Third-degree Polynomial Research Articles

Density, thermal expansion, dynamic viscosity of halogenated arenes

Purpose. Experimental study of the density, thermal expansion and dynamic viscosity of halogenated arenes at temperatures from 293.15 to 343.15 K and atmospheric pressure 97.992 kPa.Methods. Density was determined by the pycnometric method, viscosity by the capillary method. A quartz pycnometer type PZh2 with a nominal capacity of 10 ml and a glass capillary viscometer type VPZh-2 with a nominal capillary diameter of 0.34 mm were used. The mass of liquids was measured using an electronic scale VSL-200/0.1A with a division value of 0.0001 g. Numerical methods were used to process the experimental results.Results. Experimental data were obtained on the density, coefficient of volumetric thermal expansion and dynamic viscosity of liquid o-xylene, ethylbenzene, fluorobenzene, chlorobenzene, bromobenzene, toluene, o-fluorotoluene, mfluorotoluene, p-fluorotoluene, o-chlorotoluene, m-chlorotoluene, p-chlorotoluene, 2,4-dichlorotoluene, 2,6-dichlorotoluene. Density and dynamic viscosity data are approximated by a third-degree polynomial. Data on the coefficient of volumetric thermal expansion are obtained from approximated measured density data. The maximum estimate of the measurement error for density was 0.13 %, for dynamic viscosity – 3.5 %. The maximum calculation error for the coefficient of thermal expansion is estimated at 3 %.Conclusion. Mathematical processing of the obtained experimental data on density and dynamic viscosity made it possible to obtain analytical relations in the form of power polynomials that allow calculating the values of these quantities at any temperature from the studied temperature range and atmospheric pressure with an error not exceeding the error of experimental determination. The calculated values are in good agreement with the data provided in the reference and scientific literature. The experimental data obtained complement the information on the properties of some of the liquids under consideration, for which the dependences of density and viscosity on temperature are poorly understood. The substances under study are used in various sectors of the economy and are therefore technically important liquids. The measurement results can be used in condensed matter physics, for the analysis of liquid hydrocarbons, and can be useful in the chemical industry.

Analiza pełzania w przetwornikach momentu siły dla turbin wiatrowych

A crucial aspect to consider when assessing the effectiveness of wind turbines is the phenomenon of torque creep, both under load and without load. This phenomenon significantly affects the proper functioning of torque transducers, thus necessitating the utilization of suitable algorithms for analysing measurement data. The least squares method is well-suited for this type of analysis. Linear regression was employed to study the creep trend, while a third-degree non-linear polynomial curve enabled a more precise visualization of creep, yielding valuable insights.

Prediction of Cancer Proneness under Influence of X-rays with Four DNA Mutability and/or Three Cellular Proliferation Assays.

All these assays were applied to skin untransformed fibroblasts derived from eight major cancer syndromes characterized by their excess of relative cancer risk (ERR). Significant correlations with ERR were found between hyper-recombination assessed by the plasmid assay and G2/M arrest and described a third-degree polynomial ERR function and a sigmoidal ERR function, respectively. The product of the hyper-recombination rate and capacity of proliferation described a linear ERR function that permits one to better discriminate each cancer syndrome. Hyper-recombination and cell proliferation were found to obey differential equations that better highlight the intrinsic bases of cancer formation. Further investigations to verify their relevance for cancer proneness induced by exogenous agents are in progress.

Retrograde orbits associated separatrices in perturbed restricted three-body problem

This study develops single and multivariate nonlinear regression models for predicting Jacobi constant related to separatrix associated with simply symmetric retrograde periodic orbits in the framework of CRTBP with and without perturbations effects. These models are constructed using data from real and hypothetical systems considering that the parameter of mass is independent variable, while the Jacobi constant is displayed as a function of mass and oblateness parameters. Third-degree polynomials from single-variable regression and fourth-degree polynomials from multivariate regression accurately predict the Jacobi constant for given mass and oblateness values, facilitating the identification of separatrices in the PSS without intensive construction efforts. Error analysis confirms the model’s high accuracy across all parameters values. Additionally, chaos detection techniques, including the SALI, GALI, and Lyapunov exponent methods, along with bifurcation analysis, are employed to identify the regions of local and global chaos.

A New Constitutive Model Based on Taylor Series and Partial Derivatives for Predicting High-Temperature Flow Behavior of a Nickel-Based Superalloy.

