Exponential Method Research Articles

A diverse array of optical solitons in the damped (2 + 1)-dimensional nonlinear Schrödinger equation via the modified exponential rational function method and other distinct strategies

A diverse array of optical solitons in the damped (2 + 1)-dimensional nonlinear Schrödinger equation via the modified exponential rational function method and other distinct strategies

The Mathematical Modeling, Diffusivity, Energy, and Enviro-Economic Analysis (MD3E) of an Automatic Solar Dryer for Drying Date Fruits

Date fruit drying is a process that consumes a significant amount of energy due to the long duration required for drying. To better understand how moisture flows through the fruit during drying and to speed up this process, drying studies must be conducted in conjunction with mathematical modeling, energy analysis, and environmental economic analysis. In this study, twelve thin-layer mathematical models were designed utilizing experimental data for three different date fruit varieties (Sakkoti, Malkabii, and Gondaila) and two solar drying systems (automated solar dryer and open-air dryer). These models were then validated using statistical analysis. The drying period for the date fruit varieties varied between 9 and 10 days for the automated solar dryer and 14 to 15 days for open-air drying. The moisture diffusivity coefficient values, determined using Fick’s second law of diffusion model, ranged from 7.14 × 10−12 m2/s to 2.17 × 10−11 m2/s. Among the twelve thin-layer mathematical models, we chose the best thin drying model based on a higher R2 and lower χ2 and RMSE. The Two-term and Modified Page III models delivered the best moisture ratio projections for date fruit dried in an open-air dryer. For date fruit dried in an automated solar dryer, the Two-term Exponential, Newton (Lewis), Approximation diffusion or Diffusion Method, and Two-term Exponential modeling provided the best moisture ratio projections. The energy and environmental study found that the particular amount of energy used varied from 17.936 to 22.746 kWh/kg, the energy payback time was 7.54 to 7.71 years, and the net CO2 mitigation throughout the lifespan ranged from 8.55 to 8.80 tons. Furthermore, economic research showed that the automated solar dryer’s payback period would be 2.476 years.

Price Forecasting of Marine Fish Based on Weight Allocation Intelligent Combinatorial Modelling.

China is a major player in the marine fish trade. The price prediction of marine fish is of great significance to socio-economic development and the fisheries industry. However, due to the complexity and uncertainty of the marine fish market, traditional forecasting methods often struggle to accurately predict price fluctuations. Therefore, this study adopts an intelligent combination model to enhance the accuracy of food product price prediction. Firstly, three decomposition methods, namely empirical wavelet transform, singular spectrum analysis, and variational mode decomposition, are applied to decompose complex original price series. Secondly, a combination of bidirectional long short-term memory artificial neural network, extreme learning machine, and exponential smoothing prediction methods are applied to the decomposed results for cross-prediction. Subsequently, the predicted results are input into the PSO-CS intelligence algorithm for weight allocation and to generate combined prediction results. Empirical analysis is conducted using data illustrating the daily sea purchase price of larimichthys crocea in Ningde City, Fujian Province, China. The combination prediction accuracy with PSO-CS weight allocation is found to be higher than that of single model predictions, yielding superior results. With the implementation of weight allocation intelligent combinatorial modelling, the prediction of marine fish prices demonstrates higher accuracy and stability, enabling better adaptation to market changes and price fluctuations.

Investigating the properties of octane isomers by novel neighborhood product degree-based topological indices

A topological index is a real number calculated from the structure of a chemical compound to describe its topology. The use of molecular descriptors has been increasing in recent years, helping to determine the physicochemical and biological properties of drugs. The main purpose of this article is to investigate the properties of the octane isomers using the theoretical method. To study the structures of octane isomers, we have introduced a new approach called “neighborhood product degree” to calculate all the classical degree-based topological indices. The np-degree approach is applied to approximate eight properties of octane isomers, such as the acentric factor, density, refractive index, critical volume, molar volume, radius of curvature, critical pressure, and LogP. The np-degree-based topological indices are the estimated values of the properties of octane structures, so the linear and quadratic regression models and correlation coefficients are applied to check the validity of the estimated results. The quantitative structure property relation are obtained by using the linear, quadratic, exponential, logarithmic and sinusoidal regression methods with the help of SPSS. Two models are applied to all the compuations and three regression models are applied to the np-degree Randic index. The computation showed that quadratic regression model is suitable for study octane isomers and np-degree based graph invariants. If the values of the correlation coefficient r ⩾ 0.7, p-values ⩽ 0.05, and F-values ⩾ 2.5, then the results are significant. The results of np-degree-based topological indices satisfy all the criteria for being significant, so these newly introduced indices are valid to study octane isomers. The information determined in this article is beneficial for chemists and pharmacists.

