Asymptotic behavior of the continuous and discrete solutions to a multi-term fractional differential equation

A central event-triggered nonlinear MPC approach to reduce the computational time of WMR.

Halide perovskite single crystals hold great promise for photovoltaic applications, yet their iodine-deficient surfaces critically hinder device efficiency and stability. Herein, a hierarchical surface defect management strategy combining growth engineering with postmodification is proposed to eliminate depth-dependent iodide vacancies. Controlled crystal growth in a metastable region via continuous solute replenishment effectively removes iodide vacancies within micrometer depths, while subsequent organic ammonium treatment eliminates residual vacancies at the outermost crystal surface. This synergistic approach significantly optimizes carrier transport and suppresses nonradiative recombination, thereby boosting the efficiency of single-crystal perovskite solar cells (PSCs) from 22.8 to 25.5%. Moreover, suppression of multidirectional iodide migration extends the operational T90 (remaining 90% of initial efficiency) lifetime from 200 to 1000 h. These results highlight the critical role of hierarchical iodide vacancy management in resolving surface issues of perovskite single crystals, which is valuable for developing high-performance, diverse optoelectronic devices, including solar cells, X-ray detectors, light-emitting diodes, and field-effect transistors.

Modern wireless networks operate in a complex interference environment that requires to develop continuous technical solutions in order to improve the reliability and efficiency of communications. In wireless telecommunication systems, methods for transmitting information flows using multiple parallel orthogonal carrier frequencies are actively applied – for example, OFDM technology. When inter-symbol interference is detected, processing OFDM signals using classical methods or the algorithm «reception «as a whole» with element-wise decision-making requires knowledge of channel parameters. Specifically, the impulse response can be estimated by use of the regularization method, and the results of estimation with the use of the regularization method for «bad» channels with intersymbol interference can be improved through optimal selection of test combinations. To confirm all of the above, simulation using statistical trials for basic OFDM technology as well as applicable to N-OFDM, COFDM, and OFDMA technologies was performed.

The increasing prevalence of cardiovascular diseases demands affordable, accessible, and continuous cardiac monitoring solutions. Although an Electrocardiogram (ECG) is considered the clinical gold standard, long-term real-time monitoring of healthy individuals is limited. On the other hand, photoplethysmography is a simple and cost-effective technique, but it can be susceptible to noise and signal distortion. This study attempts to bridge the gap by proposing a novel framework for Photoplethysmogram (PPG) to ECG transformation, using spectral transformation methods such as Short-Time Fourier Transform (STFT), Discrete Cosine Transform (DCT), Wavelet Transform (WT), and Fast Fourier Transform (FFT). Deep learning models, namely Convolutional Neural Network (CNN), Convolutional Neural Network-Gated Recurrent Unit (CNN-GRU), and Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM), were trained on the UCI Machine Learning Repository version of the MIMIC II dataset and PulseDB Vital datasets to reconstruct ECG from PPG, achieving a correlation coefficient of 0.9731. Validated on MIMIC III, robustness was confirmed with a correlation of 0.9639. The proposed framework leverages frequency-domain representations and lightweight, efficient deep learning models, making it well-suited for integration into real-time and resource-limited environments, such as wearable health monitoring systems, and serves as a foundation for future non-invasive blood pressure estimation using only PPG input.

Respiration volume, i.e., the amount of air inhaled/exhaled during breathing, is a critical measure for health and fitness in daily life, such as helping optimize sports performance, tracking wellness, and early anomaly detection. Current continuous respiration volume monitoring solutions either require specialized and cumbersome instrumentation setup (e.g., RF transceivers), or rely on customized and non-portable wearables (e.g., masks and chest straps), limiting their usage scenarios. In this paper, we introduce EarMeter, the first continuous respiration volume monitoring system that utilizes in-ear microphones on earbuds to seamlessly track respiration volume across varying breathing intensities, making the measurement more accessible in diverse scenarios. The underlying idea is that breathing sounds, which correlate with breathing volume, can propagate through the body to the ear canals, where they are captured by in-ear microphones. To achieve this, we propose a deep-learning approach to address four unique challenges: limited labeled data, faint breathing sounds, interference from footsteps, and generalization to unseen users. Our approach features fine-tuning an audio encoder pretrained on a broad range of audio datasets, knowledge transfer from high-quality nose audio, performance boosting with breathing-heartbeat coupling, and alignment of both earphone channels with normalization. Extensive experiments under the Leave-One-Subject-Out (LOSO) setting across varying breathing intensities demonstrate the effectiveness of EarMeter, with an average Mean Absolute Percentage Error (MAPE) of 18.19%, meeting the clinically required standard of 20%.

In this research work, we are interested in the discrete study of the blow-up time of the solution of certain nonlinear parabolic Partial Differential Equations (PDEs) subject to nonlinear boundary conditions. We have been able to establish the necessary and sufficient conditions under which the discrete solution of the problem blows up in a finite discrete time and, at the same time, we have given an estimate of this blow up time. Also, using a convergence study, we showed that the discrete time and solution converge respectively to the continuous time and solution when the discretization steps in space and time tend towards zero. Finally, we illustrated our analysis with graphical representations and some numerical results.