Ni-based superalloys are widely used in aerospace applications. However, traditional constitutive equations often lack the necessary accuracy to predict their high-temperature behavior. A novel constitutive model, utilizing Taylor series expansions and partial derivatives, is proposed to predict the high-temperature flow behavior of a nickel-based superalloy. Hot compression tests were conducted at various strain rates (0.01 s-1, 0.1 s-1, 1 s-1, and 10 s-1) and temperatures (850 °C to 1200 °C) to gather comprehensive experimental data. The performance of the new model was evaluated against classical models, specifically the Arrhenius and Hensel-Spittel (HS) models, using metrics such as the correlation coefficient (R), root mean square error (RMSE), sum of squared errors (SSE), and sum of absolute errors (SAE). The key findings reveal that the new model achieves superior prediction accuracy with an R value of 0.9948 and significantly lower RMSE (22.5), SSE (16,356), and SAE (5561 MPa) compared to the Arrhenius and HS models. Additionally, the stability of the first-order partial derivative of logarithmic stress with respect to temperature (∂lnσ/∂T) indicates that the logarithmic stress-temperature relationship can be approximated by a linear function with minimal curvature, which is effectively described by a second-degree polynomial. Furthermore, the relationship between logarithmic stress and logarithmic strain rate (∂lnσ/∂lnε˙) is more precisely captured using a third-degree polynomial. The accuracy of the new model provides an analytical basis for finite element simulation software. This helps better control and optimize processes, thus improving manufacturing efficiency and product quality. This study enables the optimization of high-temperature forming processes for current superalloy products, especially in aerospace engineering and materials science. It also provides a reference for future research on constitutive models and high-temperature material behavior in various industrial applications.

Start-Ups and Entrepreneurship in Renewable Energy: Investments and Risks

Advances in renewable energy technologies, particularly in solar, wind, energy storage, and grid integration solutions, are accelerating the growth of in startups in this sector. Despite the promising outlook, renewable energy startups face several risks, including technological, regulatory, financial and market risks. The article carries out a bibliometric analysis of scientific publications related to the problem of investment and risks associated with the development of entrepreneurship and start-ups in the field of renewable energy. After multi-level filtering of the dataset, the research base consists of 82 publications by 232 scientists for 2005-2023, indexed by Scopus, and the analysis tools used are Biblioshiny and Excel. In 2005-2016, the number of publications grew annually at a rate of 10.47%, with peaks in 2006, 2007, and 2016; in 2017-2023, the number of papers increased (the dependence is described by a third-degree polynomial trend). The article examines 3 different types of Three-field plots in the topic of the investments and risks of the startups and entrepreneurship in renewable energy: 1) “References – Authors – Keywords”, 2) “Countries – Institutions – Authors”, 3) “Authors – Sources – Keywords”. A quantitative and qualitative analysis of the scientific journals that make the largest / periodic but noteworthy / minimal contribution to the dissemination of knowledge in this area was carried out, the top 10 authors and papers were analysed by the levels of local and global influence, the most powerful research networks (based on the results of the analysis of joint citations) were identified both in terms of authors and countries, and the leading countries were identified in terms of the volume of research output of their scientists and the intensity of citation of these works. Building clouds of the most used keywords allowed us to identify priority thematic areas of research, as well as to analyse the structural and logical relationships between different thematic blocks in the research landscape. With the help of multiple correspondence analysis (factorial analysis) and longitudinal thematic map analysis, the scientific landscape in this area is clustered and evolutionary changes and interdependence of individual topics are identified.

Implementation of a high dose routine dosimetry in a self-shielded irradiator

Introduction: Ionizing radiation is applied in various fields, and dosimetric control guarantees the quality and safety of products during the irradiation process. There is a need for dosimetric calibration procedures in industrial irradiation plants, specifically for self-shielded irradiation systems. Objective: To implement high dose dosimetry in the routine control of irradiated materials within a self-shielded irradiator. Methods: We worked with 32 dosimeters; we divided the dose range used into 8 points and used four RED Perspex dosimeters per point. We measured the specific absorbance for each dosimeter; plotted these values against dose and produced a third-degree polynomial fit as a calibration curve. Results: We obtained the calibration curve with an r2 of 0,9997. The uncertainties due to the dispersion of the dosimeters and the calibration curve were 1,39% and 0,22%, respectively, for a total uncertainty of 4,80%. This uncertainty includes dose determination with a factor coverage (k) equal to 2 for a 95% confidence interval. Conclusion: Perspex RED dosimeters can be used for routine control of irradiated products in a self-shielded irradiator system.

