## 3 Results and Discussion
The curves’ numbering is consistent with Figure 1.  
From Figure 4, it could be concluded that increasing \(\Phi\) led to a rapid decrease in the interval of linearity or shift toward high temperatures (measurements were carried out up to 300 K); regarding the increase in \(z\), the situation was even more diverse, and namely, for concentration number 8 (of the experimental measurements) there was no linearity (up to 300 K), and the derivative decreased by increasing the temperature. That is, there was a contradiction such that by (with) increasing defectiveness, the parameters of the linear dependence \(\rho\)(T)-T\({}^{2}\) increased, but the linear dependence itself showed a tendency to disappear due to the narrowing of the interval of its existence. As noted above, there were noticeable differences in the evolution of resistivity curves under irradiation or doping with praseodymium. Figure 1 reveals that irradiation resulted in an anomalously strengthened (in comparison to the change in composition [1; 16; 22]) decrease in T\({}_{\rm c}\) in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-8}\). Nevertheless, the nature of the change in the electrical and superconducting properties of HTSC with a change in composition [1; 22] and under the action of irradiation was somewhat different. The primary difference was for Y\({}_{1-x}\)Pr\({}_{x}\)Ba\({}_{2}\)Cu\({}_{3}\)O\({}_{7-8}\) single crystals with \(T_{\rm c}<85\) K, where as a rule, a change in the shape of the \(\rho\)(\(T\)) curves was observed from metallic to the so-called \"S-shaped\" with a characteristic thermally activated deflection [1; 17; 18] (\(z>0.2\), Figure 1b); during irradiation, a similar \"S-shaped\" shape of the \(\rho\)(\(T\)) curves was observed for \(T_{c}<35\) K (\(\Phi>60\) e/cm\({}^{2}\), Figure 1a). A key reason for the strong decrease in T\({}_{\rm c}\) in irradiated samples was the appearance of dielectric inclusions under the influence of irradiation because of the redistribution of oxygen between the O(4) and O(5) positions and the formation of local regions with a tetragonal structure. With increased fluence, the T\({}_{\rm c}\) decreased from -92 to-24 K, and \(\rho_{ab}\)(300 K) increased from \(\rho\)-158 to 384 uOhm-cm, respectively, which is consistent with previous studies [26; 30]. Clearly similar effects were avoided when supplemented with praseodymium [1; 18]. The dependencies of \(T_{c}\) and \(\rho\)(300 K) on \(\Phi\) and \(z\) are shown in the insets in Figure 1a,b. As shown from Figure 1, below, for the characteristic temperature \(T^{*}\), the dependencies for all \(\rho_{ab}\)(\(T\)) curves were \"rounded off\", which may have been caused by the emergence of excess conductivity \(\Delta\sigma_{ab}\). [PERSON] and [PERSON] [13] used the following relation for the fluctuation conductivity in the plane of layers in the immediate vicinity of the SC transition:  
\[\Delta\sigma_{ab}=\frac{e^{2}}{16\hbar d}\frac{1}{\sqrt{[\varepsilon( \varepsilon+r)]}}, \tag{2}\]  
Figure 4: Interval of linearity as a function of \(\Phi\) or z for the cases of irradiation with different fluences of electrons or changes in praseodymium concentration. Numbers 1\(-\)8 correspond to the numbers of the curves in Figure 1.  
where \(d=11.7\) A and is the interlayer distance [31]. \[\varepsilon=\frac{T-Tc}{Tc}\ll 1;\ r=\frac{4\xi_{c}^{2}(0)}{d^{2}}. \tag{3}\]  
Equation (1) describes a \(2D\)-\(3D\) crossover that occurs in a certain temperature interval: when \(\varepsilon<<r\ \sigma_{ab}{}^{\mathrm{AL}}\infty(\varepsilon\ r)^{-1/2}\) (\(3D\) mode), but at \(\varepsilon>>r\ \sigma_{ab}{}^{\mathrm{AL}}\infty\varepsilon^{-1}\) (\(2D\) mode).