## 8 Conclusions (with Elements of Results Analysis)
Comparison of numerical values of temperatures \({\rm T}_{\rm c}\) and \({\rm T}_{\rm cr,relax}\) is established from the solution of Equation (8c) or (8d). 9. The theoretical scheme has been developed for a more stringent, in comparison with item 7 of the conclusions, analysis of the behavior of the real component of the dielectric constant in the low-frequency range \(\omega T_{\rm D}\)\(<<\)\(1\), with a mixed dielectric relaxation mechanism (\(\frac{T_{\rm D}}{T_{\rm M}}>0\)) when the relaxation parameters (33a), (47), (48) are converted to the form (60a), (60b). This, as in the case of (42), also allows us to proceed to the study of the quasi-stationary polarization mode, according to the condition \(\omega T_{\rm D}\to 0\), when \(\Gamma_{\rm 1}^{(\omega=0)}\!\left(\frac{T_{\rm D}}{T_{\rm M}}\!\cdot\!0\right)=1- \frac{\hbar\Omega_{\rm c}}{\zeta}\), \(\Gamma_{\rm 2}^{(\omega=0)}\!\left(\frac{T_{\rm D}}{T_{\rm M}}\!\cdot\!0\right)\to 0\). _Variable_\(\zeta=\frac{\pi}{2}\sqrt{\frac{T_{\rm D}}{T_{\rm M}}}\) has been entered. The first of the dispersion expressions (38) is brought to a stationary form, which made it possible to present the generalized analytical expression for static dielectric constant in the form convenient for comparing the results of the theory and experiment \({\rm Re}\!\left[\hat{\varepsilon}^{(\omega=0)}\right]=\varepsilon_{\infty}\frac{1 }{1-\Gamma_{\rm 1}^{(\omega=0)}\left(\frac{T_{\rm D}}{T_{\rm M}}\!\cdot\!0\right)}= \varepsilon_{\infty}c\)tch\(\zeta\). This is a relevant result for this field of research, allowing us to identify, at the theoretical level, in the wide temperature range (0-1500 K), the influence of the microscopic and macroscopic mechanisms of relaxation processes in dielectric (diffusion and Maxwell relaxation; tunnel and thermally activated relaxation; electret effect; quasi-ferroelectric effect, etc.) on the nonlinear polarization effects associated primarily with the interactions of relaxation modes of the volumetric charge at the fixed frequency of an alternating field. In this matter, we limited ourselves to the fundamental frequency harmonic of polarization in the form of (8) in the framework of this paper. The study of the non-linear relaxation processes on the frequency harmonics of the polarization of the higher orders of magnitude, at least from the third \({\rm P}^{(3\omega)}(t)\)(see formula (25)), etc., is the subject of a separate research and will be carried out in subsequent works. 10. The results obtained in this paper relate primarily to the category of applied theoretical studies in the field of dielectric physics and condensed state physics. They are aimed at improving existing and developing additional schemes for the theoretical analysis of nonlinear kinetic phenomena associated with the relaxation transfer of the most mobile charge carriers (relaxers) in the crystal structure of dielectrics with an ion-molecular type of chemical bonds (ceramics, layered silicates, crystalline hydrates, perovskites, vermiculites, clay minerals, halloysite, etc.) when polarizing dielectrics in variable external fields. The results obtained in this paper described in claims one to eight of the conclusions are relevant and scientifically significant for a number of fields of modern science. In particular, we could point out their potential application in the development of theoretical ideas about quantum mechanisms for the formation of a ferroelectric state due to the tunneling of protons in the hydrogen sublattice of KDP, DKDP crystals, which are of significant practical importance for laser technology (regulators of radiation parameters), nonlinear optics and optoelectronics (electro-optical sensors, the sensors of the deformations of hard rocks and building materials, the parts of machines and mechanisms, etc.). They are also significant for information technologies (thin-film ferroelectric elements of microcircuits for fast-acting non-volatile memory devices with abnormally long residual polarization retention time (up to 10 years)).