## 5 Concluding Remarks
Several of these computational procedures have been build on the basis of famous traditional and newer investigations [42; 43; 44; 45; 46; 47; 48; 49; 50]. These units are enhancing the analogous ones that are implemented in CASs that are scheduled for scientific computations. The presented units are a part of the wider plan for researching nonlinear differential systems. We are deploying scalable cloud software tools through server-free architectures [51]. Server-free architectures enable the auto-scaling of the software system when the load is higher. Furthermore, these can be used for the simultaneous performance of proper computational processes in pursuit of the best performance. Where this can be implemented, we engage many optimizing tools for high-precision computations, involving multi-processor and multi-threading computations; moreover, hardware-specific software improvements can be made [52; 53; 54]. The software framework is presented alongside the realized computational procedures through regular APIs with REST and HTTP, with data serialization using XML and JSON formats. The API can be utilized by reporting and analytic software systems such as Excel and PowerBI to study the outcomes further [55]. For more details, see [24]. The research can pursue the following avenues for test theory and e-learning: developmental evolution to e-learning from CBT [56], studying ambiance [57], DeLC study e-portal [58], Virtual Educational Space [59], and production of exam issues [60]. We define the hypothetical normalized antenna factor, as follows:  
\[M^{*}(\theta)=\frac{1}{D}|M(K\cos\theta+k_{1})|\]  
where  
* \(\theta\) is the azimuth angle;
* \(K=kd\); \(k=\frac{2\pi}{\lambda}\); \(\lambda\) is the wave length; \(d\) is the distance between emitters;
* \(k_{1}\) is the phase difference. A typical antenna factor for (1) is \(A=0.13\); \(\omega=0.6\); \(g_{1}=-0.09\); \(g_{2}=-0.05\); \(K=5\); \(k_{1}=3.1\) and for (2) it is \(A=0.129\); \(\omega=0.6\); \(g_{1}=-0.06\); \(g_{2}=-0.054\); \(K=4.65\); \(k_{1}=-1.882\) (from Proposition 2). These are depicted in Figure 17.  
Let us now focus on \(M(t)\) from Proposition 4. Following the classical Dolph-Chebyshev, Gegenbauer, and Soltis antenna arrays, we will call \(M(\theta)\) the Melnikov antenna array. For fixed \(A=0.0001\); \(\omega=0.2\); \(g_{1}=0.005\); \(K=9\); \(k_{1}=0.01\), see Figure 18.  
Of course, after serious consideration from specialists working in this scientific field, the hypothetical Melnikov array proposed by us can be seen as a supplementation to the array antenna theory. In our application, we also use a computational procedure for the oversight and depiction of the antenna factor (with an appropriate user-chosen magnitude for sideways radiation). This is based on the research presented in [27; 61]. Based on the theoretical results presented in Section 4, we envisage an inclusion of this in our web-based application of specialized algorithms for controlling the oscillations caused by the new probability-based constructions. Regarding other options for control, see [21]. At this stage, the web-based application is the intellectual property of the authors. Early next year, the multilayered architecture will be published with all its connections, attributes, and functionalities--calculation timing, graphics refinement, built-in computing mechanisms, and more. **Author Contributions:** Conceptualization, N.K. and V.K. ; methodology, T.Z. and V.K. ; software, V.K., A.I., and A.R. ; validation, N.K., A.R., T.Z. and V.K. ; formal analysis, V.K. and N.K. ; investigation, A.I., T.Z., A.R. and N.K. ; resources, A.R., T.Z., V.K. and N.K. ; data curation, N.K. and A.I. ; writing--original draft preparation, V.K., A.I. and A.R. ; writing--review and editing, N.K. and T.Z. ; visualization, V.K. ; supervision, N.K. and T.Z. ; project administration, N.K. ; and funding acquisition, A.R., T.Z., N.K. and A.I. All authors have read and agreed to the published version of the manuscript. This research received no external funding.