Search Results (471)

In this work, we study a nonlinear system of p-Biharmonic hyperbolic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the initial data and the damping terms, we establish the global existence of solutions. Furthermore, we derive a general decay result, and finally, we prove the occurrence of blow-up for solutions with negative initial energy. Full article

A probabilistic version of geometry is introduced. The fifth postulate of Euclid (Playfair’s axiom) is adopted in the following probabilistic form: consider a line and a point not on the line—there is exactly one line through the point with probability P, where $0\le P\le 1$. Playfair’s axiom is logically independent of the rest of the Hilbert system of axioms of the Euclidian geometry. Thus, the probabilistic version of the Playfair axiom may be combined with other Hilbert axioms. $P=1$ corresponds to the standard Euclidean geometry; $P=0$ corresponds to the elliptic- and hyperbolic-like geometries. $0<P<1$ corresponds to the introduced probabilistic geometry. Parallel constructions in this case are Bernoulli trials. Theorems of the probabilistic geometry are discussed. Given a triangle and a line drawn from a vertex parallel to the opposite side, the event that this line is actually parallel occurs with probability P. Otherwise, the line may intersect the side or diverge. Parallelism is not transitive in the probabilistic geometry. Probabilistic geometry occurs on the surface with a stochastically variable Gaussian curvature. Alternative geometries adopting various versions of the probabilistic Playfair axiom are introduced. Probabilistic non-Archimedean geometry is addressed. Applications of the probabilistic geometry are discussed. Full article

In this study, we explore the soliton solutions of the truncated M-fractional fifth-order Korteweg–de Vries (KdV) equation by applying the improved modified extended tanh function method (IMETM). Novel analytical solutions are obtained for the proposed system, such as brigh soliton, dark soliton, hyperbolic, exponential, Weierstrass, singular periodic, and Jacobi elliptic periodic solutions. To validate these results, we present detailed graphical representations of selected solutions, demonstrating both their mathematical structure and physical behavior. Furthermore, we conduct a comprehensive linear stability analysis to investigate the stability of these solutions. Our findings reveal that the fractional derivative significantly affects the amplitude, width, and velocity of the solitons, offering new insights into the control and manipulation of soliton dynamics in fractional systems. The novelty of this work lies in extending the IMETM approach to the truncated M-fractional fifth-order KdV equation for the first time, yielding a wide spectrum of exact analytical soliton solutions together with a rigorous stability analysis. This research contributes to the broader understanding of fractional differential equations and their applications in various scientific fields. Full article

The escalating frequency and severity of natural disasters present significant challenges to the stability and sustainability of global financial systems, with the US stock market being especially vulnerable. This study examines sector-level exposure and contagion dynamics during climate-related disaster events, providing insights essential for sustainable investing and resilient financial planning. Using an advanced econometric framework—dynamic conditional correlation GARCH (DCC-GARCH) augmented with Generalized Hyperbolic Processes (GHPs) and an asymmetric specification (ADCC-GARCH)—we model daily stock returns for 20 publicly traded US companies across five sectors (insurance, energy, automotive, retail, and industrial) between 2017 and 2022. The results reveal considerable sectoral heterogeneity: insurance and energy sectors exhibit the highest vulnerability, with heavy-tailed return distributions and persistent volatility, whereas retail and selected industrial firms demonstrate resilience, including counter-cyclical behavior during crises. GHP-based models improve tail risk estimation by capturing return asymmetries, skewness, and leptokurtosis beyond Gaussian specifications. Moreover, the ADCC-GHP-GARCH framework shows that negative shocks induce more persistent correlation shifts than positive ones, highlighting asymmetric contagion effects during stress periods. The results present the insurance and energy sectors as the most exposed to extreme events, backed by the heavy-tailed return distributions and persistent volatility. In contrast, the retail and select industrial firms exhibit resilience and show stable, and in some cases, counter-cyclical, behavior in crises. The results from using a GHP indicate a slight improvement in model specification fit, capturing return asymmetries, skewness, and leptokurtosis indications, in comparison to standard Gaussian models. It was also shown with an ADCC-GHP-GARCH model that negative shocks result in a greater and more durable change in correlations than positive shocks, reinforcing the consideration of asymmetry contagion in times of stress. By integrating sector-specific financial responses into a climate-disaster framework, this research supports the design of targeted climate risk mitigation strategies, sustainable investment portfolios, and regulatory stress-testing approaches that account for volatility clustering and tail dependencies. The findings contribute to the literature on financial resilience by providing a robust statistical basis for assessing how extreme climate events impact asset values, thereby informing both policy and practice in advancing sustainable economic development. Full article