Variable Time-stepping Exponential Integrators for Chemical Reactors with Analytical Jacobians

Chemical combustion problems are known to be stiff and therefore difficult to efficiently integrate in time when numerically simulated. Implicit methods, such as backwards differentiation formula (BDF), are widely considered to be the state-of-the-art methods owing their capability of taking relatively large time-steps while maintaining accurate combustion characteristics. Exponential time integration methods have recently demonstrated the ability to accurately and efficiently solve large scale systems of ordinary differential equations. This study introduces a novel adaptive time stepping exponential integrator named EPI3V. Its performance is measured on spatially homogeneous isobaric reactive mixtures involving three hydrocarbon fuel mechanisms. The full combustion process is simulated using gas compositions with sufficient temperature to obtain auto-ignition. Simulations are run until the steady state is obtained, then a comparison of the computational efficiency and accuracy between a BDF and EPI3V method is made. The novel EPI3V method exhibits comparable computational efficiency to a well-established implementation of the variable time-stepping BDF implicit methods for two of the mechanisms investigated. In certain situations it even demonstrates a slight advantage over the implicit solver. However, in one specific case, the EPI3V shows relative performance degradation compared to the implicit method, but it still converges for this case. These results indicate that exponential time integration methods may be applicable to a larger variety of combustion problems.

Improved uniform error bounds on an exponential wave integrator method for the nonlinear Schrödinger equation with wave operator and weak nonlinearity

In this paper, we establish the improved uniform error bounds for the Lawson-type exponential wave integrator Fourier pseudo-spectral (LEWIFP) method for the nonlinear Schrödinger equation with wave operator (NLSW) and weak nonlinearity characterized by a small constant ε∈(0,1]. We first convert the NLSW to a coupled system and then consider the LEWIFP method for the coupled system. The LEWIFP method is proved to be time symmetric and mass-conservative which is very important from the point of view of numerical geometric integration. Through careful and rigorous convergence analysis, we establish improved uniform error bounds for the full-discretization at O(hm+ε2pτ2) in the long-time domain up to O(1/ε2p) where m is determined by the regularity conditions. These error bounds are much better than the classical error bounds O(hm+τ2) provided by the traditional error analysis. In error analysis, in addition to the classical tools such as mathematical induction and energy method, we adopt the regularity compensation oscillation (RCO) technique to analyze the accumulation of errors carefully. The numerical experiments support our error estimates and demonstrate the discrete mass-conservation. In addition, the numerical results show that the discrete energy is stable in the time domain up to O(1/ε2p).

COVID-19 Case Growth Prediction Using a Hybrid Fuzzy Time Series Forecasting Model and a Machine Learning Approach

The COVID-19 pandemic has evolved into a global health crisis, with Indonesia particularly affected due to its high death rates compared to the rest of Asia. A significant number of unacknowledged, undocumented, or unaddressed cases further exacerbate the situation in Indonesia. Challenges arise from the growing patient population and a scarcity of resources, medical experts, and facilities. This study analyzes the daily development of COVID-19 cases in Indonesia, aiming to estimate the number of confirmed cases, recoveries, and fatalities. Introducing a novel hybrid forecasting model, we utilize the Holt-Winter triple exponential smoothing statistical method and the fuzzy time series rate of change algorithm. We apply the Triple Exponential Smoothing Holt Winter statistical model to predict future periods to the fuzzy time series. Based on the testing results, our proposed hybrid forecasting model demonstrates a very high level of predictive capacity. The acquired data are highly accurate, with a 0.15 percent confirmation rate, 0.15 percent recovery rate, and a 0.20 percent mortality rate, along with an average absolute error of less than 10% for each COVID-19 case. The findings indicate that early awareness by the COVID-19 Task Force of the status of cases is highly advantageous. This awareness can aid in formulating appropriate policies for future planning, organization, and accelerated treatment of COVID-19 in Indonesia. Consequently, successful efforts can be made to slow the emergence and spread of COVID-19 in the country.