Empirical models and artificial intelligence for estimating hourly diffuse solar radiation in the state of Alagoas, Northeastern Brazil

Diffuse solar irradiation (HD) data are essential for the design and management of photovoltaic solar systems, biosphere-atmosphere modeling, and other applications. However, HD observations are scarce in several locations, especially in tropical regions. Employing hourly diffuse solar irradiation (HDh) and global solar irradiation (HGh) data collected between 2002─2003 and 2007─2008 in Alagoas State, Northeast Brazil, this study assesses various modeling techniques. Empirical models, including third-degree polynomial, logistic, sigmoidal, and rational functions, were compared with AI methods such as artificial neural networks (ANN), support vector machine (SVM), and adaptive neuro-fuzzy inference system (ANFIS). Additionally, it explores how solarimetric and meteorological variables impact the performance of these models. The empirical models showed similar performance in estimating KDh(=HDh/HGh) (r2 > 0.726, modified Willmott – dm > 0.704, and RMSD < 0.103), with the third-degree polynomial model standing out. The empirical models had difficulty estimating KDh for hourly atmospheric transmittance (KTh) > 0.80, which indicated that they are not able to adequately simulate clear sky conditions, mostly due to surface reflections and clouds at the end of the day. ANN (r2 > 0.718, dm > 0.702, and RMSD < 0.105) showed better precision and accuracy of estimates for a greater number of schemes in relation to SVM and ANFIS (r2 > 0.704, dm > 0.699, RMSD < 0.108) and to empirical models. AI methods were able to represent the complexity of these conditions, with overall performance in estimating KDh superior or equivalent to empirical models. This study underscores the significance of exploring diverse methods for HD estimation, demonstrating promising potential for accurate and reliable estimation of hourly diffuse solar irradiation.

Cole type Pitot tube, discharge factor survey and calibration

This article proposes that the Pitot Cole tube used for measuring water flow in the distribution does not require calibration, as it is an intrinsically self-calibrated equipment. Its function is to transform flow speed (kinetic energy) into manometric pressure, where the measurement is made by manometers or Pitometry Cases. The article also cites a third-degree polynomial equation that automatically corrects the Pitot Cole tube discharge factor rangeability from 3:1 up to 35:1. As a fundamental highlight, added to other article contributions, the credibility achieved today during a flow measurement is cited, reaching an accuracy from 3:1 or better, in the entire measurement range, of 35:1. In the water industry, the Pitot Cole tube interconnected in the Pitometry Case measure and record electronically the flow of treated and distributed water in the consumer sectors and, through specific software, it executes and issues a report comparing the Pitometric measurements against installed and fixed measurement equipment on the same network.

Updating to Optimal Parametric Values by Memory-Dependent Methods: Iterative Schemes of Fractional Type for Solving Nonlinear Equations

In the paper, two nonlinear variants of the Newton method are developed for solving nonlinear equations. The derivative-free nonlinear fractional type of the one-step iterative scheme of a fourth-order convergence contains three parameters, whose optimal values are obtained by a memory-dependent updating method. Then, as the extensions of a one-step linear fractional type method, we explore the fractional types of two- and three-step iterative schemes, which possess sixth- and twelfth-order convergences when the parameters’ values are optimal; the efficiency indexes are 6 and 123, respectively. An extra variable is supplemented into the second-degree Newton polynomial for the data interpolation of the two-step iterative scheme of fractional type, and a relaxation factor is accelerated by the memory-dependent method. Three memory-dependent updating methods are developed in the three-step iterative schemes of linear fractional type, whose performances are greatly strengthened. In the three-step iterative scheme, when the first step involves using the nonlinear fractional type model, the order of convergence is raised to sixteen. The efficiency index also increases to 163, and a third-degree Newton polynomial is taken to update the values of optimal parameters.

A Low-Cost Wearable Device to Estimate Body Temperature Based on Wrist Temperature.

