Determination Of Coefficients Research Articles

Experimental Measurements of Explosion Effects Propagating in the Real Geological Environment—Correlation with Small-Scale Model

This research focuses on comparing small-scale and full-scale measurements of wave propagation from explosions by using scaling relationships to find significant correlations between the two. The study investigates how seismic waves generated by explosions behave in the geological environment. The research covers various aspects such as the development of the model, the explosive materials used, measurement methods, evaluation techniques, and relevant software. A scientific approach based on the principle of backward Fourier transform was used to process and evaluate the data, which helps to filter the frequencies. One of the important calculations discussed is the determination of the attenuation coefficient, which helps to describe how waves attenuate as they pass through a material. The research also deals with dynamic scaling, using the dynamic exponent as a scaling factor to provide a better understanding of the behavior of waves at different scales. By comparing real in situ data with results from small-scale models, the study provides a robust framework for predicting the effects of explosions in complex geological environments. The research results show a high correlation coherence of the statistical data files of up to 4.1%. For dynamic tasks and model scaling, an important result can be pointed out, namely the approximately fourfold decrease in the exponents of the dependence on the distance from the excitation source and the amplitudes between P-waves (0.4316) and R-waves (0.1219). Conclusions are targeted at the possibility of correlating three types of results: small-scale simulations, numerical simulations, and a real full-scale experiment.

Clinical significance of PET/CT in the diagnosis of primary adrenal malignancies

Background. According to the literature, the role of combined positron-emission and X-ray computed tomography (PET/CT) in diagnosing primary adrenal tumors (AT) remains limited due to both the frequency of these neoplasms and the availability of the method. Various research is required to assess the diagnostic resources of PET/CT with 18-fluorodeoxyglucose (18F-FDG). Aim. To evaluate the clinical role of PET/CT with 18F-FDG in the diagnosis of primary adrenal malignancies (PAM). Materials and methods. The study included 9 patients, 5 males and 4 females aged 44–76, with a median age of 59.3 years, with a morphologically confirmed diagnosis of the PAM. All patients underwent PET/CT with 18F-FDG. Visual and quantitative analysis of the obtained images was performed, including determination of the standardized maximum accumulation coefficient (SUVmax) in the tumor, liver, and spleen, the ratio of SUVmax of the primary tumor to SUVmax in the liver and spleen. Tumors were more often localized on the right (5/55.6%), and one case was bilateral. The maximum size of the adrenal mass averaged 6.8 cm (3.2–11.2) and the minimum size was 6.0 cm (2.3–9.0). The median SUVmax in AT was 10.0 (3.54–22.29), while in liver and spleen, it was 3.16 and 2.34, respectively, and the ratio of tumor SUVmax to liver and spleen SUVmax was 3.33 and 4.48, respectively. Conclusion. Hybrid PET/CT with 18F-FDG is a medical imaging method with a high diagnostic accuracy of PAM. PET/CT showed significant 18F-FDG tumor uptake, with a median SUVmax of 10.0 and a ratio of tumor SUVmax to liver and spleen SUVmax of 3.33 and 4.48, respectively. PET/CT with 18F-FDG may be a method of choice for diagnosing primary ATs.

Second Hankel determinant of logarithmic coefficients of inverse strongly starlike functions

Abstract The sharp bound of the second Hankel determinant of logarithmic coefficients of inverse functions of strongly starlike functions is computed.

Determination of hydrodynamic coefficients for open-frame ROVs through free oscillation tests in 1-DOF

ABSTRACT This study introduces an economical experimental approach for measuring the hydrodynamic inertia ( C M ) and drag ( C D ) coefficients of an open-frame ROV to support the stock assessment of scallops in the North Sea of Peru. A 1:3 scale ROV model was tested, suspended on springs, and set to oscillate freely in still water. The multiple spring groups provide equivalent stiffness, initial displacement, and natural frequencies for different cases. Three damping models—linear, quadratic, and linear-plus-quadratic—were applied to describe the motion equations, with the linear plus-quadratic model best fitting the experimental data. The coefficients and were analyzed against Reynolds (Re) numbers from 0.2×10 5 and 0.6×10 5 and Keulegan Carpenter (KC) numbers from 0.5 to 2. A strong correlation was observed with previous forced oscillation tests on cylinders and irregular bodies; thus, this methodology can be used to determine the hydrodynamic coefficients of ROVs.

