‎This paper presents a method for Characteristic function assignment on rational functions by adding perturbation in systems with irrational Characteristic functions‎. ‎Generally‎, ‎in systems with irrational Characteristic loci‎, ‎commutative compensator designs are not possible‎. ‎Irrational Characteristic functions have different forms‎. ‎In our previous work‎, ‎mentioned in the introduction section‎, ‎a form of these Characteristic functions was presented‎. ‎Another form of irrational Characteristic functions is considered in this paper‎. ‎This approach is not based on the transfer function inverting‎, ‎and Characteristic loci are not used directly in the design process‎. ‎The efficacy of the proposed approach is investigated through two numerical examples‎.

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The duals of Gabor frames have an essential role in reconstruction of signals. In this paper we find a necessary and sufficient  condition for two Gabor systems $\left(\chi_{\left[c_1,d_1\right)},a,b\right)$ and $\left(\chi_{\left[c_2,d_2\right)},a,b\right)$ to form dual frames for $L_2\left(\mathbb{R}\right)$, where $a$ and $b$ are positive numbers and $c_1,c_2,d_1$ and $d_2$ are real numbers such that $c_1

Deriving an accurate and simple current-voltage (I-V) Characteristic for photovoltaic (PV) module is highly significant for condition monitoring, fault detection and maximizing power production in PV systems. Equivalent circuits consist of one or more diodes are mostly utilized for I-V curve modelling. However, these models are inherently implicit, relatively complex and nonlinear in their parameters. Here, a piecewise quadratic function with four different intervals is generated from the measured I-V data at standard test condition (STC). The intervals are chosen such that the best model performance can be achieved, especially at maximum power point. Each quadratic function is obtained from least square technique according to the experimental data in the corresponding interval. It is easy to obtain the voltage value at MPP from the extracted model, analytically. Also, a suggestion is provided for extending the generated I-V model to the real environmental condition by utilization of artificial neural network. The derived PV module model is highly suitable for maximum power point tracking, monitoring and fault detection due to its simplicity, explicit structure and accuracy.

A general concept of wavelets and multiresolution analysis on Sobolev space over local fields of positive Characteristic (Hs(K)) is given. A characterization of the scaling functions associated with an MRA is also given