Search Results (1,781)

This paper investigates the optimal portfolio control problem under a stochastic volatility model, whose dynamics are governed by a highly nonlinear Hamilton–Jacobi–Bellman equation. We employ a separable value function and introduce a novel exponential approximation technique to simplify the nonlinear terms of the auxiliary function. The simplified HJB equation is solved numerically using the advanced Fréchet–Newton method, which is known for its rapid convergence properties. We rigorously analyze the numerical outcomes, demonstrating that the iterative sequence converges quickly to the trivial fixed point ($g^{*}=1$) under zero risk and zero excess return conditions. This convergence is mathematically justified through rigorous functional analysis, including the principles of contraction mapping and the Kantorovich theorem, which validate the stability and efficiency of the proposed numerical scheme. The results offer theoretical insight into the behavior of the HJB equation in simplified solution spaces. Full article

The resummation of Stieltjes series remains a key challenge in mathematical physics, especially when Padé approximants fail, as in the case of superfactorially divergent series. Weniger’s $\delta$-transformation, which incorporates a priori structural information on Stieltjes series, offers a superior framework with respect to Padé. In the present work, the following fundamental question is addressed: Is the $\delta$-transformation, once it is applied to a typical Stieltjes series, capable of correctly simulating the branch cut structure of the corresponding Stieltjes function? Here, it is proved that the intrinsic log-convexity of the Stieltjes moment sequence (guaranteed via the positivity of Hankel’s determinants) allows the necessary condition for $\delta$ to have all real poles to be satisfied. The same condition, however, is not sufficient to guarantee this. In attempting to bridge such a gap, we propose a mechanism rooted in the iterative action of a specific linear differential operator acting on a class of suitable auxiliary log-concave polynomials. To this end, we show that the denominator of the $\delta$-approximants can always be recast as a high-order derivative of a log-concave polynomial. Then, on invoking the Gauss–Lucas theorem, a consistent geometrical justification of the $\delta$ pole positioning is proposed. Through such an approach, the pole alignment along the negative real axis can be viewed as the result of the progressive restriction of the convex hull under differentiation. Since a fully rigorous proof of this conjecture remains an open challenge, in order to substantiate it, a comprehensive numerical investigation across an extensive catalog of Stieltjes series is proposed. Our results provide systematic evidence of the potential $\delta$-transformation ability to mimic the singularity structure of several target functions, including those involving superfactorial divergences. Full article

The increasing complexity of modern electrical networks poses significant challenges in terms of monitoring, maintenance, and operational efficiency. However, current planning approaches often lack a unified integration of real-time data and predictive modeling. In this context, Digital Twins (DTs) emerge as a promising solution, as they enable the creation of virtual replicas of physical assets. This research addresses the lack of standardized technical frameworks by proposing a novel mathematical optimization model for grid planning based on DTs. The proposed methodology integrates comprehensive architecture (frontend/backend), specific data standards (IEC 61850), and a linear optimization formulation to minimize operational costs and enhance reliability. Case studies such as DTEK Grids and American Electric Power are analyzed to validate the approach. The results demonstrate that the proposed framework can reduce planning errors by approximately 15% and improve fault prediction accuracy to 99%, validating the DTs as a key tool for the digital transformation of the energy sector towards Industry 5.0. Full article

