Volume 16 – Issue 4

Twin primes are pairs of successive primes which differ by 2. They have been conjectured to be infinite in number but this awaits a proof. The consistent presence in higher number ranges is shown here. A detail analysis of twin primes, considering their starter partners, is done. For blocks of 1–10^n , 1 ≤ n ≤ 12, first and last twin prime pair starters are determined. Minimum number of twin primes in blocks, minimum occurrence frequency, first and last minimum twin prime container blocks are given. Similar analysis for maximum number of twin primes in blocks is also carried out.

New classes of integral inequalities are established in this paper by using a family of n positive functions, ( n ∈ N) with the help of Saigo’s fractional integral operator. Some consequent results and special cases of the main results are also pointed out.

An efficient method for the characterization of some important classes of matrices, using the rank, is the method of elementary operations in the partitioned matrices. We will use this method for idempotent matrices, involutory matrices, tripotent matrices and other classes of matrices with annihilator polynomials of the form f(x) = x^k -x^p

In this study, a reliable Homotopy Analysis Method (HAM) is applied to obtain analytical solutions of dielectric relaxation processes equation of fractional order. The, fractional derivatives are based on Jumarie’s fractional derivative sense. The obtained solutions which are valid at low temperatures are applied to the dielectric relaxation processes. The graphical representation of the obtained results is courageous

Evolution equation is among one of the important nonlinear partial differential equations and its exact solutions are of great interest for the researchers around the globe. In this article, a new analytical technique is used to search for exact solutions of nonlinear evolution equation with the aid of symbolic computation. To check the validity of the method developed, we choose the SRLW equation and many new and more general exact solutions have been obtained for the equation, which are of great importance. The efficiency of the developed scheme is confirmed since it provides more exact solutions than other techniques used now a day.

In this paper, we introduce the comparative study of derivative free new two step iterative method for finding the zeros of the nonlinear equation f(x) = 0 without the evaluation of the derivatives . It is established that the new method has convergence order three. The efficiency index of new method is equal to 1.442. The Convergence and error analysis are given. Numerical comparisons are made with other existing methods to show the performance of the presented methods.

The variational iteration method (VIM) is applied to find the approximate solutions of the Whitham-Broer-Kaup (WKB) shallow water model. The results obtained are compared with the exact solutions. The results show that the variational iteration method is efficient and practically well suited for solving coupled nonlinear water wave equations.

In this paper, we study the local properties of the intersection curve of a spacelike surface and a timelike surface. We derive the curvature vector, curvature and torsion for the transversal intersection for parametric-parametric intersection problem. Furthermore, we investigate some characteristic features of the intersection curve

The present paper is the investigation of some integrals for the generalized Bessel-Maitland functions, which are expressed in the terms of hypergeometric and beta function. Some interesting special cases involving Jacobi, Legendre polynomial are deduced. The integrals established in this paper are of general character.

Hastelloy C2000 is a nickel-base superalloy. With the addition of copper to nickel-chromium-molybdenum system, it is resistant to a wide range of corrosive chemicals as well as the combination of molybdenum and copper creates an excellent corrosion resistance to reducing media, while the high content of the chrome provides a good oxidation resistance. Its structure is face-centered cubic. The value of our work is to study the stability of the Hastelloy C2000 on its microstructure and mechanical properties and this by a heat treatment at four temperatures: 700 °C, 800 °C, 900 °C and 1000 °C with a prolonged maintenance at each temperature for three hours. The monitoring of these two aspects is performed using the following experimentals techniques: optical microscopy and hardness measurement. After heat treatment, the pictures obtained by optical microscopy revealed the presence of different morphologies of carbides, joints and inside the grains, also we remark the appearance of the discontinuous transformations and the coalescence phenomenon of grain to form a larger area of precipitation. For hardness in the over-aging, it attains a final value of 47 for the four samples treated at 700 °C, 800°C, 900 °C and 1000 °C.

