Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

A Novel Slotless Halbach-Array Permanent-Magnet Brushless DC Motor for Spacecraft Applications

This paper presents the design and analysis of a novel machine family—the enclosed-rotor Halbach-array permanentmagnet brushless dcmotors for spacecraft applications. The initial design, selection of major parameters, and air-gap magnetic flux density are estimated using the analytical model of the machine. The proportion of the Halbach array in the machine is optimized using finite element analysis to obtain a near-trapezoidal flux pattern. The machine is found to provide uniform air-gap flux density along the radius, thus avoiding circulating currents in stator conductors and thereby reducing torque ripple. Furthermore, the design is validated with experimental results on a fabricated machine and is found to suit the design requirements of critical spacecraft applications

A Multi-Objective Antenna Placement Genetic Algorithm for Matched Array Synthesis on Complex Platforms

A Multi-Objective Antenna Placement Genetic Algorithm (MO-APGA) has been proposed for the synthesis of matched antenna arrays on complex platforms. The total number of antennas required, their position on the platform, location of loads, loading circuit parameters, decoupling and matching network topology, matching network parameters and feed network parameters are optimized simultaneously. The optimization goal was to provide a given minimum gain, specific gain discrimination between the main and back lobes and broadband performance. This algorithm is developed based on the non-dominated sorting genetic algorithm (NSGA-II) and Minimum Spanning Tree (MST) technique for producing diverse solutions when the number of objectives is increased beyond two. The proposed method is validated through the design of a wideband airborne SAR