Search Results (54)

This paper investigates an integrable spin system known as the Myrzakulov-XIII (M-XIII) equation through geometric and gauge-theoretic methods. The M-XIII equation, which describes dispersionless dynamics with curvature-induced interactions, is shown to admit a geometric interpretation via curve flows in three-dimensional space. We establish its gauge equivalence with the complex coupled dispersionless (CCD) system and construct the corresponding Lax pair. Using the Sym–Tafel formula, we derive exact soliton surfaces associated with the integrable evolution of curves and surfaces. A key focus is placed on the role of geometric and gauge symmetry in the integrability structure and solution construction. The main contributions of this work include: (i) a commutative diagram illustrating the connections between the M-XIII, CCD, and surface deformation models; (ii) the derivation of new exact solutions for a fractional extension of the M-XIII equation using the Kudryashov method; and (iii) the classification of these solutions into trigonometric, hyperbolic, and exponential types. These findings deepen the interplay between symmetry, geometry, and soliton theory in nonlinear spin systems. Full article

This paper presents the fatigue limit of flax/PLA composites with different fiber reinforcement architectures. The configurations of the analyzed flax/PLA composites are [0°]₈, [0°/90°]_s, [+45°/−45°]_s, [90°]₄, stacking sequences, and basket weave laminates. The methods used to estimate the fatigue limit are the fitting of stress versus number of cycles data using Weibull and Basquin equations, the surface thermographic technique with bilinear and exponential models to analyze the evolution of temperature increment, and volumetric dissipated energy. According to the results found, superficial temperature and the maximum strain reached stabilization over 2000 cycles for σ_max/σ_ut < 0.7, which was used to determine cyclic stress–strain curves and the fatigue limit. The cyclic stress–strain shows a nonlinear behavior for all laminates, having a good correlation to the Ramberg–Osgood model. Furthermore, having the stabilized temperature and volumetric dissipated energy, the exponential model was used to evaluate the fatigue limit and compared to the values found by Basquin and bilinear models. The fatigue limit found by Basquin and bilinear models shows conservative values compared to the exponential models. The results also show that temperature measurement using infrared thermography is quite sensitive to the environmental temperature variation, especially at low stress applied, and finally, the comparison of these methods on different reinforcement configurations provides a guide to select a proper technique in each case. Full article

Maritime transportation is responsible for most global trade and is generally considered more environmentally efficient compared to other modes of transport, particularly for long-distance trade. With increasingly stringent emission regulations, however, accurately quantifying emissions and identifying their key determinants has become essential for effective environmental management. This study introduced a structured and comparative statistical modeling framework for ship-based emission modeling using gross tonnage (GT) as the primary predictor variable, due to its strong correlation with emission levels. Emissions for hydrocarbon (HC), carbon monoxide (CO), particulate matter with an aerodynamic diameter of less than 10 μm (PM10), carbon dioxide (CO₂), sulfur dioxide (SO₂), nitrogen oxides (NO_x), and volatile organic compounds (VOC) were estimated using a bottom-up approach based on emission factors and formulas defined by the U.S. Environmental Protection Agency (EPA), using data from 38,304 vessel movements through the Bosphorus in 2021. These EPA-estimated values served as dependent variables in the modeling process. The modeling framework followed a three-step strategy: (1) outlier detection using Rosner’s test to reduce the influence of outliers on model accuracy, (2) curve fitting with 12 regression models representing four curve types—polynomial (e.g., linear, quadratic), concave/convex (e.g., exponential, logarithmic), sigmoidal (e.g., logistic, Gompertz, Weibull), and spline-based (e.g., cubic spline, natural spline)—to capture diverse functional relationships between GT and emissions, and (3) model comparison using difference performance metrics to ensure a comprehensive assessment of predictive accuracy, consistency, and bias. The findings revealed that nonlinear models outperformed polynomial models, with spline-based models—particularly natural spline and cubic spline—providing superior accuracy for HC, PM₁₀, SO₂, and VOC, and the Weibull model showing strong predictive performance for CO and NO_x. These results underscore the necessity of using pollutant-specific and flexible modeling strategies to capture the intricacies of maritime emission dynamics. By demonstrating the advantages of flexible functional forms over standard regression techniques, this study highlights the need for tailored modeling strategies to better capture the complex relationships in maritime emission data and offers a scalable and transferable framework that can be extended to other vessel types, emission datasets, or maritime regions. Full article