The remote monitoring of vital signs and healthcare provision has become an urgent necessity due to the impact of the COVID-19 pandemic on the world. Blood oxygen level, heart rate, and body temperature data are crucial for managing the disease and ensuring timely medical care. This study proposes a low-cost wearable device employing non-contact sensors to monitor, process, and visualize critical variables, focusing on body temperature measurement as a key health indicator. The wearable device developed offers a non-invasive and continuous method to gather wrist and forehead temperature data. However, since there is a discrepancy between wrist and actual forehead temperature, this study incorporates statistical methods and machine learning to estimate the core forehead temperature from the wrist. This research collects 2130 samples from 30 volunteers, and both the statistical least squares method and machine learning via linear regression are applied to analyze these data. It is observed that all models achieve a significant fit, but the third-degree polynomial model stands out in both approaches. It achieves an R2 value of 0.9769 in the statistical analysis and 0.9791 in machine learning.

The Effects of Post-Surgical Pregnancy on Weight Loss Trajectories after Bariatric Surgery: Are Initial Weight and Age Prognostic Factors?

Introduction: A substantial percentage of patients undergoing bariatric surgery are of childbearing age. Pregnancy outcomes after bariatric surgery are known. However, there are limited data on the impact of pregnancy on weight loss after surgery. Objectives: This study aims to evaluate the effects of pregnancy on post-bariatric surgery weight loss trajectories (WLTs) and to determine the association with age and initial weight. Methods: All who had primary bariatric surgeries (Roux-en-Y gastric bypass or sleeve) between September 2015 and July 2020 were classified into two groups: post-surgery gravid (GG) and post-surgery non-gravid (NG). WLTs were examined using a random intercept mixed-effects model with repeated measures nested within patients. The post-surgery/pre-gravid time phase (PoPG) was modelled using a third-degree polynomial. For GG, two third-degree spline functions modelled the post-surgery while gravid (PoWG) and post-partum (PoPP) time phases. Age and initial weight were used to control for pre-existing differences during PoPG. Weight differences at 6 months PoPP were examined by applying general linear hypothesis testing to the mixed-model results. Results: A total of 508 patients were included, 20 in GG and 488 in NG. The mean age at surgery was 33 years in GG and 37 years in NG. The mean initial BMI was 47 kg/m2 and 43 kg/m2, respectively. During PoPG, adjusted average weight in both groups follows the path across time. For GG, weight decreases and then increases during PoWG. For GG during PoPP, weight immediately decreases after delivery and then increases over time to levels similar to NG. Weight differences at 6 months PoPP for GG and NG were not statistically different. Older age was associated with reduced weight loss during PoPG by Baseline Age, while higher initial weight was associated with increased weight loss during PoPG by Baseline Weight. In both instances, these effects attenuate over time. Conclusions: This model indicates that pregnancy following bariatric surgery affects WLT during PoWG and PoPP, and no difference in weight is expected after 6 months post-gravid. Age and initial weight could be considered prognostic factors during PoPG. Patients wishing to conceive should undergo preconception counselling and be advised to avoid pregnancy during the period of rapid weight loss. They also should be informed that WLT may vary during pregnancy and early post-partum.

Algorithms Utilized for Creep Analysis in Torque Transducers for Wind Turbines

One of the fundamental challenges in analyzing wind turbine performance is the occurrence of torque creep under load and without load. This phenomenon significantly impacts the proper functioning of torque transducers, thus necessitating the utilization of appropriate measurement data analysis algorithms. In this regard, employing the least squares method appears to be a suitable approach. Linear regression can be employed to investigate the creep trend itself, while visualizing the creep in the form of a non-linear curve using a third-degree polynomial can provide further insights. Additionally, calculating deviations between the measurement data and the regression curves proves beneficial in accurately assessing the data.

Digitalisierung und Georeferenzierung einer überdimensionalen historischen Karte der Landvogtei Neuland (Winsen/Luhe) mittels Structure-from-Motion (SfM) Photogrammetrie