The end-to-end efficiency of radio-frequency (RF)-powered wireless communication networks (WPCNs) in post-disaster underground mine environments can be enhanced through adaptive beamforming. The primary challenges in such scenarios include (i) identifying the most energy-constrained nodes, i.e., nodes with the lowest residual energy to prevent the loss of tracking and localization functionality; (ii) avoiding reliance on the computationally intensive channel state information (CSI) acquisition process; and (iii) ensuring long-range RF wireless power transfer (LoRa-RFWPT). To address these issues, this paper introduces an adaptive and safety-aware deep reinforcement learning (DRL) framework for energy beamforming in LoRa-enabled underground disaster networks. Specifically, we develop a Safe Adaptive Deep Q-Network (SADQN) that incorporates residual energy awareness to enhance energy harvesting under mobility, while also formulating a SADQN approach with dual-variable updates to mitigate constraint violations associated with fairness, minimum energy thresholds, duty cycle, and uplink utilization. A mathematical model is proposed to capture the dynamics of post-disaster underground mine environments, and the problem is formulated as a constrained Markov decision process (CMDP). To address the inherent NP hardness of this constrained reinforcement learning (CRL) formulation, we employ a Lagrangian relaxation technique to reduce complexity and derive near-optimal solutions. Comprehensive simulation results demonstrate that SADQN significantly outperforms all baseline algorithms: increasing cumulative harvested energy by approximately 11% versus DQN, 15% versus Safe-DQN, and 40% versus PSO, and achieving substantial gains over random beamforming and non-beamforming approaches. The proposed SADQN framework maintains fairness indices above 0.90, converges 27% faster than Safe-DQN and 43% faster than standard DQN in terms of episodes, and demonstrates superior stability, with 33% lower performance variance than Safe-DQN and 66% lower than DQN after convergence, making it particularly suitable for safety-critical underground mining disaster scenarios where reliable energy delivery and operational stability are paramount. Full article

In this paper, an anisotropic object electromagnetic image reconstruction system based on a two-stage multi-frequency extended network is developed by deep learning techniques. We obtain the scattered field information by irradiating the TM different polarization waves to uniaxial objects located in free space. We input the measured single-frequency scattered field into the Deep Residual Convolutional Neural Network (DRCNN) for training and to be further extended to multi-frequency data by the trained model. In the second stage, we feed the multi-frequency data into the Deep Convolutional Encoder–Decoder (DCED) architecture to reconstruct an accurate distribution of the dielectric constants. We focus on EMIS applications using Transverse Magnetic (TM) and Transverse Electric (TE) waves in 2D scenes. Numerical findings confirm that our method can effectively reconstruct high-contrast uniaxial objects under limited information. In addition, the TM/TE scattering from uniaxial anisotropic objects is governed by polarization-dependent Lippmann–Schwinger integral equations, yielding a nonlinear and severely ill-posed inverse operator that couples the dielectric tensor components with multi-frequency field responses. Within this mathematical framework, the proposed two-stage DRCNN–DCED architecture serves as a data-driven approximation to the anisotropic inverse scattering operator, providing improved stability and representational fidelity under limited-aperture measurement constraints. Full article

Pumped-storage power stations (PSPSs) are vital for grid stability, yet pump-turbines (PTs) operating in the S-shaped region often induce severe hydraulic instability. To reveal the mechanism of these self-excited oscillations, this study establishes a nonlinear mathematical model based on rigid water column theory and a cubic polynomial approximation of the PT’s nonlinear characteristics. Both analytical derivations and numerical simulations were conducted. Analytical results indicate that, in the absence of surge tanks, self-excited oscillations occur when the PT’s negative hydraulic impedance modulus exceeds the pipeline impedance. With a single surge tank, the system behaves analogously to the Van der Pol oscillator, exhibiting oscillations that converge to a stable limit cycle governed by system parameters. Numerical simulations for a dual-surge-tank system further reveal that, due to initial negative damping, the PT transitions to alternative stable equilibria. Crucially, the transition direction is governed by the polarity of the initial disturbance: negative perturbations lead to the regular turbine region, while positive ones lead to the reverse pump region. Additionally, pipe friction causes the steady-state discharge to deviate slightly from the theoretical static value, with deviations remaining below 2.96%. This work provides a theoretical basis for stability prediction in PSPSs. Full article