This research proposes a novel adaptive robust fault-tolerant controller for symmetrical robotic manipulators subject to model uncertainties and actuator failures. The key innovation lies in the design of a new sliding manifold that effectively integrates the advantages of a hyperbolic tangent function-based practical sliding manifold and a fast terminal sliding manifold. This structure not only eliminates the reaching phase and accelerates error convergence but also significantly enhances system robustness while mitigating chattering. Moreover, the proposed manifold ensures the global non-singularity of the equivalent control law, thereby improving overall stability. Another major contribution is an adjustable adaptive strategy that dynamically estimates the unknown bounds of fault information and external disturbances, reducing the reliance on prior knowledge. The stability and convergence of the robotic system under the proposed scheme are theoretically analyzed and guaranteed. Finally, simulation experiments demonstrate the superior performance of the proposed scheme. Full article

With a hyperbolic U-tube as the resonant sensing element, the resonant density sensor adopts electromagnetic excitation and magnetoelectric detection for electromechanical transduction, enabling an integrated synergistic design. The resonance principle of the resonant density sensor and the electromechanical conversion method, using the electromagnetic induction principle, are analysed, and the theoretical model is investigated based on ANSYS Electronics 2022 and ANSYS Workbench 2022 R1 simulation software. In open-loop mode, the amplitude–frequency characteristics of the resonant network are measured, and the mechanical structure achieves a quality factor greater than 1000, as determined by the bandwidth method; In closed-loop mode, the measurement stability of the hyperbolic U-tube is periodically measured under various fluid loads, and the real-time ambient temperature is monitored. The sensitivity of the closed-loop system for density measurement is close to −0.1 Hz·kg⁻¹·m³, and the absolute error between the density correction value and the standard value is within ±1 kg/m³. Full article

In this paper, we develop the explicit finite difference method (FDM) to solve an ill-posed Cauchy problem for the 3D acoustic wave equation in a time domain with the data on a part of the boundary given (continuation problem) in a cube. FDM is one of the numerical methods used to compute the solutions of hyperbolic partial differential equations (PDEs) by discretizing the given domain into a finite number of regions and a consequent reduction in given PDEs into a system of linear algebraic equations (SLAE). We present a theory, and through Matlab Version: 9.14.0.2286388 (R2023a), we find an efficient solution of a dense system of equations by implementing the numerical solution of this approach using several iterative techniques. We extend the formulation of the Jacobi, Gauss–Seidel, and successive over-relaxation (SOR) iterative methods in solving the linear system for computational efficiency and for the properties of the convergence of the proposed method. Numerical experiments are conducted, and we compare the analytical solution and numerical solution for different time phenomena. Full article

A new class of poroelastic dynamic contact problems stemming from hydraulic fracture theory is introduced and studied. The two-phase medium consists of a solid phase and pores which are saturated with a Newtonian fluid. The porous body contains a fluid-driven crack endowed with non-penetration conditions for the opposite crack surfaces. The poroelastic model is described by a coupled system of hyperbolic–parabolic partial differential equations under the unilateral constraint imposed on displacement. After full discretization using finite-element and Hilber–Hughes–Taylor methods, the well-posedness of the resulting variational inequality is established. Formulation of the complementarity conditions with the help of a minimum-based merit function is used for the semi-smooth Newton method of solution presented in the form of a primal–dual active set algorithm which is tested numerically. Full article

