Higher dimensional Lax pairs of lower dimensional chaos and turbulence systems

In this letter, a definition of the higher dimensional Lax pair for a lower dimensional system which may be a chaotic system is given. A special concrete (2+1)-dimensional Lax pair for a general (1+1)-dimensional three order autonomous partial differential equation is studied. The result shows that any (1+1)-dimensional three order semi-linear autonomous system (no matter it is integrable or not) possesses infinitely many (2+1)-dimensional Lax pairs. Especially, every solution of the KdV equation and the Harry-Dym equation with their space variable being replaced by the field variable can be used to obtain a (2+1)-dimensional Lax pair of any three order (1+1)-dimensional semi-linear equation.Comment: 8 page

Examining the Relationships Among Mindfulness, Disability, Social Support, and Stress in Emerging Adults

College students, as part of the broader population of emerging adults, are thought to be particularly vulnerable to stress compared to other age groups as they transition through adolescence into adulthood. Various internal and external factors including mindfulness, disability, and social support play an important role in students’ stress levels. The relationships among these three predictor variables and stress were analyzed in a sample of 1,049 individuals between the ages of 18-29. Responses were obtained from the dataset “Emerging Adulthood Measured at Multiple Institutions 2: The Data” (Grahe et al., 2018). The data were cleaned in Python and analyzed in SPSS using multiple regression analyses. Higher perceived levels of mindfulness and social support were significant predictors of less stress in students, while a higher perceived level of disability was a significant predictor of more stress. The combined regression model showed that mindfulness, disability, and social support accounted for a significant amount of the variance in distress. Determinants of stress are multifactorial; identification and evaluation of variables that account for a significant amount of the variance in stress within a vulnerable population can contribute to the development of effective stress management techniques