The control of nonlinear systems cannot be effectively achieved using linear mathematical methods. This paper introduces a novel mathematical model to characterize the voltage–current (V–I) characteristics of the electric arc furnace (EAF) melting process, incorporating experimental field data for validation. The proposed model integrates polynomial curve fitting, the modified Heidler function, and double S-curves, with the grey wolf optimization (GWO) algorithm applied for parameter optimization, enhancing accuracy in predicting arc dynamics. The performance of the model is compared against the exponential, hyperbolic, exponential–hyperbolic, and nonlinear resistance models, as well as real-time measurement data, to assess its effectiveness. The results show that the proposed model significantly reduces voltage and current harmonic distortion compared to existing models. Specifically, the total harmonic distortion (THD) for voltage is reduced to 2.34%, closely matching the real-time measured value of 2.30%. Similarly, in the current spectrum, the proposed model achieves a significant reduction in third harmonic distortion and a THD of 11.40%, compared to 13.76% in real-time measurements. Consequently, a more precise characterization of the EAF behavior enables more effective mitigation of harmonics and vibrations, enhancing the stability and power quality of the electrical networks to which they are connected. Full article

The moisture content is closely related to the shear creep deformation behavior of soft rock, and the linear creep deformation behavior of soft rock can be described by the classical Nishihara model. However, its accuracy in describing accelerated nonlinear creep characteristics and the effects of moisture content still needs to be improved. The innovation of this paper is to propose an improved Nishihara model that can describe the whole creep process of shale with different moisture content. The model uses a strain-triggered nonlinear sticky pot to describe the process of accelerated creep of rock, and proposes a damage factor to reflect the effect of moisture content on the creep characteristics of rock. The relationship between the moisture content and damage factor is an exponential function, and the damage factor and related model parameters are determined by the shear creep test results under moisture conditions (0%, 0.46%, 0.87%, 1.24%). The shear creep tests were carried out by a self-developed rock shear apparatus. The experimental results show that the shear creep rate decreases first and then increases. The higher the moisture content of shale, the greater the initial shear displacement and stable creep displacement, and the longer it takes to enter the stable creep stage. The improved Nishihara model proposed in this paper can accurately fit the shear creep curves of four groups of shale samples with different moisture contents, and the correlation coefficients all reach 0.99. The fitting effect is better than that of the traditional model, which has good accuracy and practicability. Full article

The present work characterized the effects of hydration on the viscoelastic tensile properties of the sclera. Scleral strips were dissected from the posterior region near the optic nerve head of porcine eyes in the superior–inferior direction. The samples were divided into four hydration groups and their mechanical response was characterized by conducting uniaxial tensile stress–relaxation experiments. An exponential relation and logarithmic expression were used to numerically represent the experimental measurements during the ramp and relaxation periods, respectively. A nonlinear increase in the tensile stress during the ramp period was observed for all strips. Furthermore, it was found that dehydrated specimens had stiffer tensile properties. In particular, it was observed that the maximum and equilibrium stresses increased significantly with decreasing hydration. Furthermore, it was found that the viscoelastic tensile response of porcine scleral strips at different hydration levels could be collapsed onto a single normalized curve. The findings of the present work showed that hydration had significant effects on the viscoelastic tensile properties of sclera. Full article

Purpose: This paper develops a high-precision yield fusion prediction model for the sugarcane industry in Chongzuo, Guangxi, based on the trend yield and meteorological yield using the long short-term memory (LSTM) model to cope with the multiple factors affecting sugarcane production. Decision support is provided to agricultural producers, policymakers, and supply chain managers so that they can plan resource allocation, market strategies, and policy directions more effectively. Methods: The paper modeled trend yield and weather yield separately to explore the complex relationship between the two in influencing sugarcane production. Trend yields were predicted using the exponential smoothing and multilayer perceptron (MLP) models, while meteorological yields were modeled using stepwise regression. The predicted yields were used again as input variables into the LSTM deep learning network to fit the nonlinear relationship between the two yields. Results: The results showed that (1) the fusion strategy of meteorological yield and MLP trend yield adopted by the model was superior to the fusion strategy of meteorological yield and exponentially smoothed trend yield, achieving a very low mean square error (MSE) of 0.011 and a goodness of fit as high as 0.979, which indicated that the model prediction was highly in agreement with the actual yield, confirming the validity of the method. (2) The prediction curve is basically consistent with the trend of actual sugarcane yield, which predicts that the sugarcane yield in Chongzuo, Guangxi, is expected to maintain a stable and small growth trend in the next eight years. (3) The fusion prediction model proposed in this study provides an accurate and practical solution for sugarcane yield prediction in Chongzuo, Guangxi, with the unique advantage of effectively analyzing and integrating the natural and socio-economic factors affecting the yield, which is of significant reference value for the prediction of sugarcane yield in the local area and even in similar ecoregions. Full article

