Volume 132

Proper time and time dilation, though well-established in special relativity, are predominantly analysed for point particles. Much less attention has been given to how proper time behaves across spatially extended rigid bodies in inertial motion. Existing studies have explored differential aging effects under relativistic rigid motion, but primarily in scenarios involving acceleration. Therefore, this paper aims to investigate how proper time varies across different points of an extended object experiencing purely inertial motion, focusing on how the different clock synchronisation conventions affect the overall desynchronisation in proper time. This paper uses classical formulations of special relativity in order to contribute to a new perspective on the role of simultaneity in distributed time frames. This paper discovered that the two primary clock synchronization conventions— the Einstein convention and slow clock transport—produce comparable desynchronization in proper time; however, each method presents distinct advantages and disadvantages in practical contexts, necessitating a complementary approach to effectively address desynchronization in applications like satellite communication.

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The advent of relativity theory, initiated by Albert Einstein in the early 1900s, ushered in the era of modern physics by reshaping fundamental concepts of space, time, and gravity. This framework emerged in response to the shortcomings of Newtonian mechanics, particularly its failure to account for the invariance of the speed of light and anomalies in Mercury’s orbital path. The paper, through a method of literature review, analyzes and summarizes the historical development and core concepts of both special and general relativity. It explores key background events, major breakthroughs, and their lasting influence on modern science. The paper concludes that the two main contributions of relativity are the famous equations: the mass-equivalence equation in special relativity and the Einstein field equations in general relativity, both of which continue to shape physics today.

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Option pricing is one of the core problems in modern financial mathematics. This paper systematically reviews the mathematical models used in option pricing, including classical models (Black-Scholes model, binomial tree model), modern stochastic models (Heston model, Merton jump-diffusion model), numerical methods (Monte Carlo simulation, finite difference method), and machine learning techniques. Through theoretical analysis and empirical comparisons, the study reveals the mathematical principles, applicability, and limitations of these models. Furthermore, the study discusses model optimization directions in the context of real financial markets, particularly for special cases such as China's A-share market. The research shows that the evolution of mathematical models has always balanced market incompleteness and computational efficiency. Future trends will focus on hybrid models integrating stochastic analysis and data science.

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This study investigates the factors influencing board game ownership using a comprehensive dataset from BoardGameGeek. By applying statistical techniques such as correlation analysis, Lasso regression, Random Forest, and a Gradient Boosting Model (GBM), the paper explores how variables such as user ratings, complexity, playtime, age rating, and year of publication affect ownership. The analysis reveals that user engagement metrics—particularly the number of users who rated a game—are the strongest predictors of ownership. However, when visibility metrics are excluded, intrinsic attributes like game complexity, playtime, and accessibility (minimum age) emerge as significant drivers. The Gradient Boosting Model, trained with log-scaled ownership values, achieves a high score of 0.975 on the validation set, confirming its strong predictive performance. These findings provide actionable insights for developers, highlighting the importance of both marketing efforts and thoughtful design choices. The study contributes to the understanding of consumer behavior in the board game industry and offers a data-driven framework for optimizing game appeal and commercial success.

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