Modern 5G+grade low power wide area network (LPWAN) technologies such as Narrowband Internet-of-Things (NB-IoT) operate utilizing a multi-channel slotted ALOHA algorithm at the random access phase. As a result, the random access phase in such systems is characterized by relatively low throughput and is highly sensitive to traffic fluctuations that could lead the system outside of its stable operational regime. Although theoretical results specifying the optimal transmission probability that maximizes the successful preamble transmission probability are well known, the lack of knowledge about the current offered traffic load at the BS makes the problem of maintaining the optimal throughput a challenging task. In this paper, we propose and analyze a new reactive access-barring scheme for NB+IoT systems based on machine learning (ML) techniques. Specifically, we first demonstrate that knowing the number of user equipments (UE) experiencing a collision at the BS is sufficient to make conclusions about the current offered traffic load. Then, we show that through utilizing ML-based techniques, one can safely differentiate between events in the Physical Random Access Channel (PRACH) at the base station (BS) side based on only the signal-to-noise ratio (SNR). Finally, we mathematically characterize the delay experienced under the proposed reactive access-barring technique. In our numerical results, we show that by utilizing modern neural network approaches, such as the XGBoost classifier, one can precisely differentiate between events on the PRACH channel with accuracy reaching 0.98 and then associate it with the number of user equipment (UE) competing at the random access phase. Our simulation results show that the proposed approach can keep the successful preamble transmission probability constant at approximately 0.3 in overloaded conditions, when for conventional NB-IoT access, this value is less than 0.05. The proposed scheme achieves near-optimal throughput in multi-channel ALOHA by employing dynamic traffic awareness to adjust the non-unit transmission probability. This proactive congestion control ensures a controlled and bounded delay, preventing latency from exceeding the system’s maximum load capacity. Full article

Northwestern Jiangxi Province is rich in metasilicic acid (as H₂SiO₃) mineral water resources. Investigating their hydrogeochemical characteristics and formation mechanism is crucial for the rational utilization of water resources and the sustainable development of the local mineral water industry. Taking the Taoping water source area in northwestern Jiangxi as a case study, 11 sets of groundwater and surface water samples were systematically collected. By comprehensively applying mathematical statistics, ionic ratios, and isotopic analyses, the hydrogeochemical characteristics and formation processes of metasilicic acid-type mineral water were examined. The results indicate that: (1) The mineral waters in the area are weakly alkaline and belong to the metasilicic acid type, with concentrations ranging from 22.0 to 67.0 mg/L, of which 75% exceed 30 mg/L. (2) The primary hydrochemical types are HCO₃⁻–Ca·Na, HCO₃⁻–Ca·Mg, and HCO₃⁻–Ca. Analysis of stable isotopes (δ¹⁸O and δ²H) and tritium (³H) indicates that metasilicic acid mineral water is primarily recharged by atmospheric precipitation, with an apparent groundwater age of approximately 60 years. (3) The enrichment of metasilicic acid primarily results from the weathering and leaching of silicate minerals, coupled with cation exchange. K⁺ and Na⁺ are mainly derived from silicate minerals such as feldspars and halite, whereas Ca²⁺ and Mg²⁺ originate primarily from carbonate minerals like calcite and dolomite. During recharge, atmospheric precipitation infiltrates the aquifer, dissolving aluminosilicate and siliceous minerals in the surrounding rocks, thereby releasing metasilicic acid into the groundwater and ultimately forming the metasilicic acid-type mineral water. Full article

This paper reviews the fracture mechanics parameters associated with the variability in the crack growth curves associated with forty-two different tests that range from additively manufactured (AM) steels to cold spray additively manufactured (CSAM) 316L steel. As a result of this review, it is found that, to a first approximation, the effects of different building processes and R-ratios on the relationship between ΔK and the crack growth rate (da/dN) can be captured by allowing for changes in the fatigue threshold and the apparent cyclic toughness in the Schwalbe crack driving force (Δκ). Whilst this observation, when taken in conjunction with similar findings for AM Ti-6Al-4V, Inconel 718, Inconel 625, and Boeing Space Intelligence and Weapon Systems (BSI&WS) laser powder bed (LPBF)-built Scalmalloy^®, as well as for a range of CSAM pure metals, go a long way in making a point; it is NOT a mathematical proof. It is merely empirical evidence. As a result, this review highlights that for AM and CSAM materials, it is advisable to plot the crack growth rate (da/dN) against both ΔK and Δκ. The observation that, for the AM and CSAM steels examined in this study, the da/dN versus Δκ curves are similar, when coupled with similar observation for a range of other AM materials, supports a prior study that suggested using fracture toughness measurements in conjunction with the flight load spectrum and the operational life requirement to guide the choice of the building process for AM Ti-6Al-4V parts. The observations outlined in this study, when taken together with related findings given in the open literature for AM Ti-6Al-4V, AM Inconel 718, AM Inconel 625, and BSI&WS LPFB-built Scalmalloy^®, as well as for a range of CSAM-built pure metals, have implications for the implementation and certification of limited-life AM parts. Full article

