Search Results (276)

In this study, we establish new oscillation criteria for solutions of the fourth-order differential equation $(a$$\varphi \left(u\right)$$u^{‴})$+q$(u\circ h)=0$, which is of a functional type with a delay. The oscillation behavior of solutions of fourth-order delay equations has been studied using many techniques, but previous results did not take into account the existence of the function $\varphi$ except in second-order studies. The existence of $\varphi$ increases the difficulty of obtaining monotonic and asymptotic properties of the solutions and also increases the possibility of applying the results to a larger area of special cases. We present two criteria to ensure the oscillation of the solutions of the studied equation for two different cases of $\varphi$. Our approach is based on using the comparison principle with equations of the first or second order to benefit from recent developments in studying the oscillation of these orders. We also provide several examples and compare our results with previous ones to illustrate the novelty and effectiveness. Full article

Slender masonry structures, in the absence of disintegration phenomena, can be idealized as rigid bodies subjected to seismic excitation. In this study, a closed-form expression for the behavior factor (q-factor) associated with overturning collapse under out-of-plane seismic loading is derived. The analysis considers five-step pulse seismic inputs. In the proposed approach, valid for slender masonry structures, sliding failure is neglected, and collapse is assumed to occur when, at the end of the seismic excitation, the rotation of the structure reaches a value equal to its slenderness. Based on this criterion, it is possible to derive a formulation for the q-factor as a function of a dimensionless parameter that combines the geometric characteristics of the slender structure and the period of the applied accelerogram. To validate the proposed formulation, a comparative analysis is conducted against the results obtained from a numerical integration of the motion equation using a set of 20 natural accelerograms recorded in Italy. The characteristic period of each accelerogram is evaluated through different methodologies, with the aim of identifying the most suitable approach for application in simplified seismic assessment procedures. Full article

The role of weirs in flow regulation in water resources infrastructure and flood control is well known. In the meantime, the study of full-width plate weirs (FWPW), due to their wide application and lacking findings, is of great importance. In this study, experimental models were conducted at Babol Noshirvani University of Technology to investigate flow passing through FWPWs with five different heights (p = 0.07, 0.09, 0.11, and 0.15 m) under eight discharge conditions (Q = 1.4 to 6.3 L/s). The experiments were carried out in a flume measuring 4 m in length, 0.6 m in width, and 0.2 m in height. The discharges were measured with a calibrated flowmeter, and the water depths upstream of the weir (h) and the tailwater depths (h₁) were measured with a point gauge with an accuracy of 0.1 mm. For each test, the discharge coefficient (C_d), relative residual energy (E₁/E₀), and relative energy dissipation ((E₀ − E₁)/E₀) were computed. The proposed equation for calculating discharge achieved good accuracy with RMSE = 0.0002, MAE=0.0002, and R² = 0.997. Results show a reducing trend of C_d by increasing h/P, which is compatible with previous results. It was observed that at a constant discharge, relative residual energy reduces by an average of 47% by increasing weir height, and at a constant P, increasing flow discharge increases it a little. A novel accurate equation for relative energy dissipation in FWPW was proposed based on h/P that provided specific constant coefficients for each p value. Full article

The two-parameter $(p,q)$-operators are a new family of operators in calculus that have shown their capabilities in modeling various systems in recent years. Following this path, in this paper, we present a new construction of the Langevin equation using two-parameter $(p,q)$-Caputo derivatives. For this new Langevin equation, equivalently, we obtain the solution structure as a post-quantum integral equation and then conduct an existence analysis via a fixed-point-based approach. The use of theorems such as the Krasnoselskii and Leray–Schauder fixed-point theorems will guarantee the existence of solutions to this equation, whose uniqueness is later proven by Banach’s contraction principle. Finally, we provide three examples in different structures and validate the results numerically. Full article