Solving the two-dimensional time-dependent Schrödinger equation using the Sinc collocation method and double exponential transformations

Over the last four decades, Sinc methods have occupied an important place in numerical analysis due to their simplicity and great performance. An incorporation of the Sinc collocation method with double exponential transformation is used to solve the two-dimensional time dependent Schrödinger equation. Numerical comparison between the double exponential and single exponential approaches is made to illustrate the superiority of the double exponential Sinc method.

Analisis Trend (Indeks Number Trend Series Analysis) PT. Adaro Energi Indonesia Tbk

PT Adaro Energy Indonesia (ADRO) is one of the leading coal companies in Indonesia. Trend analysis of the company's number trend series index is important to understand the pattern and direction of its performance movement over a certain period of time. This research aims to analyze the trend of the ADRO number trend series index using linear and exponential regression methods. The data used in this research is ADRO Financial Report data for the period 2020 to 2023. The results of the analysis show that the overall ADRO number trend series index trend has increased. Linear and exponential regression models show quite good results in explaining data trends. Trend analysis (Index Number Trend Series Analysis) is carried out by comparing financial reports for the last 5 years. In the index-number trend series analysis approach, comparisons are made by calculating the relative change (percentage) of each element of the financial report over several years based on a certain base year. Usually what is designated as the base year is the earliest year (period) of a series of financial report periods being analyzed. . However, the main consideration in determining the base year is the financial reporting period that shows the most normal conditions.

Extraction of new soliton solutions of (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation via generalized exponential rational function method and $$\left( \frac{G^{\prime }}{G},\frac{1}{G}\right) $$ expansion method

Extraction of new soliton solutions of (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation via generalized exponential rational function method and $$\left( \frac{G^{\prime }}{G},\frac{1}{G}\right) $$ expansion method

THE TRAVELING WAVE SOLUTIONS OF THE CONFORMABLE TIME-FRACTIONAL ZOOMERON EQUATION BY USING THE MODIFIED EXPONENTIAL FUNCTION METHOD

The present study focuses on the acquisition of traveling wave solutions associated with the conformable time-fractional Zoomeron equation through the utilization of the modified exponential function method (MEFM). The solution functions derived from mathematical computations encompass hyperbolic, trigonometric, and rational functions. Various graphical representations, such as 2D, 3D, contour graphs, and density graphs, are utilized to visually depict the distinct features of the solution functions derived from the determination of suitable parameters.

The Generalized Fractional-Order Fisher Equation: Stability and Numerical Simulation

This study examines the stability and numerical simulation of the generalized fractional-order Fisher equation. The equation serves as a mathematical model describing population dynamics under the influence of factors such as natural selection and migration. We propose an implicit exponential finite difference method to solve this equation, considering the conformable fractional derivative. Furthermore, we analyze the stability of the method through theoretical considerations. The method involves transforming the problem into systems of nonlinear equations at each time since our method is an implicit method, which is then solved by converting them into linear equations systems using the Newton method. To test the accuracy of the method, we compare the results obtained with exact solutions and with those available in the literature. Additionally, we examine the symmetry of the graphs obtained from the solution to examine the results. The findings of our numerical simulations demonstrate the effectiveness and reliability of the proposed approach in solving the generalized fractional-order Fisher equation.

Phase trajectories and Chaos theory for dynamical demonstration and explicit propagating wave formation