Addressing the difficulty of intuitively identifying and effectively correcting induced heave error in multibeam measurements, this paper proposes a two-stage methodology comprising error identification and correction. This scheme includes an error discrimination method based on regression diagnostics and an error correction method based on Partial Least Squares Regression (PLSR). By establishing a mathematical model between bathymetric discrepancies and attitude parameters, statistical diagnosis and effective identification of the error are achieved. To further mitigate the impact of induced heave error on bathymetric data, an elimination model based on PLSR is developed, enabling high-precision prediction and compensation of the induced heave error. Validation using field survey data demonstrates that this method can effectively estimate the installation offset parameters of the attitude sensor. After correction, the root mean square of bathymetric discrepancies between adjacent survey lines is reduced by approximately 78.8%, periodic stripe-shaped distortions along the track direction are essentially eliminated, and the quality of terrain mosaicking is significantly improved. This provides an effective solution for controlling induced heave error under complex topographic conditions. Full article

In this contribution, we propose and study long-time behaviors of a new class of N-dimensional delayed Kirchhoff–Carrier-type problems with variable transfer coefficients involving a logarithmic nonlinearity. We take into account the dependence of diffusion and damping coefficients on the position and direction, as well as the presence of different types of delays. This class of nonlocal anisotropic and nonlinear wave-type equations with multiple time-varying mixed delays and dampings, of a fairly general form, containing several arbitrary functions and free parameters, is of the following form: ${\displaystyle \frac{{\partial }^{2}u}{\partial t^2}-{div(\mathcal{K}(\Vert \sigma \nabla u\Vert }_{L^2(\Omega )}^2)A_{\sigma }{(\mathbf{x})\nabla u)+\mathcal{M}(\Vert u\Vert }_{L^2(\Omega )}^2)u-div(\zeta (t)A_{\sigma }(\mathbf{x})\nabla \frac{\partial u}{\partial t})+d_0(t)\frac{\partial u}{\partial t}+{\mathbb{D}}_r(\mathbf{x},t;\frac{\partial u}{\partial t})=\mathbb{G}(u),}$ where $u(\mathbf{x},t)$ is the state function, $\mathcal{M}$ and $\mathcal{K}$ are the nonlocal Kirchhoff operators and the nonlinear operator $\mathbb{G}(u)$ corresponds to a logarithmic source term. The symmetric tensor $A_{\sigma }$ describes the anisotropic behavior and processes of the system, and the operator ${\mathbb{D}}_r$ represents the multiple time-varying mixed delays related to velocity ${\displaystyle \frac{\partial u}{\partial t}}$. Our problem, which encompasses numerous equations already studied in the literature, is relevant to a wide range of practical and concrete applications. It not only considers anisotropy in diffusion, but it also assumes that the strong damping can be totally anisotropic (a phenomenon that has received very little mathematical attention in the literature). We begin with the reformulation of the problem into a nonlinear system coupling a nonlocal wave-type equation with ordinary differential equations, with the help of auxiliary functions. Afterward, we study the local existence and some necessary regularity results of the solutions by using the Faedo–Galerkin approximation, combining some energy estimates and the logarithmic Sobolev inequality. Next, by virtue of the potential well method combined with the Nehari manifold, conditions for global in-time existence are given. Finally, subject to certain conditions, the exponential decay of global solutions is established by applying a perturbed energy method. Many of the obtained results can be extended to the case of other nonlinear source terms. Full article

