Shirali Kadyrov

S. Kadyrov, P. S. Skrzypacz, Y. L. Familiant

The paper aims to emphasise how switched systems can be analysed with elementary techniques which require only undergraduate-level linear algebra and differential equations. It is also emphasised how math software can become useful for simplifying analytic complications. The time domain voltage balance methodology is used for stability analysis. As for deriving formulas for the asymptotic average of both capacitor voltage and inductor current, a new simple analytic method is introduced. It was shown analytically that the time average of capacitor voltage converges to half of the source voltage. A formula for the time average of the current of the inductor is also computed. As a by-product it was discovered that the period of the current is half of the switching period. Numerical simulations are obtained to illustrate the accuracy of the results. Higher dimensional generalisations could become a bit complicated as stability analysis of higher dimensional exponential matrices are not so easy to handle. On the other hand, the new discovery on the period of the current is more likely to give new insights in handling higher dimensional systems. Analytical formulas are exact and it helps in accurately modelling flying capacitor converts in practice. FCC is well studied in engineering society. However, not much is done in obtaining exact formulas using analysis. Also, math software is much used in computation of numerical results and obtaining simulations. In this paper, one more important aspect of math software is emphasised, namely, use symbolic computations in analysis.

Farid Bozorgnia, Vyacheslav Kungurtsev, Shirali Kadyrov et al.

In this work, we introduce novel algorithms for label propagation and self-training using fractional heat kernel dynamics with a source term. We motivate the methodology through the classical correspondence of information theory with the physics of parabolic evolution equations. We integrate the fractional heat kernel into Graph Neural Network architectures such as Graph Convolutional Networks and Graph Attention, enhancing their expressiveness through adaptive, multi-hop diffusion. By applying Chebyshev polynomial approximations, large graphs become computationally feasible. Motivating variational formulations demonstrate that by extending the classical diffusion model to fractional powers of the Laplacian, nonlocal interactions deliver more globally diffusing labels. The particular balance between supervision of known labels and diffusion across the graph is particularly advantageous in the case where only a small number of labeled training examples are present. We demonstrate the effectiveness of this approach on standard datasets.

Meraryslan Meraliyev, Cemil Turan, Shirali Kadyrov

We study last-mile delivery with one truck and one drone under explicit battery management: the drone flies at twice the truck speed; each sortie must satisfy an endurance budget; after every delivery the drone recharges on the truck before the next launch. We introduce a hybrid reinforcement learning (RL) solver that couples an ALNS-based truck tour (with 2/3-opt and Or-opt) with a small pointer/attention policy that schedules drone sorties. The policy decodes launch-serve-rendezvous triplets with hard feasibility masks for endurance and post-delivery recharge; a fast, exact timeline simulator enforces launch/recovery handling and computes the true makespan used by masked greedy/beam decoding. On Euclidean instances with $N{=}50$, $E{=}0.7$, and $R{=}0.1$, the method achieves an average makespan of \textbf{5.203}$\pm$0.093, versus \textbf{5.349}$\pm$0.038 for ALNS and \textbf{5.208}$\pm$0.124 for NN -- i.e., \textbf{2.73\%} better than ALNS on average and within \textbf{0.10\%} of NN. Per-seed, the RL scheduler never underperforms ALNS on the same instance and ties or beats NN on two of three seeds. A decomposition of the makespan shows the expected truck-wait trade-off across heuristics; the learned scheduler balances both to minimize the total completion time. We provide a config-first implementation with plotting and significance-test utilities to support replication.