The Effect of Knowledge and Ease of Use of Quick Response Code Indonesia Standard (QRIS) on the Decision to Use E-Wallet as a Payment Means in UMKM in Yogyakarta City

The use of QRIS in MSMEs in Yogyakarta has increased and spread to small MSMEs. This makes the development of payment services more advanced and easier. However, there are also quite a few small MSMEs or consumers who still have minimal knowledge about QRIS and how to use it. For this reason, it is necessary to know the extent of knowledge about QRIS and what benefits can be obtained from QRIS. Socialization of QRIS is very helpful in the development of QRIS in the community, especially among MSMEs in Yogyakarta. The purpose of this study is to determine the knowledge and responses of culinary MSME consumers in Yogyakarta about the Quick Response Code Indonesia Standard (QRIS) and its ease of use. In this study, the author used a descriptive quantitative research method with a data collection method using a questionnaire based on the Likert Scale. While the data research process uses descriptive analysis, associative analysis which includes multiple linear regression analysis, correlation coefficient analysis and determination coefficient analysis, and hypothesis testing in the form of simultaneous tests (F Test). Furthermore, describing the results of the analysis using descriptive sentences.

Spectral resolution techniques for the simultaneous spectrophotometric determination of anti-Parkinson drugs in their combined pharmaceutical dosage form and biological sample based on multivariate calibration and absorbance subtraction methods

In this study, simultaneous determination of levodopa (LEV) and carbidopa (CBD) in binary mixtures, pharmaceutical formulation, and biological sample was conducted using the application of simple, fast, sensitive, and accurate UV-spectrophotometry in combination with chemometrics methods. The first method is net analyte signal (NAS) based on the multivariate calibration methods. The limit of detection (LOD) and limit of quantification (LOQ) were 0.9758, 0.7633 µg/mL and 2.956, 2.313 µg/mL over the linear range of 5–40 and 0.5–20 µg/mL for LEV and CBD, respectively. In the NAS approach, the mean recovery values of mixtures were 100.12 % for LEV and 99.65 % for CBD, where root mean square error (RMSE) values were 0.0106 and 0.0141 for LEV and CBD, respectively. The second method is absorbance subtraction (AS) based on the absorption factor technique for analyzing the isosbestic point. This model was constructed at an isosbestic point of 261 nm in the range of 5–40 and 0.5–20 µg/mL with coefficient determination (R2) of 0.9985 and 0.9996 for LEV and CBD, respectively. AS method could estimate LEV and CBD with LOD values of 1.924 and 0.5657 μg/mL and LOQ values of 5.833 and 1.714 μg/mL, respectively. The recovery percentage was between 91.50 % to 104.60 % with RMSE of 0.1455 for LEV and 92.00 % to 106.66 % with RMSE of 0.2508 for CBD. The introduced approaches have the benefit of concurrent analysis of the mentioned components without any pretreatment. Statistical comparison of the results of real sample analysis with high-performance liquid chromatography (HPLC) did not show a significant difference. These methods can replace HPLC in quality control laboratories when fast, precise, and low-cost analysis is needed.

Simultaneous Determination of Transformation Plasticity Coefficients of Bainite and Martensite Transformations by Oil Quenching of Steel Sheet for Machine Structural Use and Accurate Prediction of Distortion by Oil Quenching

Simultaneous Determination of Transformation Plasticity Coefficients of Bainite and Martensite Transformations by Oil Quenching of Steel Sheet for Machine Structural Use and Accurate Prediction of Distortion by Oil Quenching

Machine Learning-Based Prediction of the Adsorption Characteristics of Biochar from Waste Wood by Chemical Activation.

This study employs machine learning models to predict the adsorption characteristics of biochar-activated carbon derived from waste wood. Activated carbon is a high-performance adsorbent utilized in various fields such as air purification, water treatment, energy production, and storage. However, its characteristics vary depending on the activation conditions or raw materials, making explaining or predicting them challenging using physicochemical or mathematical methods. Therefore, using machine learning techniques to determine the adsorption characteristics of activated carbon in advance will provide economic and time benefits for activated carbon production. Datasets, consisting of 108 points, were used to predict the adsorption characteristics of biochar-activated carbon derived from waste wood. The input variables were the activation conditions, and the iodine number of activated carbon was used as the output variable. The datasets were randomly split into 75% for training and 25% for model validation and normalized by the min-max function. Four models, including artificial neural networks, random forests, extreme gradient boosting, and support vector machines, were used to predict the adsorption properties of biochar-activated carbon. After optimization, the artificial neural network model was identified as the best model, with the highest coefficient determination (0.96) and the lowest mean squared error (0.004017). As a result of the SHAP analysis, activation time was the most crucial variable influencing the adsorption properties. The machine learning model precisely predicts the adsorption characteristics of biochar-activated carbon and can optimize the activated carbon production process.