Cloud computing has become the backbone of modern business operations, yet it remains vulnerable to a range of disruptive crises that can cripple organizations overnight. This research examines the real-world incidents that have affected millions of users globally—from unexpected service outages and security breaches to performance degradation and vendor lock-in scenarios. By analysing the root causes behind these failures, we identify six critical contributing factors: infrastructure vulnerabilities cantered on single points of failure, human error in configuration management, the inherent complexity of interconnected systems, insufficient testing protocols, rapid scaling limitations, and evolving cyber security threats. Rather than dwelling on problems alone, this work presents a practical framework of mitigation strategies that organizations can implement today. These include adopting multi-region and multi-cloud architectures to build resilience, conducting regular security assessments, establishing automated backup and recovery systems, deploying continuous monitoring solutions, embracing zero-trust security principles, and fostering a culture of cloud security awareness through employee training. The research demonstrates that while cloud crises are inevitable, their impact can be significantly reduced through proactive planning, strategic redundancy, and a comprehensive incident response capability

The continuous solid solution series based on the ion exchangeable Dion-Jacobson layered perovskites, A1−xA′xLaNb2O7 (A/A′ = Li, Na, K, Rb, Cs; 0 ≤ x ≤ 1), has been investigated to illuminate the relationship between composition and structure. Topochemical synthesis of the solid solutions from combinations of various alkali metal cations has been achieved by reacting pure end members (ALaNb2O7) at appropriate ratios and temperatures. All adjacent sets of alkali metals (Li/Na, Na/K, K/Rb, and Rb/Cs) readily formed solid solutions, while only the one non-adjacent solid solution, K1−xCsxLaNb2O7 (K/Cs), could be obtained. Local cation coordination and the corresponding layer alignments vary as a function of composition where the relative concentration of the larger cation dictates structure. Thermal analysis of the solid solutions, A1−xA′xLaNb2O7 (A/A′ = Li, Na, K) showed that the lithium- and sodium-containing compositions were thermally unstable. This study demonstrates that the systematic variation in average cation sizes in the solid solution series allows for structural control in these important perovskite hosts.

The critical chain method is often used to improve robustness in single-project scheduling, but there are two challenges when applying it to multi-project scheduling. First, the existing robustness measure focuses on time elasticity within sub-projects but neglects elasticity across sub-projects, making it difficult to balance drum resource requirements. Second, the differential evolution (DE) algorithm is adopted to solve this problem, but continuous evolutionary operators have limited flexibility, leading to numerous transformations between the continuous solution space and the discrete problem space. Therefore, we adjust the critical chain multi-project scheduling model by incorporating the drum buffer and the capacity constraint buffer and propose a robustness measure that considers both time elasticity within and among sub-projects. Meanwhile, we design an enhanced discrete DE algorithm, which not only discretizes the encoding–decoding strategy and evolutionary operators but also uses a hill-climbing algorithm to enhance local search. Experiments are conducted to verify the effectiveness of the robustness measure and the algorithm. The results indicate that, averaged over the eight instances, the enhanced discrete DE algorithm achieves an improvement of more than 3.3% in robustness compared with the overall mean of the benchmark algorithms. Furthermore, our robustness measure strengthens the stability of the scheduling plan and reduces buffer consumption and overflow during multi-project scheduling.

A bstract We investigate the dynamics of black hole critical collapse in the limit of a large number of spacetime dimensions, D . In particular, we study the spherical gravitational collapse of a massless, scale-invariant scalar field with continuous self-similarity (CSS). The large number of dimensions provides a natural separation of scales, simplifying the equations of motion at each scale where different effects dominate. With this approximation scheme, we construct matched asymptotic solutions for this family, including the critical solution. We then compute the mass critical exponent of the black hole for linear perturbations that break CSS, finding that it asymptotes to a constant value in infinite dimensions. Additionally, we present a link between these solutions and closed Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies with a dimension-dependent equation of state and cosmological constant. The critical solution corresponds to an unstable Einstein-like universe, while subcritical and supercritical solutions correspond to bouncing and crunching cosmologies respectively. Our results provide a proof of concept for the large- D expansion as a powerful analytic tool in gravitational collapse and suggest potential extensions to other self-similar systems.

In this paper, we define the nonlinear delayed Abel fractal integral equation of the second kind. The existence of solutions in the two classes, of continuous C[0, T] and integrable L1[0, T] functions, will be proved. The continuous dependence of the unique solution on the parameters will be proved. The Hyers-Ulam stability of the problem itself will be studied.

This article presents an innovative multi-source uninterrupted power system designed to address critical reliability requirements in mission-essential facilities where power interruptions can result in catastrophic consequences. The proposed architecture integrates diverse energy sources, including grid power, renewable inputs, backup generators, and battery storage under unified intelligent control, eliminating single-point failure vulnerabilities inherent in conventional UPS systems. Through advanced hybrid alternator technology incorporating power electronics and DC link voltage regulation, the article achieves frequency-independent operation adaptable to global electrical standards without hardware modifications. The intelligent control framework employs hierarchical decision-making with predictive algorithms enabling zero-delay source transitions while optimizing energy utilization based on real-time conditions. Experimental validation demonstrates superior efficiency across all loading conditions, particularly at partial loads where traditional systems exhibit significant losses. Practical deployments in data centers, healthcare facilities, and defense installations confirm operational reliability exceeding industry standards while reducing environmental impact through maximized renewable energy utilization. This article establishes a comprehensive framework for next-generation power continuity solutions capable of meeting the evolving demands of increasingly digitalized and sustainability-focused critical infrastructure.