AbstractThe study of historical maps has gained significant importance in recent years due to their ability to shed light on past geographical and topographic landscapes since they serve as crucial sources for understanding past conditions. They not only provide insights into the geography and topography during the time they were created but also allow for studying long-term changes over time. In this study, an oversized historical map of the Bailiwick of Neuland from the years 1780 to 1790 was discovered in the archives of the municipal building office in Winsen an der Luhe, Germany. The map, measuring approximately 5 m × 2 m, was digitised by photogrammetric methods and subsequently georeferenced. The process involved photographing the map with two different cameras and two UAV systems at the Geodetic Laboratory of HafenCity University Hamburg. This allowed to generate a high-resolution orthophoto from each data set. The resulting orthophoto achieved a pixel size of 0.2 mm, ensuring a detailed representation of the map. To ensure accuracy, the best photo block was scaled in a bundle block adjustment using ground control points with an accuracy of 1 mm and scale bars with an accuracy of 0.1 mm. Georeferencing of the historical map was conducted using current digital orthophotos of Lower Saxony with a resolution of 20 cm. A third-degree polynomial transformation was applied during georeferencing, resulting in mean residuals of 2.5 m at the ground control points. This process ensured that the historical map was accurately aligned with the current digital orthophotos, allowing for precise spatial referencing.

Memory-Accelerating Methods for One-Step Iterative Schemes with Lie Symmetry Method Solving Nonlinear Boundary-Value Problem

In this paper, some one-step iterative schemes with memory-accelerating methods are proposed to update three critical values f′(r), f″(r), and f‴(r) of a nonlinear equation f(x)=0 with r being its simple root. We can achieve high values of the efficiency index (E.I.) over the bound 22/3=1.587 with three function evaluations and over the bound 21/2=1.414 with two function evaluations. The third-degree Newton interpolatory polynomial is derived to update these critical values per iteration. We introduce relaxation factors into the Dzˇunic´ method and its variant, which are updated to render fourth-order convergence by the memory-accelerating technique. We developed six types optimal one-step iterative schemes with the memory-accelerating method, rendering a fourth-order convergence or even more, whose original ones are a second-order convergence without memory and without using specific optimal values of the parameters. We evaluated the performance of these one-step iterative schemes by the computed order of convergence (COC) and the E.I. with numerical tests. A Lie symmetry method to solve a second-order nonlinear boundary-value problem with high efficiency and high accuracy was developed.

Carbon and financial performance nexus of the heavily polluting companies in the context of resource management during COVID-19 period

The depletion of fossil fuels and the new EU climate policy goals to achieve a zero-emission economy after 2050 encourage highly polluting companies to increase the efficiency of energy conversion from non-renewable energy sources, develop renewable energy sources and implement resource management systems in production. Studying the relationship between environmental performance and financial performance of firms is particularly important in times of the Covid-19 pandemic, as companies' decisions to limit or continue green investments and low-emission transformation may impact access to external financing sources. The aim of this study is to identify the shape of the relationship between the carbon and financial results of heavily polluting enterprises in the context of resource management and to assess the impact of the Covid-19 pandemic on the considered relationship. For a panel sample of Polish enterprises representing highly polluting industries with manufacturing plants covered by the EU ETS in 2009–2021, a third-degree polynomial describing this relationship was estimated. A U-shaped relationship was identified between carbon emission intensity and return on sales and return on assets, which can be explained by the ‘too-little-of-a-good-thing’ effect. Increase in share of renewable energy in the production structure significantly reduces firms’ profitability, which can be explained by the relatively high costs associated with the development of renewable energy and the changing legal regulations regarding this type of investment. It has been shown that companies with high carbon emission intensity achieved lower sales profits and return on assets compared to companies with lower carbon intensity during the Covid-19 pandemic. The lower scale of allocation of free emission allowances compared to previous years, combined with the increase in emission allowance prices under the influence of shocks generated by the pandemic, had a negative impact on the profitability of heavily polluting companies. The modelling results provide important information to managers who, based on them, can make more informed decisions regarding the use of natural resources in production and the involvement of enterprises in investments aimed at the use of cleaner production technologies and the development of renewable energy.

Leachate Treatment via TiO2/UV Heterogeneous Photocatalysis: A Multiple Polynomial Regression Model

Advanced oxidation processes such as TiO2/UV heterogeneous photocatalysis are suitable treatment methods for wastewater with high pollutant loads such as landfill leachates. Optimizing the variables that influence the process is a fundamental aspect. However, in this regard, experimental conditions are limited in terms of resources and time, which is why modeling allows obtaining a general understanding of the phenomenon from a set of experimental data. This work sought to model the photocatalytic process via multivariate polynomial regression, considering variables such as the catalyst concentration, the pH level, and the accumulated energy concerning the percentage of degradation in terms of dissolved organic carbon (DOC). The implemented fitting method resulted in a third-degree polynomial with an R2 of 0,8652, concluding that the model and its conclusions are valid. Moreover, with greater degrees, the model curve overfitted, even with better R2. DOC abatement showed a negative correlation with pH and the catalyst dose, while an opposite trend was observed for the accumulated energy. The model predictions allow inferring that, at low catalyst doses and medium and high pH levels, it is possible to find maximum degradations at low cumulative energies.

