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By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price. This is the case because imposing gauge symmetry implies the appearance of an additional field, which corresponds to the stochastic volatility. The gauge symmetry then imposes some constraints over the free parameters of the Merton-Garman Hamiltonian. Finally, we analyze how the stochastic volatility gets massive dynamically via Higgs mechanism.
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We demonstrate that black hole evaporation can be modeled as a process where one symmetry of the system is spontaneously broken continuously. We then identify three free parameters of the system. The sign of one of the free parameters governs whether the particles emitted by the black hole are fermions or bosons. The present model explains why the black hole evaporation process is so universal. Interestingly, this universality emerges naturally inside certain modifications of gravity.
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By using both, the weak-value formulation as well as the standard probabilistic approach, we analyze the Hardy's experiment introducing a complex and dimensionless parameter ($\epsilon$) which eliminates the assumption of complete annihilation when both, the electron and the positron departing from a common origin, cross the intersection point $P$. We then find that the paradox does not exist for all the possible values taken by the parameter. The apparent paradox only appears when $\epsilon=1$; however, even in this case we can interpret this result as a natural consequence of the fact that the particles can cross the point $P$, but at different times due to a natural consequence of the energy-time uncertainty principle.
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In any physical system, when we move from short to large scales, new spacetime symmetries emerge which help us to simplify the dynamics of the system. In this letter we demonstrate that certain variations on the symmetries of general relativity at large scales generate the effects equivalent to dark matter ones. In particular, we reproduce the Tully-Fisher law, consistent with the predictions proposed by MOND. Additionally, we demonstrate that the dark matter effects derived in this way are consistent with the predictions suggested by MOND, without modifying gravity.
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Teacher turnover is a global issue that has not received much research attention in Macau despite studies indicating that teachers in the region experience high levels of stress and burnout. Given that private school teachers account for a significant proportion (88.6%) of the non-tertiary education system in Macau, this qualitative study focused on this specific group who voluntarily resigned from their positions. Through in-depth interviews with 13 former teachers from different kindergartens, primary, and secondary schools, the research identified 50 reasons categorized into 15 factors under three categories. Although schoolrelated factors account for the most, personal reasons were found to be the primary driver. The findings of the study highlight the complex nature of teacher turnover which can be attributed to both single and multiple factors, in both direct and indirect forms. The factors could also interplay in both unidirectional and mutual relationships. A conceptual framework for teacher turnover in Macau was developed to address the 15 contributing factors and the complex interplay of these factors. This study could fill the gap in the literature and serve as a valuable resource for policymakers and school leaders seeking to reduce teacher attrition rates in the region
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The present study aimed to analyse the differences in the internalising problems (anxiety, depression, somatic complaints), assessed by different informants (teachers and students), according to the level of academic achievement and school adaptation level in secondary students. Furthermore, we examine the gender difference in the level of internalising symptoms. Finally, we analyzed the differences between teacher-rated and adolescents' self-reported internalising symptoms. The Achenbach System of Empirically Based Assessment (ASEBA) was used for collecting informants’ data. The sample consisted of 882 secondary students (349 males and 473 females), while 50 came from public schools and 772 from private schools. No significant differences are found in internalising problems according to the level of academic achievement from both teachers’ and students’ perspectives. Generally, students who are well-adapted to the school context have the least symptoms of internalising problems compared to average and less-adapted groups from the teachers' perspective. In addition, from students’ perspectives, adolescent females present more internalising problems than males. Finally, teachers rated fewer internalising problems when compared to the students. In conclusion, the low level of awareness of teachers towards the internalising problems of students arouse attention. It is suggested that teachers should attend professional development programs in order to address to students’ internalising problems
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