From Cuffs to Code: Machine Learning in Non-Invasive Blood Pressure Monitoring.

ABSTRACT Microplastics pollution is a growing environmental concern, particularly in aquatic ecosystems, where it poses significant threats to organisms and ecosystems. Originating from the widespread use of consumer products and inadequate waste management, microplastics are commonly found in aquatic environments, presenting various physical and chemical hazards to aquatic life. These risks include ingestion, which can lead to blockages in the digestive system, reduced nutrient intake and death. Additionally, microplastics absorb and transport toxic chemicals, contributing to bioaccumulation and biomagnification in the food chain. The impacts of microplastic exposure include oxidative stress, inflammation and potential reproductive issues in aquatic organisms. Southeast Asia, known for its abundant aquatic resources, confronts particular challenges in managing pollution, and effective management strategies are needed. We can safeguard the health and sustainability of Southeast Asia's aquatic ecosystems by addressing these issues comprehensively. This review provides detailed insights into the dual physical and chemical effects of microplastics on aquatic organisms in Southeast Asia, underscoring the need for continued research and innovative solutions.

Schemes comparation of layered and continuous solution mining in bedded salt formations by horizontal interconnected wells

Modern distribution systems must clearly distinguish between halal and non-halal items, particularly in areas with sizable Muslim populations and rising awareness of halal integrity. Consumer confidence may suffer, halal principles may be broken, and cross-contamination may result from failing to maintain this separation. This research uses the Green Vehicle Routing Problem (GVRP) approach, which is solved with the Salp Swarm Algorithm (SSA), to develop a joint distribution optimization model for halal and non-halal products in an effort to address these issues. With complete separation and adherence to halal logistics regulations, this methodology aims to reduce Total Distribution Cost (TDC), which comprises fuel expenses, carbon emissions, and operating costs. The SSA method is combined with Large Rank Value (LRV) to convert continuous solutions into practical and feasible route sequences. Simulation results using synthetic data from 20 customer locations show that increasing the population size and SSA iterations consistently reduces the TDC value until stable convergence is achieved. The model also proves to be robust to changes in fuel costs, emissions, and vehicles without altering the route structure. Overall, the results of the research show that the SSA-based GVRP model is capable of providing efficient and sustainable halal logistics solutions. The novelty of this research lies in the explicit integration of halal and non-halal segregation with the SSA-based GVRP optimization framework in a single sustainable distribution system.

The reconstruction of continuous solutions using all available mechanisms and data is essential for high-precision simulations and forecasts. This paper presents an improved random feature method (IRFM) that combines observational data with models for solution reconstruction. For the multi-region neuron approximation, we employ a global activation function with robust local approximation capabilities instead of the traditional piecewise method. This enhances smoothness across regions and accelerates convergence. We also derived the equivalence condition for the optimal solution of multi-constrained optimization problems, established criteria for determining the weights in the cost function and the distribution of randomly generated collocation points, reducing biases from subjective choices. Additionally, we introduce a weighted scheme for computing the cost function related to sparse observations, reducing interpolation errors and improving stability against noise. Numerical examples demonstrate that the IRFM is more accurate and converges faster than the original RFM. Its efficiency and accuracy are validated through comparisons with physics-informed neural networks, and its flexibility is shown by successful continuous solution reconstruction in complex domains.

In this article, a numerical analysis of the asymptotic behavior of the discrete energy associated with a dissipative coupled wave system is conducted. The numerical approximation of the system is constructed using the P1 finite element method for spatial discretization, combined with the implicit Euler scheme for time integration. An a priori error analysis is established, showing that, under extra regularity assumptions on the continuous solution, the numerical scheme exhibits linear convergence. Then, for the first time in the literature, the exponential decay of the fully discrete energy is shown using the energy method. Finally, several numerical simulations are provided to illustrate the convergence behavior and to analyze the evolution of the discrete energy.

We consider a bounded open subset Ω of R n of class C 1 , α for some α ∈ ] 0 , 1 [ , and we define a distributional outward unit normal derivative for α-Hölder continuous solutions of the Helmholtz equation in the exterior of Ω that may not have a classical outward unit normal derivative at the boundary points of Ω and that may have an infinite Dirichlet integral around the boundary of Ω. Namely for solutions that do not belong to the classical variational setting. Then we show a Schauder boundary regularity result for α-Hölder continuous functions that have the Laplace operator in a Schauder space of negative exponent and we prove a uniqueness theorem for α-Hölder continuous solutions of the exterior Dirichlet and impedance boundary value problems for the Helmholtz equation that satisfy the Sommerfeld radiation condition at infinity in the above mentioned nonvariational setting.