The time-fractional generalized Burger–Fisher equation (TF-GBFE) is utilized in many physical applications and applied sciences, including nonlinear phenomena in plasma physics, gas dynamics, ocean engineering, fluid mechanics, and the simulation of financial mathematics. This mathematical expression explains the idea of dissipation and shows how advection and reaction systems can work together. We compare the homotopy perturbation transform method and the new iterative method in the current study. The suggested approaches are evaluated on nonlinear TF-GBFE. Two-dimensional (2D) and three-dimensional (3D) figures are displayed to show the dynamics and physical properties of some of the derived solutions. A comparison was made between the approximate and accurate solutions of the TF-GBFE. Simple tables are also given to compare the integer-order and fractional-order findings. It has been verified that the solution generated by the techniques given converges to the precise solution at an appropriate rate. In terms of absolute errors, the results obtained have been compared with those of alternative methods, including the Haar wavelet, OHAM, and q-HATM. The fundamental benefit of the offered approaches is the minimal amount of calculations required. In this research, we focus on managing the recurrence relation that yields the series solutions after a limited number of repetitions. The comparison table shows how well the methods work for different fractional orders, with results getting closer to precision as the fractional-order numbers get closer to integer values. The accuracy of the suggested techniques is greatly increased by obtaining numerical results in the form of a fast-convergent series. Maple is used to derive the approximate series solution’s behavior, which is graphically displayed for a number of fractional orders. The computational stability and versatility of the suggested approaches for examining a variety of phenomena in a broad range of physical science and engineering fields are highlighted in this work. Full article

To address the issues of uneven initial distribution and limited search accuracy with the traditional divergent quantum-inspired differential search (DCS) algorithm, a hybrid multi-strategy variant, termed DQDCS, is proposed. This improved version overcomes these limitations by integrating the refined set strategy and clustering process for population initialization, along with the double Q-learning model to balance exploration and exploitation This enhanced version replaces the conventional pseudo-random initialization with a refined set generated through a clustering process, thereby significantly improving population diversity. A novel position update mechanism is introduced based on the original equation, enabling individuals to effectively escape from local optima during the iteration process. Additionally, the table reinforcement learning model (double Q-learning model) is integrated into the original algorithm to balance the probabilities between exploration and exploitation, thereby accelerating the convergence towards the global optimum. The effectiveness of each enhancement is validated through ablation studies, and the Wilcoxon rank-sum test is employed to assess the statistical significance of performance differences between DQDCS and other classical algorithms. Benchmark simulations are conducted using the CEC2019 and CEC2022 test functions, as well as two well-known constrained engineering design problems. The comparison includes both recent state-of-the-art algorithms and improved optimization methods. Simulation results demonstrate that the incorporation of the refined set and clustering process, along with the table reinforcement learning model (double Q-learning model) mechanism, leads to superior convergence speed and higher optimization precision. Full article

The hydrodynamics characteristics of artificial water diversion canals with long-distance and inter-basin multi-stage sluice gate regulations are prone to sudden increases and decreases, and sluice gate discharge differs from that of natural rivers. Research on the change characteristics of hydrological elements in artificial canals under the control of sluice gates is lacking, as are scientifically accurate calculations of sluice gate discharge. Therefore, addressing these gaps in long-distance artificial water transfer is of great importance. In this study, real-time operation data of 61 sluice gates, pertaining to the period from May 2019 to July 2021, including data on water levels, flow discharge, velocity, and sluice gate openings in the main canal of the Middle Route of the South-to-North Water Diversion Project of China, were analyzed. The discharge coefficient of each sluice gate was calculated by the dimensional analysis method, and the unit-width discharge was modeled as a function of gate opening ($e$), gravity acceleration ($g$), and energy difference ($H$). Through logarithmic transformation of the Buckingham Pi theorem-derived equation, a linear regression model was used. Data within the relative opening orifice flow regime were selected for fitting, yielding the discharge coefficients and stage–discharge relationships. The results demonstrate that during the study period, the water level, discharge, and velocity of the main canal showed an increasing trend year by year. The dimensional analysis results indicate that the stage–discharge response relationship followed a power function ($Q\propto {(\frac{H}{e})}^{constant}$) and that there was a good linear relationship between $l{g}^{(\frac{H}{e})}$ and $l{g}^{(\frac{K}{e})}$ (R² > 0.95, $K={(q^2/g)}^{1/3}$). By integrating geometric, operational, and hydraulic parameters, the proposed method provides a practical tool and a scientific reference for analyzing sluice gates’ regulation and hydrological response characteristics, optimizing water allocation, enhancing ecological management, and improving operational safety in long-distance inter-basin water diversion projects. Full article

