time connection between the contributing departments, a correct view of market supply.