The role of moment for inertia in rotational dynamics is equivalent to mass in linear dynamics and can be understood as an object's resistance to rotational motion. It establishes the relationship between several quantities such as angular momentum, angular velocity, torque, and angular acceleration. Accurately calculating the moment of inertia is crucial for designing various rotating systems and mechanical devices in engineering. For example, when dealing with rotating mechanical parts or machines, their moment of inertia ensures stability and performance in design needs to be considered. In physics and engineering, the analysis of rotational motion for rigid bodies relies on the concept of moment of inertia. It allows us to understand the dynamic behavior of a rigid body around an axis, including applications such as rotational stability, gyroscopic motion, and conservation of angular momentum. In this paper, the rotational inertia of a rigid body is studied by different method. Calculating the moment of inertia helps us gain a deeper understanding of an object's inertial properties during rotational motion while providing an important foundation for engineering design, scientific research, and material analysis.

The Fourier Transform (FT) is a linear transformation for the primitive function. It takes some set of functions to be an orthogonal basis. Its physical meaning is to transfer the primitive function onto each set of base functions. Because it can convert functions between the time and frequency domains, the FT is widely employed in many fields. The Fractional Fourier Transform (FrFT) is an improvement and progress based on the FT. This paper will define the FT and FrFT. Then the distinction between FrFT and FT is discussed. Finally, specific examples of its application in processing digital image are provided. FrFT is the process of transforming an image function into a series of periodic functions. The FrFT is used as a powerful mathematical tool to understand non- smooth signals, nonlinear systems and complicated phenomena, which is significant and has broad possibilities in the fields of signal processing, communication, image processing, optical imaging and quantum information processing.

This article is a modeling study on the self-rating of board games. This article has reviewed and understood board games and various indicators of board games and stated the background of the topic and the questions raised. It has determined the dimensions of game characteristics that need to be evaluated. Through keyword retrieval, the text is transformed into the required numerical information, and through public calculation, the required data is obtained to fit the geek ratings and average player ratings of the 25 games in the target. Next, analyze the specific issues of each data through descriptive statistics. Then, through correlation analysis, which indicators are related were obtained, and a series of conclusions were drawn. Next, a second linear regression analysis will be conducted on the Geek rating and average rating, and a series of conclusions will be drawn. Summarize the conclusion, consider the advantages of the model, and reflect on the shortcomings of the model. Use sensitivity analysis to check if the conclusion is complete. This article randomly selected a game and analyzed it through a model. And draw relevant conclusions. Finally, the analysis and summary improved the modeling.

Image inpainting has always been a major problem in the field of scientific research. How to fill in the damaged area of the image to make the image look realistic is the main goal of the image inpainting task. In recent years, with the rapid development of machine learning, the researchers started using machine learning to assist in image inpainting. The most representative one is image inpainting based on generative models. The classic idea of restoration is to generate a restoration result with the highest quality and the most realistic appearance. However, as long as the result is reasonable, image inpainting allows for multiple restoration results. For this reason, the field of pluralistic image completion was born. This paper introduces pluralistic image completion and reviews past research in this field. This paper divides pluralistic image completion methods into three categories: VAE-based, GAN-based, and Transformer-based, and gives examples of various representative methods and the latest research in this field. This paper also introduces the available datasets and evaluation metrics. A discussion is given based on the performance of these three categories of methods and the prospects for the development of the field of pluralistic image completion. This review can serve as a reference for researchers in the field of image inpainting. It provides a table of datasets that can be used to evaluate and compare the listed methods and looks forward to possible developments and applications in this field in the future.

The emergence of cardiac disease is influenced by numerous variables. Every year a large percentage of people around the world die from heart attacks. This study was to look at how important clinical variables are connected to the chance of having CVD. The analysis used a Kaggle dataset with details from 70,000 patients and 10 different variables. The study examined how factors such as age, gender and changes in cardiac activity during exercise affect overall heart health. Multiple linear regression models were used to analyze these effects. The results show a significant correlation between these factors and an increased risk of heart disease. This emphasizes the importance of these predictors in clinical assessments. It can be concluded from this study that regular medical check-ups, early prevention and treatment should be carried out for these vulnerable groups. The general prevalence of heart disease in the nation can be decreased by implementing these strategies. According to the study, personalized health strategies have the potential to improve CVD outcomes and strengthen preventive measures. All of the experimental results suggest that continued documentation and study of these pathogenic factors in medical diagnostics and experiments could aid in drug development as well as improve medical technology and help more patients with cardiovascular disease recover.

