A note on "Relaxation Oscillators with Exact Limit Cycles"

In this note we give a family of planar polynomial differential systems with a prescribed hyperbolic limit cycle. This family constitutes a corrected and wider version of an example given in the work of M.A. Abdelkader entitled ``Relaxation Oscillators with Exact Limit Cycles'', which appeared in J. Math. Anal. Appl. 218 (1998), 308--312. The result given in this note may be used to construct models of Li\'enard differential equations exhibiting a desired limit cycle.Comment: 8 pages, no figure

Modelling thermal effects in agitated vessel and reactor design consideration

The knowledge of the heat transfer coefficient on the inner side of a heated vessel wall is of utmost importance for the design of agitated vessels. The present contribution deals with heat transfer in an agitated vessel containing non-Newtonian liquid. The impellers used are six-blade Turbine (TPD) and a Propeller (TPI). The following aspects are discussed: description of the heat transfer process with the aid of dimensional analysis, heat transfer correlations for agitated liquid and influence of impeller speed on heat transfer

Moments of order statistics from nonidentically Distributed Lomax, exponential Lomax and exponential Pareto Variables

In this paper, the probability density function and the cumulative distribution function of the rth order statistic arising from independent nonidentically distributed (INID) Lomax, exponential Lomax and exponential Pareto variables are presented. The moments of order statistics from INID Lomax, exponential lomax and exponential Pareto were derived using the technique established by Barakat and Abdelkader. Also, numerical examples are given

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer: the effect of conducting bounding plates

The aim of this study was to investigate the effect of conducting boundaries on the onset of convection in a binary fluid-saturated porous layer. The isotropic saturated porous layer is bounded by two impermeable but thermally conducting plates, subjected to a constant heat flux. These plates have identical conductivity. Moreover, the conductivity of the plates is generally different from the porous layer conductivity. The overall layer is of large extent in both horizontal directions. The problem is governed by seven dimensionless parameters, namely the normalized porosity of the medium ε, the ratio of plates over the porous layer thickness δ and their relative thermal conductivities ratio d, the separation ratio δ, the Lewis number Le and thermal Rayleigh number Ra. In this work, an analytical and numerical stability analysis is performed. The equilibrium solution is found to lose its stability via a stationary bifurcation or a Hopf bifurcation depending on the values of the dimensionless parameters. For the long-wavelength mode, the critical Rayleigh number is obtained as Racs=12(1+2dδ )/[1+ψ (2dδLe+Le+1)] and kcs=0 for ψ> ψ uni> 0. This work extends an earlier paper by Mojtabi and Rees (2011 Int. J. Heat Mass Transfer 54 293-301) who considered a configuration where the porous layer is saturated by a pure fluid

CUCKOO SEARCH ALGORITHM TO SOLVE THE PROBLEM OF ECONOMIC EMISSION DISPATCH WITH THE INCORPORATION OF FACTS DEVICES UNDER THE VALVE-POINT LOADING EFFECT

The essential objective of optimal power flow is to find a stable operating point which minimizes the cost of the production generators and its losses, and keeps the power system acceptable in terms of limits on the active and reactive powers of the generators. In this paper, we propose the nature-inspired Cuckoo search algorithm (CSA) to solve economic/emission dispatch problems with the incorporation of FACTS devices under the valve-point loading effect (VPE). The proposed method is applied on different test systems cases to minimize the fuel cost and total emissions and to see the influence of the integration of FACTS devices. The obtained results confirm the efficiency and the robustness of the Cuckoo search algorithm compared to other optimization techniques published recently in the literature. In addition, the simulation results show the advantages of the proposed algorithm for optimizing the production fuel cost, total emissions and total losses in all transmission lines