RATIONAL SHIFTS OF THE BASIC RACK’S PROFILE FOR WHEELS OF A CYLINDRICAL SPUR GEAR PAIR TO DECREASE TEETH WEAR

Purpose. It is to create a method for determination of such shift coefficients of the basic rack’s profile for driving and driven wheels of a cylindrical spur gear pair, that during gear pair operation time the wear rate of a surface layer on the most wearing sections of the teeth’ involute surfaces will be minimal. Research methods are based on integrated application of the involute gear pair theory and tribological laws. The golden section method is used to minimize the function. Results. We have obtained a dimensionless quantity, which is a function of shift coefficients of the basic rack’s profile for driving and driven wheels of a cylindrical spur gear pair. Values of this function are proportional to the greatest wear rate in the neighborhood of characteristic points on teeth’ involute profiles of these wheels. The method is created for determination of rational shift coefficients of the basic rack’s profile, which minimize the obtained dimensionless function, and which maximize the service life of the spur gear pair until the greatest worn-layer thickness on the teeth’ active surfaces reaches limiting permissible value. Scientific novelty. It is proved, that increasing of the worn-layer thickness during spur gear pair operation time will be occurring most rapidly in the neighborhood of certain characteristic points on teeth’ involute profiles of the wheels. Calculation model is elaborated for determination of the worn-layer thicknesses in the neighborhood of extreme active points on teeth’ profiles of the cylindrical spur gear pair and in the neighborhood of the lowest and the highest bounding points of single-pair contact. This model takes into account the influence of specific slides and numbers of wheels’ teeth as well as hardness values of teeth’ surface layer on the wear rates at characteristic points of teeth’ profiles. In addition, the model takes into account sharing of total force of the wheels interaction between two teeth pairs in double-pair contact and also a change of force transmitted by single pair of teeth when it comes into or go out of engagement. Practical value. Application of the created method for determination of shift coefficients of the basic rack’s profile is expedient in design of cylindrical spur gear pairs for machines and equipment, which operate in conditions when ingress of abrasive particles in the teeth engagement region is possible. An example of application of this method in design calculation of the cylindrical spur gear pair is given.

Determination of creep function coefficients of viscoelastic pipes using a transient-guided machine learning model

ABSTRACT This study introduces a novel framework for the estimation of creep function coefficients in viscoelastic pipelines, employing a combination of machine learning (ML) and transient hydraulics. Specifically, the efficacy of eXtreme Gradient Boosting (XGBoost) as an advanced regression method is evaluated within this framework. A transient simulation model, utilizing the method of characteristics, is formulated to create the reservoir-pipe-valve (RPV) scenarios under diverse boundary conditions. After conducting model calibration, the model is used to generate datasets with the transient hydraulic responses at the measurement points. The fast Fourier transform (FFT) is then applied to transform the generated samples into the frequency domain. Feature selection is accomplished through principal component analysis (PCA) to identify optimal input variables for XGBoost. In estimating the creep function, six coefficients are employed, with the feature selection analysis indicating that each coefficient is associated with a specific signal. Importantly, it is demonstrated that attempting to estimate all six coefficients using a single set of signals is unfeasible. The results affirm the accuracy of the proposed ML-based framework in determining creep function coefficients.

Experimental study in steady-state for determining the coefficient of external heat transfer on the outer wall of rotating tubes during the quenching process by immersion in water tank

The quenching process by immersion is one of the steel tube industry's most commonly used heat treatment processes. For mathematical models to be reliably used as tools capable of simulating different geometries and cooling mechanisms, knowledge of the heat transfer coefficient between the surface of the tube and the water is essential. The present work's primary objective is the experimental determination of the heat transfer coefficient between the external surface of the tube and the water. For this purpose, an experimental apparatus capable of representing the conditions of a real process was built. The predominant heat transfer regime in the single-phase region was mixed convection for the conditions tested. Two correlations were proposed to represent the data obtained for this region. Based on existing correlations in the literature, the first one returned a mean absolute error of 13.97 %. The second one was proposed based on an optimization tool, returning a mean absolute error of 6.29 %. Concerning the two-phase region, the obtained data characterized a transition regime and the beginning of the nucleated boiling. In this region, it was possible to observe that the effect of increasing rotation on the external heat transfer coefficient decreases with increasing tube surface temperature, which follows studies in the literature. The repeatability test shows that the apparatus could replicate the heat transfer coefficient values for the free convection region, staying within the range of uncertainties. However, for the boiling region, the data showed more significant disagreement. This behavior is mainly due to the difficulty of keeping the surface under the same conditions, which have greatly influenced the formation of bubbles and heat transfer.

