The majority of real-world problems involve not only finding the optimal solution, but also this solution must satisfy one or more constraints. Differential evolution (DE) algorithm with constraints handling has been proposed to solve one of the most fundamental problems in cellular network design. This proposed method has been applied to solve the radio network planning (RNP) in the forthcoming 5G Long Term Evolution (5G LTE) wireless cellular network, that satisfies both deployment cost and energy savings by reducing the number of deployed micro base stations (BSs) in an area of interest. Practically, this has been implemented using constrained strategy that must guarantee good coverage for the users as well. Three differential evolution

The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex

    The ion-pair formation method has been applied for the spectrophotometric determination of Cimetidine and Erythromycin ethylsuccinate, in bulk samples and in dosage form. The methods are accurate, simple, rapid, inexpensive and sensitive depending on the extraction of the formed ion-pair with brompthymol blue (BTB) as a chromogenic reagent in chloroform, use phthalate buffer of pH 5.5 and 4.0 for Cimetidine and Erythromycin ethylsuccinate respectively.  The formed complexes show absorbance maxima at 427.5 nm and 414.5 nm for Cimetidine and Erythromycin ethylsuccinate respectively against reagent blank. The calibration graphs are linear in the ranges of 0.5-15 µg.mL-1 with detection limit of 0.222 µg.mL-1 for

Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

The maximization of the net present value of the investment in oil field improvements is greatly aided by the optimization of well location, which plays a significant role in the production of oil. However, using of optimization methods in well placement developments is exceedingly difficult since the well placement optimization scenario involves a large number of choice variables, objective functions, and restrictions. In addition, a wide variety of computational approaches, both traditional and unconventional, have been applied in order to maximize the efficiency of well installation operations. This research demonstrates how optimization approaches used in well placement have progressed since the last time they were examined. Fol

A new, simple, accurate, fast and sensitive spectrophotometric method has been
developed for the analysis of Pyrocatechol, Resorcinol, and pyrogallolin pure
commercial samples by continuous flow injection analysis. The method was based on
the oxidation of the organic compounds with Ce(IV)sulfate in acidic medium to
formed a brown colored species which determined using homemade Ayah 3SBGR x3-
3D solar cell flow injection microphotometer. Optimum conditions were obtained
using a high intensity green light emitted diode as an irradiation source
forPyrocatechol, Resorcinol, whileblue light emitted diode as an irradiation source for
pyrogallol. The linear dynamic range for the instrument response versus Pyrocatechol,

        The aim of this paper is to obtain a set of traveling wave solutions for klein –Gorden equation with kerr law non-linearity. More precisely, we apply a new path of popularized homogeneous balance (HB) method in terms of using linear auxiliary equations to find the results of non-linear klein-Gorden equation, which is a fundamental approach to determine competent solutions. The solutions are achieved as the integration of exponential, hyperbolic, trigonometric and rational functions. Besides, some of the solutions are demonstrated by the3D graphics.

Theoretical and experimental investigations of free convection through a cubic cavity with sinusoidal heat flux at bottom wall, the top wall is exposed to an outside ambient while the other walls are adiabatic saturated in porous medium had been approved in the present work. The range of Rayleigh number was and Darcy number values were . The theoretical part involved a numerical solution while the experimental part included a set of tests carried out to study the free convection heat transfer in a porous media (glass beads) for sinusoidal heat flux boundary condition. The investigation enclosed values of Rayleigh number (5845.6, 8801, 9456, 15034, 19188 and 22148) and angles of inclinations (0, 15, 30, 45 and 60 degree). The numerical an