This paper is subjected to study the nonlinear integrable model which is the (3+1)-dimensional Boussinesq equation which has a lot of applications in engineering and modern sciences. To find and examine the analytical exact solitary wave solutions of (3+1)-dimensional Boussinesq equation, a modified generalized exponential rational functional method is exerted. As a result, waves, singular periodic, hyperbolic, and trigonometric type solutions are obtained. These acquired solutions are more innovative and encouraging to researchers in their endeavor to study physical marvels. To illustrate how some selected exact solutions propagate, the graphical representation in 2D, Contour, and 3D of those solutions is provided with various parametric values. The considered equation is additionally transformed into the planar dynamical structure by applying the Galilean transformation. All potential phase portraits of the dynamical system are investigated using the theory of bifurcation. The Hamiltonian function of the dynamical system of differential equations is established to see that, the system is conservative over time. The presentation of energy levels through graphics provides valuable insights, and it demonstrates that the model has solutions that can be expressed in closed form. The periodic, quasi-periodic, and chaotic behaviors of the 2D, 3D, and time series are also observable once the dynamical system is subjected to an external force. Meanwhile, the sensitivity of the derived solutions is carefully examined for a range of initial conditions.

A reduced-order computational homogenization framework for locally resonant metamaterial structures

A computational homogenization framework is presented to study the dynamics of locally resonant acoustic metamaterial structures. Modelling the resonant units at the microscale as representative volume elements and building on well-established scale transition relations, the framework brings as a main novelty a reduced-order macroscopic homogenized continuum whose governing equations involve no additional variables to describe the microscale dynamics unlike micromorphic homogenized continua obtained by alternative computational homogenization approaches. This model-order reduction is obtained by formulating the governing equations of the micro- and macroscale problems in the frequency domain, introducing a finite-element discretization of the two problems and performing an exact dynamic condensation of all the degrees of freedom at the microscale. An appropriate inverse Fourier transform approach is implemented on the frequency-domain equations to capture transient dynamics as well; notably, the implementation involves the Exponential Window Method, here applied for the first time to calculate the time-domain response of undamped locally resonant acoustic metamaterial structures. The framework may handle arbitrary geometries of micro- and macro-structures, any transient excitations and any boundary conditions on the macroscopic domain.

Seismic fragility analysis of structures via an Adaptive Gaussian Mixture Model and its application to resilience assessment

Seismic fragility analysis and seismic resilience assessment are pivotal tasks within the performance-based earthquake engineering framework. The former aims to quantitatively assess the probability of engineering structures sustaining various degrees of damage when subjected to earthquakes of varying intensity levels. In contrast to many traditional seismic fragility methods, this paper introduces a precise and versatile approach grounded in reliability analysis, with the goal of eliminating the restrictive lognormal assumption. Initially, the proposed method involves conducting seismic reliability analysis of structures using the Fractional Exponential Moments-based Maximum Entropy Method (FEM-MEM). This approach efficiently yields failure probabilities. Subsequently, an Adaptive Gaussian Mixture Model (AGMM) is presented for fitting a set of failure probability points, producing comprehensive and continuous seismic fragility curves. Notably, AGMM offers remarkable flexibility in modeling fragility curves, ensuring precise estimations for subsequent resilience assessments. Building upon the results of the fragility analysis, the paper proceeds to assess the seismic resilience of structures. The proposed method’s feasibility and effectiveness are validated through two illustrative numerical examples. The results demonstrate that, in comparison to the conventional lognormal assumption, the proposed method offers superior accuracy and broader applicability for conducting seismic fragility analyses of structures.

Generalized exponential rational function method for solving nonlinear conformable time-fractional Hybrid-Lattice equation

Generalized exponential rational function method for solving nonlinear conformable time-fractional Hybrid-Lattice equation

Research on energy-saving control of agricultural hybrid tractors integrating working condition prediction.

To address the issues of tractors using too much fuel and not being energy efficient, a predictive control strategy based on Pontryagin's minimum principle integrating working condition prediction is proposed for agricultural hybrid tractors. The Dongfanghong 1804 tractor is being used for research. Firstly, the main parameters of the hybrid drive system are determined and modeled. Secondly, based on the adaptive cubic exponential forecasting method, the working condition information for a period of time in the future is predicted through historical working condition information. Furthermore, combining the predicted working conditions information, the goal is to minimize the total energy consumption cost of the entire machine. Motor power and diesel engine power are control variables. The battery state of charge is a state variable. Subsequently, a predictive control strategy based on Pontryagin's minimum principle integrating working condition prediction is proposed. Finally, the simulation test is carried out based on the MATLAB simulation platform. Research indicates: under plowing conditions, compared with the power following control strategy, the proposed predictive control strategy can effectively manage the performance of the diesel engine and motor, ensuring they operate at their most efficient level. The total energy consumption costs of the power following control and predictive control strategies are 37.17 China Yuan (CNY) and 33.67 CNY, respectively. The cost of energy used is decreased by 9. 42%, which helps make tractor field plowing more efficient and economical.