This paper develops a mathematically grounded neuro-fuzzy control framework for IoT-enabled irrigation systems in precision agriculture. A discrete-time, physically motivated model of soil moisture is formulated to capture the nonlinear water dynamics driven by evapotranspiration, irrigation, and drainage in the crop root zone. A Mamdani-type fuzzy controller is designed to approximate the optimal irrigation strategy, and an equivalent Takagi–Sugeno (TS) representation is derived, enabling a rigorous stability analysis based on Input-to-State Stability (ISS) theory and Linear Matrix Inequalities (LMIs). Online parameter estimation is performed using a Recursive Least Squares (RLS) algorithm applied to real IoT field data collected from a drip-irrigated orchard. To enhance prediction accuracy and long-term adaptability, the fuzzy controller is augmented with lightweight artificial neural network (ANN) modules for evapotranspiration estimation and slow adaptation of membership-function parameters. This work provides one of the first mathematically certified neuro-fuzzy irrigation controllers integrating ANN-based estimation with Input-to-State Stability (ISS) and LMI-based stability guarantees. Under mild Lipschitz continuity and boundedness assumptions, the resulting neuro-fuzzy closed-loop system is proven to be uniformly ultimately bounded. Experimental validation in an operational IoT setup demonstrates accurate soil-moisture regulation, with a tracking error below 2%, and approximately 28% reduction in water consumption compared to fixed-schedule irrigation. The proposed framework is validated on a real IoT deployment and positioned relative to existing intelligent irrigation approaches. Full article

This work presents a straightforward procedure for constructing the solution to the steady-state energy-transfer process in a system of two convex, opaque, gray bodies, with the aim of determining the temperature distribution within these bodies when separated by a vacuum. The methodology proposed in this work combines a sequence of elements that are functions obtained from the solution of uncomplicated, well-known linear, uncoupled heat transfer problems, thereby enabling solutions to be obtained using tools found in basic engineering textbooks. Specifically, these well-known problems resemble classical conduction-convection heat transfer problems, in which the boundary condition is described by the noteworthy Newton’s law of cooling. The limit of sequences of elements that are solutions to straightforward linear problems corresponds to the original, complex, coupled nonlinear problem. The convergence of these sequences is mathematically proven. The phenomenon (considered in this work) encompasses those involving black bodies. Since each element of the sequence arises from a well-known linear problem, numerical approximations can be used to obtain it, yielding a simple and powerful tool for simulations. Some presented results highlight the importance of considering thermal interaction between the two bodies, even in the absence of physical contact. In particular, the alterations in the temperature distributions of two separate gray bodies are explicitly shown to result from their thermal interaction. Full article

Landslide dams, typically composed of newly deposited, loose, and heterogeneous materials, are highly susceptible to failure induced by overtopping and seepage, particularly under extreme hydrological conditions. Accurate prediction of such breaching processes is essential for flood risk management and emergency response, yet existing models generally consider only a single failure mechanism. This study develops a mathematical model to simulate landslide dam breaching under the coupled action of overtopping and seepage erosion. The model integrates surface erosion and internal erosion processes within a unified framework and employs a stable time-stepping numerical scheme. Application to three real-world landslide dam cases demonstrates that the model successfully reproduces key breaching characteristics across overtopping-only, seepage-only, and coupled erosion scenarios. The simulated breach hydrographs, reservoir water levels, and breach geometries show good agreement with field observations, with peak outflow and breach timing predicted with errors generally within approximately 5%. Sensitivity analysis further indicates that the model is robust to geometric uncertainties, as variations in breach outcomes remain smaller than the imposed parameter perturbations. These results confirm that explicitly accounting for the coupled interaction between overtopping and seepage significantly improves the representation of complex breaching processes. The proposed model therefore provides a reliable computational tool for analyzing landslide dam failures and supports more accurate hazard assessment under multi-mechanism erosion conditions. Full article

The magnetic field generation studies in astronomy lead to a number of interesting problems in mathematical physics. In the dynamo theory, the problem is reduced to a system of parabolic equations for the field components. Assuming that the field grows exponentially, we obtain an eigenvalue problem for the corresponding elliptic operator. The possibility of the field generation and behaviour of the system is characterized by the spectra of the operator. If all eigenvalues lie in the left half of the complex plane, the perturbations will decay. On the other hand, if some of the eigenvalues have positive real parts, the large-scale structures of the field can be generated. From the astrophysical point of view, galactic magnetic fields are very important to study. One of the main problems is connected with the peripheral regions, where the properties of the medium complicate the operator structure. We can use the perturbation theory to find the eigenvalues. However, the problem can be solved analytically by considering some specific approximations. We can find the spectra using numerical approaches in the case of the conditions that are close to the real ones. In this paper, we solve eigenvalue problems for different operators which are connected with magnetohydrodynamic processes in outer parts of galaxies. Full article