Concrete pavements frequently develop subsurface voids between surface and base layers during long-term service due to cyclic loading, environmental effects, and subgrade instability, which compromise structural integrity and traffic safety. Ground-penetrating radar (GPR) has been widely used as a non-destructive method for detecting such voids. However, the presence of coarse aggregates with strong electromagnetic scattering properties often introduces pseudo-reflection signals in radar images, hindering accurate void identification. To address this challenge, this study develops a high-fidelity three-phase concrete model incorporating aggregates, mortar, and the interfacial transition zone (ITZ). The Finite-Difference Time-Domain (FDTD) method is used to simulate electromagnetic wave propagation in both voided and intact structures. Simulation results reveal that aggregate-induced scattering can blur or distort reflection interfaces, generating pseudo-hyperbolic anomalies even in the absence of voids. In cases of thin-layer voids, real echo signals may be masked by aggregate scattering, leading to missed detections. GPR systems can be broadly classified into impulse, continuous-wave, and multi-frequency types. To validate the simulations, field tests using multi-frequency 2D/3D GPR systems and borehole verification were conducted. The results confirm the consistency between simulated and actual radar anomalies and validate the proposed model. This work provides theoretical insight and modeling strategies to enhance the interpretation accuracy of GPR data for subsurface void detection in concrete pavements. Full article

In this study, the complete discrimination system for the polynomial method (CDSPM) is employed to analyze the integrable Gardner Equation (IGE). Through a traveling wave transformation, the model is reduced to a nonlinear ordinary differential equation, enabling the derivation of a wide class of exact solutions, including trigonometric, hyperbolic, rational, and Jacobi elliptic functions. For example, a bright soliton solution is obtained for parameters $A=1.3$, $\beta =-0.1$, and $\gamma =0.8$. Qualitative analysis reveals diverse phase portraits, indicating the presence of saddle points, centers, and cuspidal points depending on parameter values. Chaos and quasi-periodic dynamics are investigated via Poincaré maps and time-series analysis, where chaotic patterns emerge for values like ${\nu }_1=1.45$, ${\nu }_2=2.18$, ${\Xi }_0=4$, and $\lambda =2\pi$. Sensitivity analysis confirms the model’s sensitivity to initial conditions $\chi =2.2,2.4,2.6$, reflecting real-world unpredictability. Additionally, the energy balance method (EBM) is applied to approximate periodic solutions by conserving kinetic and potential energies. These results highlight the IGE’s ability to capture complex nonlinear behaviors relevant to fluid dynamics, plasma waves, and nonlinear optics. Full article

Curved roofs constructed using hyperbolic paraboloid (HP) modules are gaining popularity in structural engineering due to their unique aesthetic and structural advantages. Consequently, these studies have investigated steel bar modules based on HP geometry, focusing on how variations in geometric configuration and bar topology affect internal force distribution and overall structural performance. Each module was designed on a 4 × 4 m square plan, incorporating external bars that formed the spatial frame and internal grid bars that filled the frame’s interior. Parametric modeling was conducted using Dynamo, while structural analysis and design were performed in Autodesk Robot Structural Analysis Professional (ARSAP). Key variables included the vertical displacement of frame corners (0–1.0 m at 0.25 m intervals), the orientation and spacing of internal bar divisions, and the overall mesh topology. A total of 126 structural models were analyzed, representing four distinct bar topology variants, including both planar and non-planar mesh configurations. The results demonstrate that structural efficiency is significantly influenced by the geometry and topology of the internal bar system, with notable differences observed across the various structural types. Computational analysis revealed that asymmetric configurations of non-planar quadrilateral subdivisions yielded the highest efficiency, while symmetric arrangements proved optimal for planar panel applications. These findings, along with observed design trends, offer valuable guidance for the development and optimization of steel bar structures based on HP geometry, applicable to both single-module and multi-module configurations. Full article