Predicting electricity demand in Cameroon with enhanced modified exponential models: A focus on the southern integrated grid (S.I.G)

This paper is centered on the prediction of electricity demand within the Southern Integrated Grid (S.I.G) for the forthcoming six years (2022–2027) through the utilization of advanced forecasting techniques. These methodologies encompass modified exponential, probabilistic or stochastic extrapolation and linear regression models. The foundation of these forecasts is established on a comprehensive examination of load curve data spanning 12 years (2010–2021) and an analysis of the factors influencing electricity demand in Cameroon. The models are implemented using Matlab and Excel, enabling the projection of results. The results of this analysis reveal a consistent growth trend in Cameroon's electricity demand between 2022 and 2027. the modified exponential model foresees an increase from 991.16MW to 1189.25MW, the probabilistic model from 969.68MW to 1109.20MW, and the linear regression model from 853.46MW to 975.89MW. Despite the inherent limitations, the outcomes prove to be satisfactory, marked by a high level of accuracy and reliability, as evidenced by mean absolute percentage error (MAPE) values of 0.2% for the modified exponential and probabilistic methods and 0.55% for the linear regression method. These scores fall well below the industry-accepted benchmark of MAPE < 10% outlined by the Lewis benchmark. In a comparative analysis, it is evident that the modified exponential and probabilistic models exhibit superior accuracy.

Analyzing Soliton Solutions of the Extended (3 + 1)-Dimensional Sakovich Equation

This work focuses on the utilization of the generalized exponential rational function method (GERFM) to analyze wave propagation of the extended (3 + 1)-dimensional Sakovich equation. The demonstrated effectiveness and robustness of the employed method underscore its relevance to a wider spectrum of nonlinear partial differential equations (NPDEs) in physical phenomena. An examination of the physical characteristics of the generated solutions has been conducted through two- and three-dimensional graphical representations.

Production of the Proinflammatory Cytokine TNF-α in Patients with Chronic Epstein-Barr Virus Infection

Aim of the Study: Study of the production of the pro-inflammatory cytokine tumor necrosis factor-alpha (TNF-α) in patients with Chronic Epstein-Barr Viral Infection (CEBI). Material and Methods: 90 patients with CVEBI were examined. The group consisted of 66 women and 24 men. The average age of the patients was 38.37 ± 1.15 years. The duration of the course of CVEBI from the appearance of the patient’s first complaints to diagnosis was 3.73 ± 0.22 years. The amount of EBV DNA in saliva samples (PCR method) and the level of production of the cytokine TNF-α ware examined in patients. Results: The copy number of EBV DNA in saliva samples from patients was 135898.61±23196.21 cop/ml. The level of induced TNF-α in the general group was 3288.73±260.88. All patients were divided into three groups: group 1 (n = 49) - the level of induced TNF-α was reduced - 1624.69±105.53 (pg/ ml) (95% CI: 1412.52; 1836.86) ; Group 2 (n =30) - the level of induced TNF-α is normal - 3819.19 ±427.00 (pg/ml) (95% CI: 3045.27; 4701.81); Group 3 (n =11) the level of induced TNF-α is high – 7203.00 ± 627.50 (pg/ml) (95% CI: 6135.37 - 8609.87). Patients did not differ in age, disease duration, or number of EBV DNA copies in saliva samples. The linear and exponential regression method was used to show the effect of disease duration on the level of TNF-α production in the general group of patients (R2 =0.386 F=55.925 p=0.0001 β=0.621 and R2 =0.735 F=246.808 p=0.0001 β=0.857, respectively). TNF-α influences the development of headaches in patients (Pearson correlation R = 0.223 p = 0.040) and the severity of postnasal drip (r = -0.231 p = 0.033 τ = - 0.171 p = 0.039). Conclusion: The study showed that the duration of the disease affects the level of production of induced TNF-α. TNF-α levels contribute to the development of headaches and postnasal drip in patients in the general group.