Oil and gas are two crucial resources in modern life and the development of technology. Investors are not only concerned about their own price, but their stock price is also an important part of formulating investment plans. This article will focus on the adjusted closing price since it consists of adjustments for splits, dividends, and capital gain distributions, which can demonstrate the situation of oil and gas in the stock market better. After the occurrence of COVID-19, the economic market of the whole world including the US. encountered great changes in many aspects. Thus, this article considered applying the model with the best performance from ARIMA, exponential smoothing, and Holt-Winters’ method to forecast the future adjusted closing prices of two large and representative companies in oil and gas from the US. According to the predicted results, the US oil and gas market is likely to experience a small but steady increase.

As a global chronic disease, diabetes has a serious impact on human health and imposes a significant economic burden. Facing this challenge, researchers are actively developing and optimizing predictive models to improve early diagnosis and management of diabetes. This paper analyzed the influence of independent variables on the risk of diabetes by logistic regression from 8 aspects including body mass index (BMI), glycosylated hemoglobin (HbA1c) and heart disease. The logistic regression model, an effective binary classification method, optimizes parameters using maximum likelihood estimation to predict diabetes probability. The model will be evaluated by ROC curve, cross-validation, standardized residual analysis and confusion matrix to comprehensively test its predictive power, stability and classification performance. The results showed that hemoglobin A1c level (HbA1c.level) had the most significant effect on diabetes risk. Other relevant variables, including blood glucose level and body mass index (BMI), demonstrated significant positive correlations, particularly with hypertension and heart disease. The findings will enhance early diabetes identification and provide data to support the development of targeted prevention and intervention measures to reduce the burden of diabetes on individuals and society.

Real estate price prediction plays a vital role in urban planning, investment decision-making, and risk management. However, existing prediction models often show problems such as insufficient generalization ability and susceptibility to outliers when faced with complex nonlinear relationships, multidimensional features, and noisy data. Therefore, choosing a model that can accurately capture complex patterns and has strong robustness has become the focus of research. This paper introduces the random forest model and compares it with multivariate linear regression, XGBoost, and support vector machine (SVM). Compared with the traditional regression model, the random forest model combines the flexibility of decision trees and the multi-level feature extraction ability of deep learning, and can better handle the complex nonlinear relationships in the Boston housing price dataset. The experimental results show that the random forest model has achieved excellent performance in all evaluation indicators, and the model accuracy indicators are distributed as MSE=8.2502, RMSE=2.8723, MAE=2.0668, and R^2=0.8875. These results show that the random forest model not only outperforms other models in prediction accuracy but also shows significant advantages in dealing with data complexity and improving generalization ability. Therefore, the random forest model provides an efficient and reliable tool for future real estate price prediction research and applications.

The mass balance of the Antarctic Ice Sheet is forecasted in this study using ARIMA models, with a particular emphasis on the distinct regions of East and West Antarctica. The research endeavours to forecast the trends in ice mass balance over the next 12 years by examining data from 1992 to 2021, thereby elucidating the potential impacts of climate change on these critical regions. The ARIMA model, which is renowned for its capacity to capture and predict time series data, has identified substantial trends that indicate a persistent loss of ice mass, particularly in West Antarctica, which has experienced substantial declines in recent decades. The model's predictions suggest that, despite the potential for a reduction in the rate of loss, the overall trend is consistent with the ongoing reduction of ice mass. These results underscore the pressing necessity for ongoing research and monitoring to gain a more comprehensive understanding of the consequences of these developments. The study also emphasises the necessity of enhancing predictive models by incorporating supplementary environmental variables to provide more comprehensive insights into the future of the Antarctic Ice Sheet and its global impacts, thereby increasing their accuracy.

This study aims to improve the accuracy of rainfall forecasting in Pakistan by comparatively analyzing the performance of two models, ARIMA and SARIMA, to optimize the forecasting methodology. The study points out that although the ARIMA model performs well in time series analysis, it has shortcomings in handling data with significant seasonal variations. Therefore, the SARIMA model was introduced and it performed better in forecasting seasonal variations. Future research should consider combining the SARIMA model with models that can explain global climate phenomena such as El Niño and La Niña to enhance the accuracy of forecasts. In addition, ways to automate and improve the selection of model parameters should be explored to make the SARIMA model more efficient and accurate. The introduction of the SARIMA model has significantly improved prediction accuracy and contributed to more efficient planning and management of water resources. Areas where improvements can be made include reserving water resources in advance during the dry season or allocating water resources appropriately during the rainy season to support irrigation agriculture, urban water supply, flood control measures, etc. These enhanced forecasting methods help Pakistan cope with climate change challenges.