In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partial differential equations (PDEs). The key idea of this approach is the use of the asymptotic-expansion theory, which allows us to determine the conditions for the existence and uniqueness of a solution to a given PDE with a sharp transition layer. As a by-product, we derive a simpler link equation between the source function and first-order asymptotic approximation of the measurable quantities, and based on that equation we propose an efficient inversion algorithm, AER, for inverse source problems. We prove that this simplification will not decrease the accuracy of the inversion result, especially for inverse problems with noisy data. Various numerical examples are provided to demonstrate the efficiency of our new approach. COPYRIGHT: © Global Science Press

We consider one of the cybernetic methods in biology related to the study of DNA chains. Namely, we are considering the problem of reconstructing the distance matrix for DNA chains. Such a matrix is formed on the basis of any of the possible algorithms for determining the distances between DNA chains. The objects of research of these algorithms (for mammals), as a rule, are one of the following 3 variants: the main histocompatibility complex, the mitochondrial DNA, and “the tail” of the Y chromosome. In the paper we give an improved algorithm for restoring the distance matrix for DNA chains. Compared to our previous publications, the following changes have been made to the algorithm. We abandoned the use of the branches and bounds method, but at the same time significantly improved the greedy auxiliary algorithm used in it. In this paper, we apply only this greedy algorithm to the general solution of the distance matrix reconstruction problem. As a result of the conducted computational experiments carried out on one of the two considered criteria for the quality of the algorithms, significant improvements were obtained compared to the results given in our previous publications. At the same time, the total running time of the algorithm remained almost the same as in the previous version.

Background/Objectives: The growing diversity of novel nanoparticle synthesis methods, particularly for silver nanoparticles (AgNP), coupled with their significant biological activity and wide range of applications across various medical fields, necessitates a comprehensive investigation into the consequences of particle-induced cellular damage. This study aimed to investigate AgNP-induced damage to macrophage plasma membranes, focusing on concentration, temperature, incubation time, and the role of pro- and antioxidant factors, using model systems based on mouse peritoneal macrophages. Methods: Mouse peritoneal macrophages were incubated with AgNP (0.1–10 μg/mL) at temperatures ranging from 4 °C to 37 °C. Membrane integrity was assessed via microfluorimetric analysis. The influence of prooxidant (UV-B) and antioxidant (serotonin) factors was also examined. A mathematical model was developed to describe the interaction between AgNP and macrophages. Results: The diameter of our synthesized silver nanoparticles, assessed via dynamic light scattering (DLS), ranged from 5 to 170 nm, with a predominant size distribution peak at 70 nm. AgNP caused dose- and temperature-dependent membrane damage, which was more pronounced at 4 °C and 37 °C than at 22 °C and increased with incubation time. UV-B enhanced membrane damage, while serotonin mitigated it. The mathematical model correlated strongly with the experimental data, emphasizing the role of ROS in membrane disruption. AgNP also dose-dependently increased ROS generation by macrophages. Conclusions: AgNP, in doses of 0.1–10 μg/mL, induces dose-dependent membrane damage in macrophages. The developed model is a useful tool for predicting nanoparticle toxicity. Together with the experimental findings, it highlights the critical role of ROS, lipid peroxidation, the lipid bilayer state, and antioxidant defenses in AgNP-induced membrane damage.

This paper presents an AI-augmented pronunciation training approach for Russian language learners through a mobile application that supports an interactive learner–system feedback loop. The system combines a pre-trained Wav2Vec2Phoneme neural network with Needleman–Wunsch global sequence alignment to convert reference and learner speech into aligned phoneme sequences. Rather than producing an overall pronunciation score, the application provides localized, interpretable feedback by highlighting phoneme-level matches and mismatches in a red/green transcription, enabling learners to see where sounds were substituted, omitted, or added. Implemented as a WeChat Mini Program with a WebSocket-based backend, the design illustrates how speech-to-phoneme models and alignment procedures can be integrated into a lightweight mobile interface for autonomous pronunciation practice. We further provide a feature-level comparison with widely used commercial applications (Duolingo, HelloChinese, Babbel), emphasizing differences in feedback granularity and interpretability rather than unvalidated accuracy claims. Overall, the work demonstrates the feasibility of alignment-based phoneme-level feedback for mobile pronunciation training and motivates future evaluation of recognition reliability, latency, and learning outcomes on representative learner data.

The paper investigates the role of solid solution strengthening on the shock wave structure and Hugoniot elastic limit (HEL) in [111] copper crystals by molecular dynamics. Cu–Ni, Cu–Zn, Cu–Ag, and Cu–Al solid solutions are chosen to cover the range of atomic size misfit parameters for the solute atoms. The results show that in crystals with dislocations, the HEL decays slower with an increase in the misfit parameter of the solute, resulting in higher HEL values at a certain shock propagation distance. The Cu–Al solid solutions with the largest misfit parameter exhibit the largest deceleration of HEL decay. When the concentration of Al atoms increases to 20 at. %, the HEL almost does not change with shock propagation distance and a plateau shape of the elastic precursor is observed, as in the case of perfect crystals. In solid solutions without dislocations, the elastic precursor forms at lower velocities compared with perfect copper crystals, except for the Cu–20 at. % Ni solid solution. The HEL values increase with increasing misfit parameters and may take values lower than that for pure copper. These results show that the formation of the elastic precursor is facilitated by the presence of solid solution atoms, but the HEL magnitude and decay exponent are related to dislocation mobility in [111] copper crystals.

In this study, we investigate the dynamics of moving fronts in three-dimensional spaces, which form as a result of in-situ combustion during oil production. This phenomenon is also observed in other contexts, such as various autowave models and the propagation of acoustic waves. Our analysis involves a singularly perturbed reaction–diffusion–advection type initial–boundary value problem of a general form. We employ methods from asymptotic theory to develop an approximate smooth solution with an internal layer. Using local coordinates, we focus on the transition layer, where the solution undergoes rapid changes. Once the location of the transition layer is established, we can describe the solution across the full domain of the problem. Numerical examples are provided, demonstrating the high accuracy of the asymptotic method in predicting the behaviors of moving fronts.