Computational Mathematicsematics

Applied and Computational Complex Analysis. I: Power Series, by Peter Henrici

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By Peter Henrici

This quantity, after laying the mandatory foundations within the concept of strength sequence and complicated integration, discusses functions and uncomplicated idea (without the Riemann mapping theorem) of conformal mapping and the answer of algebraic and transcendental equations.

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In a particular example, the total number of fuzzy rules for a NN having 4 inputs, 1 output and 3 membership functions on each input, is 3 × 3 × 3 × 3 = 81 fuzzy rules. If the case is of an existing relationships between input 1 and input 2 for example, and also between inputs 3 and 4, these input are grouped in a hierarchical structure as in Fig. 6. Every fuzzy unit is described by 3×3 fuzzy rules, which mean an important diminishing of the total number of equivalent fuzzy rules. NN Output y (a) NN Input x1 x2 x3 x4 NN Output (b) NN Input x1 x2 x3 x4 Fig.

2000). The NN-FS HIS models combine, in a single framework, both numerical and symbolic knowledge about the process. Automatic linguistic rule extraction is a useful aspect of NN-FS HIS especially when little or no prior knowledge about the process is available [4, 19]. For example, a NN-FS HIS model of a non-linear dynamical system can be identified from the empirical data. This model can give some insight about the nonlinearity and dynamicsproperties of the system. But NN-FS HIS networks by intrinsic nature can handle just a limited number of inputs.

Whereas in the classification stage, a NN-FS HIS network with more transparency is required. The following characteristics of NN-FS HIS models are important: Approximation/Generalization capabilities; Transparency – Reasoning/use of prior knowledge/rules; Training Speed/Processing speed; Complexity; Transformability – To be able to convert in other forms of NN-FS HIS models in order to provide different levels of transparency and approximation power; Adaptive learning. Two most important characteristics are the generalizing and reasoning capabilities.

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