Azerbaijan University of Architecture and Construction

ABSTRACT In this paper, we consider a system of semilinear partial differential equations (PDEs) representing a spatially extended SIR epidemic model. A brief analytical investigation of the well‐posedness and positivity of the solutions is provided in the appendix, while the main focus is on the numerical treatment of the model. We examine the performance of several time‐stepping schemes, including the standard forward Euler, semi‐implicit Crank–Nicolson, their Mickens‐type nonstandard counterparts, and explicit exponential Runge–Kutta methods. Particular attention is given to the preservation of positivity in the numerical solutions, which is crucial for maintaining biological relevance. Two step‐size functions are employed, and the results are compared in terms of theoretical accuracy and computational runtime to identify the most efficient method for simulations. Our numerical results show that positivity is preserved by the standard and exponential methods only under certain restrictions on the time‐step size. In contrast, the corresponding nonstandard methods maintain positivity unconditionally, regardless of the time‐step size. These findings underscore the effectiveness of nonstandard schemes in modeling epidemic dynamics governed by reaction‐diffusion systems.

The paper discusses the dynamic study and formulation of the problem ofoptimizing a multi-span cable-stayed bridge. The project of a multi-span bridgeunder construction in Azerbaijan along the Muganly – Ismayilli – Gabala road wastaken as an analogue. As the acting loads on the bridge, the own weight of thestructure, loads from the wind, and earthquake transport loads were taken. Stiffness,mass and attenuation matrices of the bridge structure are compiled. The crosssection of the cables and the transfer force to the pylon were optimized. As a resultof calculations, the height of the pylons was reduced from 54 m to 25 m. This ledto a decrease in the number and total cross section of cables. Such bridges areusually referred to as extradosed bridges, which are an intermediate option betweena cable-stayed and a beam bridge.

Early carcinoma detection benefits from label-free, high-sensitivity surface plasmon resonance (SPR) biosensors. We computationally evaluated multilayer SPR architectures based on CaF2/Cu/TiO2/Graphene using the transfer-matrix method at 633 nm. Across 1–5 ng/mL, we analyzed reflectance, resonance-angle shifts, and near-field profiles, and derived sensitivity, detection accuracy (DA), figure of merit, and the limit of detection (LOD). The CaF2/Cu/TiO2/Graphene stack yielded the best performance, achieving 481.29°/RIU sensitivity and DA = 0.80, with pronounced evanescent-field confinement at the sensing interface. Under identical modeling conditions, this graphene-integrated configuration outperformed TiO2-only and Cu-only baselines within the studied range. These results indicate a cost-effective platform for sensitive carcinoma biomarker detection. Calculation details for LOD and other metrics are provided in Methods, and practical considerations for experimental realization are discussed.

The unpredictable and highly dynamic nature of cryptocurrency markets has driven researchers to develop advanced forecasting techniques that can support decision-making in trading and risk management. This study proposes a hybrid deep learning framework that combines a Transformer with recurrent models for multi-step Bitcoin price forecasting. The model operates on log-differenced closing prices and is evaluated for 7-, 14-, and 21-day ahead prediction using recursive multi-step forecasting schemes. In addition to the proposed Transformer-based architectures, a comprehensive comparison was conducted against four benchmark recurrent models, namely Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), along with their bidirectional variants Bidirectional-LSTM (BiLSTM) and Bidirectional GRU (BiGRU). Model performance was assessed using standard regression metrics, including Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Directional Accuracy (DA) to quantify the accuracy of predicted price movements. The experimental results show that the Transformer-based models outperform standalone recurrent architectures across all forecasting methods, with the Transformer-LSTM achieving the lowest error values and strong trend-tracking behavior. These findings highlight the effectiveness of hybrid attention-recurrent architectures for modeling the nonlinear and volatile dynamics of Bitcoin markets.

The integration of solar energy into smart grids requires high-efficiency power conversion to support grid stability. However, Partial Shading Conditions (PSCs) remain a primary obstacle by inducing multiple local maxima on P–V characteristic curves. This paper presents a hardware-aware and memory-enhanced Maximum Power Point Tracking (MPPT) approach based on a modified Dragonfly Algorithm (DA) for grid-connected microinverter-based photovoltaic (PV) systems. The proposed method utilizes a quasi-switched Boost-Switched Capacitor (qSB-SC) topology, where the DA is specifically tailored by combining Lévy-flight exploration with a dynamic damping factor to suppress steady-state oscillations within the qSB-SC ripple constraints. Coupling the MPPT stage to a seven-level Packed-U-Cell (PUC) microinverter ensures that each PV module operates at its independent Global Maximum Power Point (GMPP). A ZigBee-based Wireless Sensor Network (WSN) facilitates rapid data exchange and supports ‘swarm-memory’ initialization, matching current shading patterns with historical data to seed the population near the most probable GMPP region. This integration reduces the overall response time to 0.026 s. Hardware-in-the-loop experiments validated the approach, attaining a tracking accuracy of 99.32%. Compared to current state-of-the-art benchmarks, the proposed model demonstrated a significant improvement in tracking speed, outperforming the most recent 2025 GWO implementation (0.0603 s) by approximately 56% and conventional metaheuristic variants such as GWO-Beta (0.46 s) by over 94%.These results confirmed that the modified DA-based MPPT substantially enhanced the microinverter efficiency under PSC through cross-layer parameter adaptation.