Liquor has a complex system with high dimensional components. The trace components in liquor are varied and have low content and complex coordination relationships. This study aimed to solve the problem of reliance on smell and taste. Based on the characteristics of near-infrared spectrum response to hydrogen-containing groups, qualitative analysis was carried out in combination with machine learning technology. Firstly, an iterative adaptive weighted penalized least squares algorithm with spectral peak discrimination was used for baseline correction to effectively retain useful information in the feature absorption peaks. Then, the convolution smoothing algorithm was used to filter the noise, and the spectral curve smoothness was adjusted using the convolution window width. The near-infrared spectrum has a high dimension. Monte Carlo random sampling combined with an improved competitive adaptive reweighting method was used to evaluate the importance of spectral sampling points. According to the importance coefficient, the dimension of the spectral data set was optimized by using an exponential attenuation function through an iterative operation, and the data set with the smallest root-mean-square error was taken as the characteristic spectrum. The nonlinear separability of characteristic spectra was further improved by kernel principal component analysis. Finally, a liquor quality recognition model based on principal component analysis was established by using the hierarchical multiclass support vector machine method. Our key findings revealed that the prediction accuracy of the model reached 96.87% when the number of principal components was 5–12, with more than 95% of the characteristic information retained. These results demonstrated that this rapid nondestructive testing method resolved the challenge posed by relying on subjective sensory evaluation for liquor analysis. The findings provide a reliable analytical approach for studying substances with high-dimensional component characteristics. Full article

Using digitized data from progression-free survival (PFS) and overall survival Kaplan–Meier curves, one can assess population survival kinetics through exponential decay nonlinear regression analyses. To demonstrate their utility, we analyzed PFS curves from published curative-intent trials of non-small cell lung cancer (NSCLC) adjuvant chemotherapy, adjuvant osimertinib in resected EGFR-mutant NSCLC (ADAURA trial), chemoradiotherapy for inoperable NSCLC, and limited small cell lung cancer (SCLC). These analyses permit assessment of log–linear curve shape and estimation of the proportion of patients cured, PFS half-lives for subpopulations destined to eventually relapse, and probability of eventual relapse in patients remaining progression-free at different time points. The proportion of patients potentially cured was 41% for adjuvant controls, 58% with adjuvant chemotherapy, 17% for ADAURA controls, not assessable with adjuvant osimertinib, 15% with chemoradiotherapy, and 12% for SCLC. Median PFS half-life for relapsing subpopulations was 11.9 months for adjuvant controls, 17.4 months with adjuvant chemotherapy, 24.4 months for ADAURA controls, not assessable with osimertinib, 9.3 months with chemoradiotherapy, and 10.7 months for SCLC. For those remaining relapse-free at 2 and 5 years, the cure probability was 74%/96% for adjuvant controls, 77%/93% with adjuvant chemotherapy, 51%/94% with chemoradiation, and 39%/87% with limited SCLC. Relatively easy population kinetic analyses add useful information. Full article

In DWI, multi-exponential signal analysis can be used to determine signal underlying diffusion components. However, the approach is very complex due to the inherent low SNR, the limited number of signal decay data points, and the absence of appropriate acquisition parameters and standardized analysis methods. Within the scope of this work, different methods for multi-exponential analysis of the diffusion signal in the kidney were compared. To assess the impact of fitting parameters, a simulation was conducted comparing the free non-negative (NNLS) and rigid non-linear least square (NLLS) fitting methods. The simulation demonstrated improved accuracy for NNLS in combination with area-under-curve estimation. Furthermore, the accuracy and stability of the results were further enhanced utilizing optimized parameters, namely 350 logarithmically spaced diffusion coefficients within [0.7, 300] × 10⁻³ mm²/s and a minimal SNR of 100. The NNLS approach shows an improvement over the rigid NLLS method. This becomes apparent not only in terms of accuracy and omitting prior knowledge, but also in better representation of renal tissue physiology. By employing the determined fitting parameters, it is expected that more stable and reliable results for diffusion imaging in the kidney can be achieved. This might enable more accurate DWI results for clinical utilization. Full article

It is difficult to determine unknown solar cell and photovoltaic (PV) module parameters owing to the nonlinearity of the characteristic current–voltage (I-V) curve. Despite this, precise parameter estimation is necessary due to the substantial effect parameters have on the efficacy of the PV system with respect to current and energy results. The problem’s characteristics make the handling of algorithms susceptible to local optima and resource-intensive processing. To effectively extract PV model parameter values, an improved hybrid Sparrow Search Algorithm (SSA) with Exponential Distribution Optimization (EDO) based on the Differential Evolution (DE) technique and the bound-constraint modification procedure, called ISSAEDO, is presented in this article. The hybrid strategy utilizes EDO to improve global exploration and SSA to effectively explore the solution space, while DE facilitates local search to improve parameter estimations. The proposed method is compared to standard optimization methods using solar PV system data to demonstrate its effectiveness and speed in obtaining PV model parameters such as the single diode model (SDM) and the double diode model (DDM). The results indicate that the hybrid technique is a viable instrument for enhancing solar PV system design and performance analysis because it can predict PV model parameters accurately. Full article