On the in-situ determination of the effective secondary electron emission coefficient in low pressure capacitively coupled radio frequency discharges based on the electrical asymmetry effect

Abstract We present a method for the in-situ determination of the effective secondary electron emission coefficient (SEEC, γ) in a capacitively coupled plasma (CCP) source based on the γ-dependence of the DC self-bias voltage that develops over the plasma due to the Electrical Asymmetry Effect (EAE). The EAE is established via the simultaneous application of two consecutive radio-frequency harmonics (with a varied phase angle) for the excitation of the discharge. Following the measurement of the DC self-bias voltage experimentally, Particle-in-Cell/Monte Carlo Collision (PIC/MCC) simulations coupled with a diffusion-reaction-radiation (DRR) code to compute the argon atomic excited level dynamics are conducted with a sequence of SEEC values. The actual γ for the given discharge operating conditions is found by searching for the best match between the experimental and computed values of the DC self-bias voltage. The γ ≈ 0.07 values obtained this way are in agreement with typical literature data for the working gas of argon and the electrode material of stainless steel in the CCP source. The method can be applied for a wider range of conditions, as well as for different electrode materials and gases to reveal the effective SEEC for various physical settings and discharge operating conditions.

Trace element partitioning between natural barite and deep anoxic groundwaters: Implications for radionuclide retention in host rocks of nuclear waste repositories

Safety assessments for deep geological repositories involve risk calculations for the release of radionuclides like Ra, U, Pu and trivalent actinides from the storage containers to the groundwater. The retention of radionuclides through water-mineral interaction along the groundwater flow path could be a crucial factor in case of a repository failure. Barite (BaSO4) assumes significance in this context, as it has the potential to (re)crystallize and incorporate significant quantities of radioactive elements under relevant physico-chemical conditions.The assessment of mineral-fluid partition coefficients provides a means to evaluate the uptake potential of elements into the mineral. Usually, partition coefficients are determined under well-defined and controlled experimental conditions in laboratories. However, these results have shown discrepancies to partitioning coefficients determined from natural systems.Furthermore, effects like diagenesis or changes in the chemical fluid parameters might lead to a secondary alteration of the phases and affecting the retention ability.Here we investigate the incorporation of trace elements in natural barite from a borehole at 415 m depth in the Äspö Hard Rock Laboratory (Sweden). High-resolution LA-ICP-MS enables the quantitative determination of field-based partition coefficients through the integrated pixel average of selected zones in element distribution maps, combined with existing fluid concentration data. Similarities between the solid solution systems (Ra,Ba)SO4 and (Sr,Ba)SO4 allowed the combination of Sr partitioning data with density-functional theory simulations for an estimation of the partition coefficient value for Ra in natural barite. Values in the 10−2 range were determined, showing a deviation from those reported in previous experimental studies in the 10° range.Moreover, lanthanum serves as an analogue element for the radioactive trivalent actinides. The partition coefficient values for La in natural barite were determined in the range of 10−2 and 10−1, aligning well with experimental partition coefficients. Although density functional theory simulations cannot directly convert a La partition coefficient into a partition coefficient for trivalent actinides, it is assumed that these elements exhibit comparable behavior. Besides primary growth zonation, La also exhibits strong secondary enrichment, probably resulting from groundwater mixing and late fluid-mediated element transport through connected intracrystalline pore space oriented at cleavage plane systems. Additional SIMS analysis provides insights into the temporal variation of the sulfate source at the sampling site reflecting the influence of different waters during mineral growth.This study demonstrates a discrepancy between natural and synthetic PRa for barite and emphasizes that secondary processes significantly impact radionuclide retention in barite. Including these effects in reactive transport models will improve the reliability and applicability of integrative risk models.