Reliability of a semi-tethered front crawl sprint performance test in adolescent swimmers.

This study aimed to evaluate the test-retest reliability of a sprint performance test with semi-tethered front crawl swimming to indirectly assess the current potential to perform at maximal anaerobic effort in adolescent swimmers. Eight adolescent swimmers participated in this study (gender: females (n = 4) aged 13.0 ± 0.8 years, body height 1.6 ± 0.0m, body mass 50.1 ± 4.5kg; and males (n = 4) aged 13.3 ± 1.3 years, body height 1.7 ± 0.1m, body mass 59.0 ± 8.2kg. The testing protocol consisted of two trials of 25m semi-tethered front crawl swimming with maximal effort and with 1kg resisted isotonic load. Velocity data were recorded automatically by the 1080 Sprint device for 15m (between 3m and 18m). The Fast Fourier Transform algorithm filtered raw instantaneous swimming velocity data in distance (time) function. A third-degree polynomial was used to extract the individual velocity profile, from which the following variables were chosen for test-retest reliability and the assessment of sprint performance: ttrial15, vmax, vmin, tvto max, tvat max, Dto vmax, Dat vmax, fatigue index. Parameters such as vmax, vmin, and ttrial15 were estimated from swimming velocity profiles and considered as reliable. The CV showed low variance <5%; while ICC2,1 demonstrated respectively good (ICC2,1: 0.88), very good (ICC2,1: 0.95), and excellent (ICC2,1: 0.98) rate of relative reliability; and the Bland-Altman index revealed an acceptable agreement (LoA ≤5%) between two measurements. The sprint performance test based on semi-tethered front crawl swimming confirmed that ttrial15, vmax, and vmin were reliable variables to indirectly indicate a potential to perform the maximal anaerobic effort among adolescent swimmers. The evaluation of the swimming velocity profiles allows coaches to monitor the adaptive changes of performance during the training process.

First-year university students’ understanding of function concepts encountered in Grade 12 Mathematics: a case study

This article focuses on first-year university students’ understanding of concepts related to third-degree polynomial and trigonometric functions that they encountered during their study of Grade 12 mathematics. In this study three online questions from two firstyear mathematics quizzes at the University of KwaZulu-Natal were analysed. The first question focused on the characteristics of a polynomial function, while the second and third questions focused on the characteristics of trigonometric functions. The characteristics included calculus-related concepts, for example, intervals of increase or decrease, concavity and local extrema. It was found that about a fifth of the participants (n = 557), science students who studied the core mathematics module Introduction to Calculus, had difficulties in answering those calculus-related questions compared to determining the general non-calculus characteristics, for example, the range and domain. The study also found that about a quarter of the participants lacked relational understanding with regard to calculus-related concepts. This study recommends that lecturers need to spend more time on calculus-related concepts of a function that focus on relational understanding.

An experimental study for efficiency modeling of grid-connected photovoltaic system

ABSTRACT As a key factor, it is vital to mathematically model the electrical efficiency of photovoltaic (PV) systems. This paper investigates the efficient modeling of a 2.5 kW grid-connected PV system, located in Mahan, Kerman, Iran, with respect to different factors like solar radiation, humidity, dust deposition, temperature, and shading. For this aim, different nonlinear models are considered and a curve-fitting approach is used to optimally determine the unknown parameters. Over the case study, simulation results show that when the dust deposition is not included in the modeling (solar radiation, ambient temperature, cell temperature, humidity, and shading as inputs), the third-degree polynomial model leads to more accurate result than the other models. By use of the third-degree polynomial model, the value of root mean square error (RMSE) for train and test data sets is obtained 0.0123 and 0.0109, respectively. In this case, the average RMSE value is 0.0116. On the other hand, when dust impact is included in the modeling (solar radiation, ambient temperature, humidity, and number of dusty days as inputs), the accuracy of the exponential model is more than the other ones. In this case, the value of RMSE for both train and test data sets is obtained 0.0018. Sensitivity analysis shows that the system efficiency depends mainly on the radiation, cell temperature, and dust and less on the humidity.