Cell wall thickness and tangential and radial cell diameter of fertilized and irrigated Norway spruce

Abstract

On the differential evolution algorithm and its appliation to training radial basis function networks

The parameter setting of a differential evolution algorithm must meet several requirements: efficiency, effectiveness, and reliability. Problems vary. The solution of a particular problem can be represented in different ways. An algorithm most efficient in dealing with a particular representation may be less efficient in dealing with other representations. The development of differential evolution-based methods contributes substantially to research on evolutionary computing and global optimization in general. The objective of this study is to investigatethe differential evolution algorithm, the intelligent adjustment of its controlparameters, and its application. In the thesis, the differential evolution algorithm is first examined using different parameter settings and test functions. Fuzzy control is then employed to make control parameters adaptive based on an optimization process and expert knowledge. The developed algorithms are applied to training radial basis function networks for function approximation with possible variables including centers, widths, and weights of basis functions and both having control parameters kept fixed and adjusted by fuzzy controller. After the influence of control variables on the performance of the differential evolution algorithm was explored, an adaptive version of the differential evolution algorithm was developed and the differential evolution-based radial basis function network training approaches were proposed. Experimental results showed that the performance of the differential evolution algorithm is sensitive to parameter setting, and the best setting was found to be problem dependent. The fuzzy adaptive differential evolution algorithm releases the user load of parameter setting and performs better than those using all fixedparameters. Differential evolution-based approaches are effective for training Gaussian radial basis function networks.

Design of axial-flux permanent-magnet low-speed machines and performance comparison between radial-flux and axial-flux machines

This thesis presents an alternative approach to the analytical design of surface-mounted axialflux permanent-magnet machines. Emphasis has been placed on the design of axial-flux machines with a one-rotor-two-stators configuration. The design model developed in this study incorporates facilities to include both the electromagnetic design and thermal design of the machine as well as to take into consideration the complexity of the permanent-magnet shapes, which is a typical requirement for the design of high-performance permanent-magnet motors. A prototype machine with rated 5 kW output power at 300 min-1 rotation speed has been designed and constructed for the purposesof ascertaining the results obtained from the analytical design model. A comparative study of low-speed axial-flux and low-speed radial-flux permanent-magnet machines is presented. The comparative study concentrates on 55 kW machines with rotation speeds 150 min-1, 300 min-1 and 600 min-1 and is based on calculated designs. A novel comparison method is introduced. The method takes into account the mechanical constraints of the machine and enables comparison of the designed machines, with respect to the volume, efficiency and cost aspects of each machine. It is shown that an axial-flux permanent-magnet machine with one-rotor-two-stators configuration has generally a weaker efficiency than a radial-flux permanent-magnet machine if for all designs the same electric loading, air-gap flux density and current density have been applied. On the other hand, axial-flux machines are usually smaller in volume, especially when compared to radial-flux machines for which the length ratio (axial length of stator stack vs. air-gap diameter)is below 0.5. The comparison results show also that radial-flux machines with alow number of pole pairs, p < 4, outperform the corresponding axial-flux machines.

Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.