Transferability of Model-Based Static Coefficient of Friction

The accurate determination of static coefficients of friction (COFs) is crucial in engineering design, yet standard reference values often show considerable variability. As a result, engineers frequently need to perform experimental COF measurements to ensure the reliable transferability of model-based COFs to real-world components. However, the effectiveness of cost-efficient laboratory tests, typically conducted on standardized samples, in reflecting actual component performance is often questioned as it is not trivial to transfer and scale the tribosystem. This study addresses this issue by conducting friction coefficient experiments on interference fits and flange connections, comparing the results with laboratory-based COF tests. The findings reveal a strong correlation when the tribological conditions of the real assembly are replicated in the lab. This research offers a method to enhance the accuracy and transferability of COF values from lab tests to practical applications, providing engineers with a more reliable approach to friction testing.

Jiajiejian gel ameliorates thyroid nodules through regulation of thyroid hormones and suppression of the (IL-6, TNF-α, IL-1β)/JAK2/STAT3/VEGF pathway.

The high incidence of thyroid nodules and their rapid growth in recent years have become an important issue affecting public health. Traditional Chinese medicine (TCM) external treatments have unique advantages in treating this disease, but the currently available external preparations are relatively few and the therapeutic mechanism is unclear. Jiajiejian gel (JJJG) is a TCM external preparation developed by our team for the thyroid nodule treatment, which has been preliminarily proven to be safe and effective in clinical practice. The current study was aimed to elucidate the therapeutic effects and the underlying mechanisms of JJJG on thyroid nodules in rats. The contents of paeonol and forsythoside A in JJJG were determined by HPLC. The thyroid nodules rat model was established through oral gavage of 0.1% propylthiouracil (PTU) for 6weeks and meanwhile the rats were treated with external JJJG (0.26, 0.52, 1.04g/kg). Subsequently, the therapeutic effect of JJJG was observed by means of ultrasonic examination, morphology observation, organ coefficients determination and histopathological analysis. Mechanismlly, the levels of FT3, FT4 and TSH in serum were measured and transcriptomics methods were used to analyse and screen the key targets and pathways of alleviating thyroid nodules by JJJG. Further, gene and protein expression levels of key factors in the pathways were measured and validated using quantitative real-time PCR, ELISA, western blotting and immunofluorescence, so as to clarify the therapeutic mechanism. The contents of the paeonol and forsythoside A were 1.160 and 0.608mg/g, respectively. JJJG reduced thyroid swelling, improved nodular lesions, decreased thyroid coefficients, and inhibited abnormal nodular hyperplasia of follicular epithelial cells. In terms of mechanism, JJJG significantly increased the levels of FT3 and FT4 and decreased TSH level in serum (P < 0.05). Transcriptomics suggested that the (IL-6, TNF-α, IL-1β)/JAK2/STAT3/VEGF pathway may be one of the key mechanisms in the treatment of thyroid nodules by JJJG. Further validation experiments demonstrated that JJJG significantly reduced the mRNA expression and protein content of IL-1β, IL-6 and TNF-α in thyroid tissue, as well as the mRNA expression of JAK2, STAT3 and VEGF and the protein expression of p-JAK2/JAK2, p-STAT3/STAT3 and VEGF (P < 0.05). This study indicates that JJJG efficiently ameliorates thyroid nodules by regulating the levels of FT3, FT4 and TSH in serum and suppressing (IL-6, TNF-α, IL-1β)/JAK2/STAT3/VEGF pathway in thyroid tissue, providing a potential therapeutic approach for thyroid nodules.

Measurement of stress optical coefficients for GFRP based on terahertz time-domain spectroscopy

Glass Fiber-Reinforced Polymer (GFRP) finds extensive applications in the high-end equipment manufacturing industry owing to its advantages of light weight, high strength, and corrosion resistance. Since the residual stress in GFRP builds up during the curing process and affect its mechanical properties and service life, the characterization of the residual stress in GFRP is crucial. In this study, we establish a theoretical model based on the anisotropic stress-optics law for the orthorhombic crystalline system to describe the terahertz-elasticity of GFRP and calibrate the stress optical coefficients of GFRP. First, the residual stress in GFRP at different curing temperatures are measured by fiber Bragg grating sensors. Then, the refractive index of GFRP with different residual stress are obtained based on transmission-type THz-TDS. Finally, based on the proposed photoelastic model of GFRP, the stress optical coefficients of GFRP are measured by combining the measurement results of residual stress and refractive index. The experimental results show that the refractive index of GFRP decreases with the increase of residual stress; the stress optical coefficients of GFRP are determined as q11 = −5.612 × 10−9 Pa−1, q12 = −2.548 × 10−9 Pa−1, q21 = −1.305 × 10−8 Pa−1, q22 = −1.408 × 10−9 Pa−1. The modeling of terahertz photoelasticity in GFRP and the determination of stress optical coefficients provide a basis for characterizing residual stress in GFRP by THz-TDS.