Over the last two decades, the number of people who practice activities in the natural environment has increased and the demand for teachers for these activities has grown. It is necessary to analyze the impact of different psychosocial and emotional factors, such as self-concept, self-esteem, satisfaction with life and well-being, in teachers of special regime sports education, as regulated training in the Spanish educational system. The purpose of this study is to analyze the relationship between physical, emotional and social self-concept and self-esteem and to study the influence of self-esteem between self-concept and life satisfaction in teachers. The participants of the study were 788 teachers of special regime sports education, from the regulated training educational system of Spain. The instruments used were the Self-Concept-Scale-AF5, the Rosenberg Self-Esteem Questionnaire and the Satisfaction with Life Scale. To present the results of the study, a structural equation model, PLS-SEM, was developed based on the theoretical framework analyzed, with an explanatory-predictive approach. The evidence showed the coefficients of determination for self-esteem (R² = 0.395; Q² = 0.268) and life satisfaction (R² = 0.334; Q² = 0.237) as being the appropriate adjustment. The acquisition of an adequate self-concept and correct self-esteem allows practitioners of sports disciplines in the natural environment to have greater life satisfaction. Full article

The high temperature performance of steel structures has long been a focus of research, but research on the damage and crack propagation mechanism of steel with initial defects at high temperature is relatively low. The high temperature performance of most steel structures in engineering has an important impact on the function and safety of the whole structure. At present, Peridynamics (PD) theory uses the integral method that has unique advantages compared with traditional methods to solve structural damage and fracture problems. Therefore, the effect of temperature change on steel properties is introduced into the PD, and the PD constitutive equation at high temperature is proposed. The damage and crack propagation mechanisms of 2D Q345 steel plates with bilateral cracks and different bolt holes at 20 °C, 300 °C, 400 °C and 600 °C were analyzed by applying temperature action and external load to double-cracked steel specimens by the direct thermostructural coupling method. At the same time, the damage values, displacement changes in X direction and Y direction under different temperatures were compared and analyzed, and the effects of temperature, bolt hole and external load on the damage, displacement and crack growth path of different parts of the structure were obtained. Full article

In this paper, we investigate the existence results of solutions for Caputo-type fractional $(p,q)$-difference equations. Using Banach’s fixed-point theorem, we obtain the existence and uniqueness results. Meanwhile, by applying Krasnoselskii’s fixed-point theorem and Leray-Schauder’s nonlinear alternative, we also obtain the existence results of non-trivial solutions. Finally, we provide examples to verify the correctness of the given results. Moreover, relevant applications are presented through specific examples. Full article

Since high complexity and uncertainty is inherent in real-world environments that can influence the strategies choices of agents, we introduce a stochastic perturbation term to characterize the interference caused by uncertain factors on multi-agent systems (MASs). Firstly, the stochastic Q learning is designed by introducing stochastic perturbation term into Q learning, and the corresponding replicator dynamic equations of stochastic Q learning are derived. Secondly, we focus on two-agent games with two and three action scenarios, analyzing the impact of learning parameters on agents’ strategy selection and demonstrating how the learning process converges to its Nash equilibria. Finally, we also conduct a sensitivity analysis on exploration parameters, demonstrating how exploration rates affect the convergence process in potential games. The analysis and numerical experiments offer insights into the effectiveness of different exploration parameters in scenarios involving uncertainty. Full article

During the last 15–20 years, the experimental methods for autonomous navigation and inter-satellite links have been developing rapidly in order to ensure navigation control and data processing without commands from Earth stations. Inter-satellite links are related to relative ranging between the satellites from one constellation or different constellations and measuring the distances between them with the precision of at least 1 $\mathsf{\mu }$m micrometer (=${10}^{-6}$ m), which should account for the bending of the light (radio or laser) signals due to the action of the Earth’s gravitational field. Thus, the theoretical calculation of the propagation time of a signal should be described in the framework of general relativity theory and the s.c. null cone equation. This review paper summarizes the latest achievements in calculating the propagation time of a signal, emitted by a GPS satellite, moving along a plane elliptical orbit or a space-oriented orbit, described by the full set of six Kepler parameters. It has been proved that for the case of plane elliptical orbit, the propagation time is expressed by a sum of elliptic integrals of the first, the second and the third kind, while for the second case (assuming that only the true anomaly angle is the dynamical parameter), the propagation time is expressed by a sum of elliptic integrals of the second and of the fourth order. For both cases, it has been proved that the propagation time represents a real-valued expression and not an imaginary one, as it should be. For the typical parameters of a GPS orbit, numerical calculations for the first case give acceptable values of the propagation time and, especially, the Shapiro delay term of the order of nanoseconds, thus confirming that this is a propagation time for the signal and not for the time of motion of the satellite. Theoretical arguments, related to general relativity and differential geometry have also been presented in favor of this conclusion. A new analytical method has been developed for transforming an elliptic integral in the Legendre form into an integral in the Weierstrass form. Two different representations have been found, one of them based on the method of four-dimensional uniformization, exposed in the monograph of Whittaker and Watson. The result of this approach is a new formulae for the Weierstrass invariants, depending in a complicated manner on the modulus parameter q of the elliptic integral in the Legendre form. Full article

