Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem

We apply the symmetry reduction method of Roberts to numerically analyze the linear stability of a one-parameter family of symmetric periodic orbits with regularizable simultaneous binary collisions in the planar pairwise symmetric four-body problem with a mass $m\in(0,1]$ as the parameter. This reduces the linear stability analysis to the computation of two eigenvalues of a $3\times 3$ matrix for each $m\in(0,1]$ obtained from numerical integration of the linearized regularized equations along only the first one-eighth of each regularized periodic orbit. The results are that the family of symmetric periodic orbits with regularizable simultaneous binary collisions changes its linear stability type several times as $m$ varies over $(0,1]$, with linear instability for $m$ close or equal to 0.01, and linear stability for $m$ close or equal to 1.Comment: 13 pages, 1 figur

Vegetation NDVI Linked to Temperature and Precipitation in the Upper Catchments of Yellow River

Vegetation in the upper catchment of Yellow River is critical for the ecological stability of the whole watershed. The dominant vegetation cover types in this region are grassland and forest, which can strongly influence the eco-environmental status of the whole watershed. The normalized difference vegetation index (NDVI) for grassland and forest has been calculated and its daily correlation models were deduced by Moderate Resolution Imaging Spectroradiometer products on 12 dates in 2000, 2003, and 2006. The responses of the NDVI values with the inter-annual grassland and forest to three climatic indices (i.e., yearly precipitation and highest and lowest temperature) were analyzed showing that, except for the lowest temperature, the yearly precipitation and highest temperature had close correlations with the NDVI values of the two vegetation communities. The value of correlation coefficients ranged from 0.815 to 0.951 (p <0.01). Furthermore, the interactions of NDVI values of vegetation with the climatic indicators at monthly interval were analyzed. The NDVI of vegetation and three climatic indices had strong positive correlations (larger than 0.733, p <0.01). The monthly correlations also provided the threshold values for the three climatic indictors, to be used for simulating vegetation growth grassland under different climate features, which is essential for the assessment of the vegetation growth and for regional environmental management

Too proactive to switch off: When taking charge drains resources and impairs detachment

Although proactive behavior is an important determinant of individual work performance, its consequences for employee well-being and other personal outcomes have been largely neglected. In this study, we adopted a within-person perspective to investigate how taking charge behavior (a form of proactivity) affects employees' life outside of work by examining when and how it impacts on their ability to detach and recover from work. Drawing upon resource drain theory, we hypothesized that taking charge has the potential to undermine the process of detachment and recovery from work by draining personal resources. However, based on self-determination theory, we identified autonomous motivation as an essential boundary condition, such that the negative effects of taking charge on detachment and recovery via resource drain occur only when daily autonomous motivation is low. We tested this model on a sample of 77 managers, who provided daily survey data 3 times per day over 5 consecutive working days. Our analyses showed that daily taking charge behavior was negatively related to detachment in the evening, via resource drain, only on days in which people reported low autonomous motivation at work. However, this conditional effect of taking charge did not reach through to next morning recovery. No negative effects of daily taking charge on detachment were observed when people had high autonomous motivation. Overall, these findings suggest that, under some motivational conditions, proactivity can consume resources and interfere with the process of detachment. We offer practical advice for how organizations might encourage proactive behavior while minimizing its drawbacks. (PsycInfo Database Record (c) 2021 APA, all rights reserved)