Univ., Diss.--Kiel, 2002.

Heidelberg, Univ., Diplomarb., 1998.

This diploma thesis deals with Catholicism in Poland and its permeation through the Polish national identity. The introductory chapter characterizes the concept of identity Polak-Katolik and its individual aspects that co-create this concept, as a rate of religiosity; the interconnection of Catholicism with polish statehood; Christianity as a part of national identity and historical events during which the Polak-Katolik connection was strengthened. Although the Polak- Katolik model was created in the 19th century, the roots of this connection can be observed from the beginnings of the Polish history to the present. The thesis then focuses in more detail on selected historical milestones in Polish history, which shows, how the elements of Catholicism permeated into the identity of Poles. The thesis assumes that the permeation of polish-catholic occurred mainly in critical periods. Therefore, for the purposes of the work, mainly events were selected when the existence of the Polish nation was threatened and faith together with the Roman Catholic Church played significant role in its preservation, such as during the siege of the monastery in Czenstochowa, the period of polish partition and the period of communism. The final chapter deals with the current situation of Catholicism in Poland, the...

A new neural network approach for performing matrix computations is presented. The idea of this approach is to construct a feed-forward neural network (FNN) and then train it by matching a desired set of patterns. The solution of the problem is the converged weight of the FNN. Accordingly, unlike the conventional FNN research that concentrates on external properties (mappings) of the networks, this study concentrates on the internal properties (weights) of the network. The present network is linear and its weights are usually strongly constrained; hence, complicated overlapped network needs to be construct. It should be noticed, however, that the present approach depends highly on the training algorithm of the FNN. Unfortunately, the available training methods; such as, the original Back-propagation (BP) algorithm, encounter many deficiencies when applied to matrix algebra problems; e. g., slow convergence due to improper choice of learning rates (LR). Thus, this study will focus on the development of new efficient and accurate FNN training methods. One improvement suggested to alleviate the problem of LR choice is the use of a line search with steepest descent method; namely, bracketing with golden section method. This provides an optimal LR as training progresses. Another improvement proposed in this study is the use of conjugate gradient (CG) methods to speed up the training process of the neural network. The computational feasibility of these methods is assessed on two matrix problems; namely, the LU-decomposition of both band and square ill-conditioned unsymmetric matrices and the inversion of square ill-conditioned unsymmetric matrices. In this study, two performance indexes have been considered; namely, learning speed and convergence accuracy. Extensive computer simulations have been carried out using the following training methods: steepest descent with line search (SDLS) method, conventional back propagation (BP) algorithm, and conjugate gradient (CG) methods; specifically, Fletcher Reeves conjugate gradient (CGFR) method and Polak Ribiere conjugate gradient (CGPR) method. The performance comparisons between these minimization methods have demonstrated that the CG training methods give better convergence accuracy and are by far the superior with respect to learning time; they offer speed-ups of anything between 3 and 4 over SDLS depending on the severity of the error goal chosen and the size of the problem. Furthermore, when using Powell's restart criteria with the CG methods, the problem of wrong convergence directions usually encountered in pure CG learning methods is alleviated. In general, CG methods with restarts have shown the best performance among all other methods in training the FNN for LU-decomposition and matrix inversion. Consequently, it is concluded that CG methods are good candidates for training FNN of matrix computations, in particular, Polak-Ribidre conjugate gradient method with Powell's restart criteria.

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