Correction to: Determination of Heat and Mass Emission Coefficients in a Hybrid Cooling Tower with Transversely Finned Radiator Pipes

Correction to: Determination of Heat and Mass Emission Coefficients in a Hybrid Cooling Tower with Transversely Finned Radiator Pipes

Fundamental study on measurement of soil pH and electrical conductivity in batch tests for the determination of soil-soil solution distribution coefficient

Soil-soil solution distribution coefficient, Kd, is used to understand the mobility of radionuclides in the soil environment. Soil pH and electrical conductivity (EC) are the important factors affecting soil Kd, but existing methods for Kd employed different conditions, as well, standard soil pH and EC methods varied in the test conditions. It would be desirable to measure both pH and EC using the same soil solution for Kd with portable meters (non-glass electrode type) that need only a small liquid volume. In this study, at first, we utilized portable pH and EC meters to examine effects of different conditions on measurements, i.e., the water/soil ratios, contact time and standing time. The results showed that portable meter measurements of soil supernatant after 1 h shaking and 1 h standing could provide comparable pH and EC values with other standard soil tests. Then measurements of pH, and EC up to 168 h were carried out, considering the Kd methods for radiocesium (Cs); only slight differences in these values were observed compared to the standard test method. Considering these results, further analysis was carried out on the correlation between soil Kd-Cs and pH and found a clear decrease of Kd-Cs at pH<5.

Experimental determination of the entropic heat coefficient of a lithium-ion cell through immersion in a dielectric fluid

The heat generation of a lithium-ion cell is predominantly comprised of irreversible and reversible heating, with the latter term dictated by the entropic heat coefficient which describes the variation of the cell’s open circuit voltage with respect to temperature. The entropic heat coefficient is also dependent upon the cell’s state of charge, and the correct description of its behaviour is required to implement numerical and analytical models which accurately describe the heat generation rate of lithium-ion cells. In this study, the entropic heat coefficient of a single 26,650 LiFePO4 cylindrical lithium-ion cell is determined through a novel liquid immersion experimental set-up, offering greater thermal uniformity and control in comparison to the environmental chambers typically utilised. The arrangement is more cost effective and easily implemented in a laboratory setting, with a thermal non-uniformity of 0.2 °C and setpoint stability of ± 0.1 °C achieved. The entropic heat coefficient is determined for six setpoint temperatures in the range of 15 °C to 40 °C across the cell’s entire state of charge, which is adjusted in increments of 10 %. This work also details the influence of open circuit voltage instability arising from cell self-discharge and relaxation, and a method to adjust for its effect is proposed and implemented. The entropic heat coefficient is subsequently utilised to determine the heat generation rate of the cell under two-phase liquid immersion cooling conditions.

Evaluation of the Performance of Kernel Non-parametric Regression and Ordinary Least Squares Regression

Researchers need to understand the differences between parametric and nonparametric regression models and how they work with available information about the relationship between response and explanatory variables and the distribution of random errors. This paper proposes a new nonparametric regression function for the kernel and employs it with the Nadaraya-Watson kernel estimator method and the Gaussian kernel function. The proposed kernel function (AMS) is then compared to the Gaussian kernel and the traditional parametric method, the ordinary least squares method (OLS). The objective of this study is to examine the effectiveness of nonparametric regression and identify the best-performing model when employing the Nadaraya-Watson kernel estimator method with the proposed kernel function (AMS), the Gaussian kernel, and the ordinary least squares (OLS) method. Additionally, it determines which method yields the most accurate results when analyzing nonparametric regression models and provides valuable insights for practitioners looking to apply these techniques in real-world scenarios. However, criteria such as generalized cross-validation (GCV), mean square error (MSE), and coefficient determination are used to select the most efficient estimated model. Simulated data was used to evaluate the performance and efficiency of estimators using different sample sizes. The results favorable the simulation illustrate that the Nadaraya-Watson kernel estimator using the proposed kernel function (AMS) exhibited favorable and superior performance compared to other methods. The coefficients of determination indicate that the highest values attained were 98%, 99%, and 99%. The proposed function (AMS) yielded the lowest MSE and GCV values across all samples. Therefore, this suggests that the model can generate precise predictions and enhance the performance of the focused data.