This paper investigates the global dynamics of timelike geodesics of a spherically symmetric black hole under Lorentz-violating effects governed by parameters $\lambda$ (scaling exponent) and ${\rm Y}$ (Lorentz violation strength). By employing dynamical system techniques, including Poincaré compactification and blow-up methods, we systematically explore finite and infinite equilibrium states of the system derived from a black hole solution with power-law corrections to the Schwarzschild metric. For varying $\lambda$ (ranging from −2 to 2) and fixed ${\rm Y}$ values, we classify the nature of equilibrium states (saddle, center, and node) and analyze their stability. Key findings reveal that the number of equilibrium states increases as $\lambda$ decreases: two states for $\lambda =2$, three for $\lambda =1$, four for $\lambda =2/3$, and additional configurations for $\lambda =-2$. The phase plane diagrams and global dynamics demonstrate distinct topological structures, including attractors at infinity and multi-horizon black hole solutions. Furthermore, degenerate equilibrium states at infinity are resolved through directional blow-ups, elucidating their non-hyperbolic behavior. This study highlights the critical role of Lorentz-violating parameters in shaping the stability and long-term evolution of timelike geodesics, offering new insights into modified black hole physics and spacetime dynamics. Full article

In recommender systems research, the data sparsity problem has driven the development of hybrid recommendation algorithms integrating multimodal information and the application of graph neural networks (GNNs). However, conventional GNNs relying on homogeneous Euclidean embeddings fail to effectively model the non-Euclidean geometric manifold structures prevalent in real-world scenarios, consequently constraining the representation capacity for heterogeneous interaction patterns and compromising recommendation accuracy. As a consequence, the representation capability for heterogeneous interaction patterns is restricted, thereby affecting the overall representational power and recommendation accuracy of the models. In this paper, we propose a hyperbolic graph neural network model with contrastive learning for rating–review recommendation, implementing a dual-graph construction strategy. First, it constructs a review-aware graph to integrate rich semantic information from reviews, thus enhancing the recommendation system’s context awareness. Second, it builds a user–item interaction graph to capture user preferences and item characteristics. The hyperbolic graph neural network architecture enables joint learning of high-order features from these two graphs, effectively avoiding the embedding distortion problem commonly associated with high-order feature learning. Furthermore, through contrastive learning in hyperbolic space, the model effectively leverages review information and user–item interaction data to enhance recommendation system performance. Experimental results demonstrate that the proposed algorithm achieves excellent performance on multiple real-world datasets, significantly improving recommendation accuracy. Full article

Stochastic resonance (SR) systems possess the remarkable ability to enhance weak signals by transferring noise energy into the signal, and thus have significant application prospects in weak signal detection. However, the classic bistable SR (CBSR) system suffers from the output saturation problem, which limits its weak signal enhancement ability. To address this limitation, this paper proposes an under-damped unsaturated SR system called the UDHQSR system. This SR system overcomes the output saturation problem through a piecewise potential function constructed by combining hyperbolic sine functions and quadratic functions. Additionally, by introducing a damping term, its weak signal detection performance is further improved. Furthermore, the theoretical output SNR of this proposed SR system is derived to quantitatively represent its weak signal detection performance. The particle swarm optimization (PSO) algorithm is used to dynamically optimize the parameters of the UDHQSR system. Finally, the simulated signal and different real bearing fault signals from public datasets are used to verify the effectiveness of the proposed UDHQSR system. Experimental results demonstrate that this UDHQSR system has better abilities for both weak signal enhancement and noise suppression compared with the CBSR system. Full article

This study focuses on analyzing the generalized HSC-KdV equations characterized by variable coefficients and Wick-type stochastic (Wt.S) elements. To derive white noise functional (WNF) solutions, we employ the Hermite transform, the homogeneous balance principle, and the $F_e$ (F-expansion) technique. Leveraging the inherent connection between hypercomplex system (HCS) theory and white noise (WN) analysis, we establish a comprehensive framework for exploring stochastic partial differential equations (PDEs) involving non-Gaussian parameters (N-GP). As a result, exact solutions expressed through Jacobi elliptic functions (JEFs) and trigonometric and hyperbolic forms are obtained for both the variable coefficients and stochastic forms of the generalized HSC-KdV equations. An illustrative example is included to validate the theoretical findings. Full article