This study characterizes the growth of weaned Large White × Landrace hybrid piglets from 6 to 20 kg live body weight (BW) under real farm conditions. Batches of 50 castrated male pigs and 50 gilts were weighed repeatedly over two 6-week breeding cycles. The data was fitted to various linear (quadratic and exponential) and nonlinear (Gompertz, Richards, logistic, Von-Bertalanffy) mixed models to find the best-performing model. During the postweaning phase, animal growth was modelled, and the effect of sex on growth was determined by incorporating the variable, sex, into the mixed models and using t-tests for paired samples. The average BW at weaning was 6.86 kg, and the average BW by the end of the cycle was 19.46 kg, with an average daily gain (ADG) of 0.324 kg/day. Over the study period, the variable, sex, did not show a significant effect (p < 0.05) on piglet growth. The nonlinear mixed models performed better than the linear mixed models, with the Gompertz (RMSE = 0.296) and Von-Bertalanffy (RMSE = 0.288) curves as the best-performing models. When fitted to the Gompertz curve, the data showed a maximum ADG of 0.508 kg/day on day 27 postweaning. Accordingly, nonlinear mixed models can provide useful information to farmers about the evolution of weaned piglet growth and can be used for the early detection of growth anomalies. Full article

Obtaining accurate values of saturated hydraulic conductivity (K_sat) is very important for managing all natural or artificial processes involving water flow into soils. Double-ring infiltration (DRI) is one of the easiest-to-work-with techniques commonly used for K_sat determination. Unfortunately, when improperly used, it leads to important variations and inaccurate results. This study was designed to investigate the necessary conditions to reach the true-value or real-world saturated hydraulic conductivity (K_{sat-real-world}) in the field. For this purpose, the effects of two factors—namely, the measured infiltration data type (cumulative, instant rate, and average rate) and the related non-linear regression equation type—were analyzed. Measurements with DRI were performed with samples from 106 locations in three West African countries, namely, Burkina Faso, Mali, and Cote d’Ivoire. The soils were composed of loam, sandy loam, and sandy clay loam. The results show that when infiltration rates are used rather than cumulative infiltration non-linear regression curves, the variability between the measured K_sat and the real-world saturated hydraulic conductivity (K_{sat-real-world}) could reach from 2.2% to 58.8%. This variability was caused by the approximate amplification—according to the procedure used—of time-increment measurement errors. Extending the test duration to more than 4 h, especially when clay soils were involved, and using the exponential one-phase decay non-linear regression of the cumulative infiltration data based on a clear measurement protocol provided the K_sat values that were closest to K_{sat-real-world}. Full article

In this paper, we present a new third-order family of iterative methods in order to compute the multiple roots of nonlinear equations when the multiplicity $(m\ge 1)$ is known in advance. There is a plethora of third-order point-to-point methods, available in the literature; but our methods are based on geometric derivation and converge to the required zero even though derivative becomes zero or close to zero in vicinity of the required zero. We use the exponential fitted curve and tangency conditions for the development of our schemes. Well-known Chebyshev, Halley, super-Halley and Chebyshev–Halley are the special members of our schemes for $m=1$. Complex dynamics techniques allows us to see the relation between the element of the family of iterative schemes and the wideness of the basins of attraction of the simple and multiple roots, on quadratic polynomials. Several applied problems are considered in order to demonstrate the performance of our methods and for comparison with the existing ones. Based on the numerical outcomes, we deduce that our methods illustrate better performance over the earlier methods even though in the case of multiple roots of high multiplicity. Full article

The Golgi complex (GC) is the main station along the cell biosecretory pathway. Until now, mechanisms of intra-Golgi transport (IGT) have remained unclear. Herein, we confirm that the goodness-of-fit of the regression lines describing the exit of a cargo from the Golgi zone (GZ) corresponds to an exponential decay. When the GC was empty before the re-initiation of the intra-Golgi transport, this parameter of the curves describing the kinetics of different cargoes (which are deleted in Golgi vesicles) with different diffusional mobilities within the GZ as well as their exit from the GZ was maximal for the piecewise nonlinear regression, wherein the first segment was horizontal, while the second segment was similar to the exponential decay. The kinetic curve describing cargo exit from the GC per se resembled a linear decay. The Monte-Carlo simulation revealed that such curves reflect the role of microtubule growth in cells with a central GC or the random hovering of ministacks in cells lacking a microtubule. The synchronization of cargo exit from the GC already filled with a cargo using the wave synchronization protocol did not reveal the equilibration of cargo within a Golgi stack, which would be expected from the diffusion model (DM) of IGT. Moreover, not all cisternae are connected to each other in mini-stacks that are transporting membrane proteins. Finally, the kinetics of post-Golgi carriers and the important role of SNAREs for IGT at different level of IGT also argue against the DM of IGT. Full article