Noninvasive glucose monitoring techniques based on optical coherence tomography (OCT) are affected by several per-turbing factors which must be taken into account, for example, variation of tissue temperature. Herein a direct method to detect the change in skin temperature based on the comparison of the peak levels that characterize the OCT signal during noninvasive OCT-based glucose monitoring is presented. A process is described for real time calibration and compensation of the induced error on blood glucose due to thermal effect by numerical analysis of B-scan OCT images.

Pollution of the production spaces within steel mills with particles in granular state may represent an environmental problem unless appropriate measures are taken. Thus, a viable solution may be the making of a composite material with a technological role, thanks to the distributed particles in granular state into metallic matrix. The research in the present paper aims at finding some obtaining technology for composite materials with metallic matrix (aluminium alloy A6061) and FeTi30 granular particles dispersed within metallic matrix, with complex deoxidant role in steel processing. Also, composite materials symbolised A6061/FeTi30 have been characterised from the chemical, structural and morphological points of view. From among the methods of obtaining composite materials, the application of vibration method has been taken into consideration, with the purpose of ensuring a high yield of embedding particles in granular state. In the process of steel making a rigorous control of technological parameters (amplitude and frequency of vibrations, temperature, time) was carried out.

OCP is the world’s largest exporter and producer of phosphate rock, In this context, OCP has adopted a new improvement plan which proposes to develop production of phosphate rock from 28 to 47 million tons in 2020. The horizon industrial advancement program of OCP excepted to increase water consumption of 73 to 181 million m3 / year for its various operations. In this paper we will do a feasibility study to achieve a positive energy balance due to the energy collected generated by an exothermic system for sulfuric acid production in two chemical processing sites (Jorf Lasfar and Asfi) and renewable energy integration in two mining operation sites: Khouribga, Ben Guerir for meet the growing needs on energy. The principal purpose of this article is to develop an innovative idea of a desalination plant to produce fresh water from seawater by using renewable marine energy, principally hydrokinetic and wave energy. The main achievements will be connected with the environment protection, low maintenance and its accessibility to small communities.

In this paper, a fuzzy PID controller has been suggested to use in attitude determination and control subsystem of kufasat equipped with three magnetic coils. Using the linearized equations of motion for a rigid body in space, the linearized stability, effectiveness and robustness of a fuzzy PID controller design were compared with that of a fuzzy PD controller design. The detailed design procedure of the fuzzy controllers is presented. When fuzzy PID controller is applied simulation results show that more precise attitude control is accomplished and less time of satellite maneuver is required comparing with applying fuzzy PD controller.

The interacting boson model (IBM-1) was used to study some properties for ^246 _96Cm _150 isotope, from important of these properties the probability of eelectric transitions B(E2), The B(E2) values for even-even ^246 _96Cm _150 isotope have been calculated and compared with the experimental data. The calculated B (E2) values are in good agreement with the experimental data. It has also been calculate reduced matrix elements < L_f || T^(E_2) || L_i> relevant the probability of electric transitions values B(E2). Furthermore, calculate the electric quadrupole moments (Q_L) to clarify the shape of the nucleus. In addition, a study square of rotational energy (ħ^2ω^2) and the moment of inertia (2ϑ/ħ^2) for each angular momentum and compared with experimental results and show that through drawing, where it was interpreted the change in the relationship between the moment of inertia (experimental and theoretical) as a function of angular momentum.

A bipolar plate design must take account of the functional role it plays within the basic nucleus of the fuel cell and consequently its functional role in the cell stack. The structure and geometry of the active, sealing, supplying and fixing surfaces is directly related to the electrochemical processes that take place in the cell and to the method of supply and distribution of the working gas and cooling water. Opting for design solutions involving the gas supply and distribution across the active surface of a bipolar plate strongly influences the performance of the basic cell. The active area cooling method is equally important for achieving high performance. H2 and O2 working gas flow simulation using the SolidWorks application’s Flow Simulation module enables the optimal design of the flow channels.