The kinetics and chemical equilibrium of the esterification reaction of acetic acid (AAc) and 2,2,3,3,4,4,4-heptafluorobutan-1-ol (HFBol) (using sulfuric acid as a catalyst) are determined experimentally. The study presents the dependences of $K_{eq}$ on the initial molar ratio of reagents, catalyst concentration and temperature. It is shown that all of the above parameters significantly affect the chemical equilibrium of the system. According to the Van’t Hoff equation, the standard enthalpy and standard entropy are calculated from the experimental data. The esterification process of AAc and HFBol is characterized by the negative heat effect (${∆}_{r}H$ > 0). The homogeneous and heterogeneous regions of the chemical equilibrium composition at different settings are given. In the homogeneous region of the chemical equilibrium composition, it is found that the rate constant and half-reaction time do not depend on the initial molar ratio of the reagents. The dependencies of the rate constant on the temperature are obtained, and the parameters of the Arrhenius equation are estimated from the experiments. Full article

In this paper, we investigate the global attractivity of a higher-order rational difference equation in the form $x_{n+1}={\displaystyle \frac{p+q{x}_n}{1+r{x}_n+s{x}_{n-k}}}$, where $p,q,r,s\ge 0$, k is a positive integer, and the initial conditions are nonnegative. This equation generalizes several well-known rational difference equations studied in the literature. By employing a combination of advanced mathematical techniques, including the use of key lemmas and intricate computations, we establish that the unique nonnegative equilibrium point of the equation is globally attractive under specific parameter conditions. Our results not only extend and improve upon existing findings but also resolve several conjectures posed by previous researchers, including those by G. Ladas and colleagues. The methods involve transforming the higher-order equation into a first-order difference equation and analyzing the properties of the resulting function, particularly its Schwarzian derivative. The findings demonstrate that the equilibrium point is globally attractive when certain inequalities involving the parameters are satisfied. This work contributes to the broader understanding of the dynamics of rational difference equations and has potential applications in various fields such as biology, physics, and cybernetics. Full article

Litter decomposition is a fundamental ecological process that drives nutrient cycling and energy flow. However, little is known about the elevational patterns of this process in different stages. We established ten sites on Dongling Mountain in Beijing, China, to investigate the elevational patterns of oak leaf (Quercus liaotungensis) decomposition, as well as the underlying mechanisms. Our results revealed distinct elevational patterns of litter decomposition in different stages. There was no significant altitudinal pattern in the mass loss of Q. liaotungensis leaves at the 2nd, 4th, and 6th months of decomposition. By the 16th month, the mass loss decreased significantly along the elevation gradient (p = 0.008). By the 28th month, a reverse pattern emerged, with greater mass loss observed at higher elevations (p < 0.001). A similar change also took place in the altitudinal pattern of the abundance of invertebrates within the litter bag, which was lower at higher elevations at the 16th month (p = 0.002), but higher at higher elevations at the 28th month (p = 0.002). In addition, we examined the elevational patterns of carbon and nitrogen concentrations in different stages. The results of the structural equation model revealed that the invertebrate abundance at the 4th month influenced the litter residues at the 16th month (p < 0.001), yet nitrogen content at the 16th month affected litter residues at the 28th month(p < 0.001). This study provides novel insights into the temporal dynamics of litter decomposition along an elevational gradient and highlights the underlying mechanisms by which litter chemistry and biological factors regulate this process. Full article