Pollutant Ground Concentrations of Nonneutrally Buoyant Particles

A methodology is suggested for the estimation of the mass density and the cumulative ground deposition of a nonvolatile, nonneutrally buoyant, air pollutant (liquid or solid) released from a polluted column (following an explosion caused during routine operation in, e.g., the chemical industry or due to any kind of hostile act) and deposited on the ground via gravitational settling. In many cases, the deposited mass due to gravitational settling constitutes a significant fraction of the original inventory released from the source. Implementation of the methodology in preliminary risk assessments can serve as an efficient tool for emergency planning for both immediate and long‐term measures such as evacuation and decontamination. The methodology considers, inter alia, an estimation of the critical particle diameter, particle size, and mass distributions along the polluted column. This methodology was developed to apply in rural regions since proper application of relevant meteorological input data can be accomplished mainly for such areas.     

Lawler’s minmax cost problem under uncertainty

The well-known \(O(n^2)\) minmax cost algorithm of Lawler (Manag Sci 19(5):544–546, 1973) was developed to minimize the maximum cost of jobs processed by a single machine under precedence constraints. We first develop a fast updating algorithm to obtain optimal solutions for two neighboring instances. This method will be used throughout this article. Then we consider job cost functions that depend on the completion time and on one or more additional numerical parameters. The parameters are uncertain and take values from given intervals. Under the uncertainty, we apply the minmax regret criterion for choosing a solution. We generalize results by Brauner et al. (J Sched, 2015) for decomposable cost functions with deterministic processing times and a single uncertain parameter to general cost functions. We describe different conditions, under which minmax regret solutions can be obtained with the time complexity \(O(n^3)\) or \(O(n^2)\). Then the updating algorithm is applied to the lateness model by Kasperski (Oper Res Lett 33:431–436, 2005) where both the processing time and the due date of each job are uncertain. The original \(O(n^4)\) running time is improved to the time complexity \(O(n^3)\). Finally, we extend the cost functions with a single uncertain parameter to those with a vector of additional uncertain parameters, improve one of the complexity results by Volgenant and Duin (Comput Oper Res 37:909–915, 2010) and solve some new problems.     

Divorce in sub‐Saharan Africa: Are Unions Becoming Less Stable?

Divorce is one of the main drivers of family instability in sub‐Saharan Africa. Using data from 101 Demographic and Health Surveys and novel estimation techniques, we 1) provide the first systematic estimates of divorce across 33 countries; 2) assess trends in divorce in 20 countries; and 3) investigate the key country‐level correlates of divorce both across and within countries. Despite considerable geographic variation, our estimates show that divorce is common in most countries. Contrary to expectations, however, we find no evidence that divorce is increasing. Instead, divorce has been either stable or declining in recent decades. We show that socioeconomic factors associated with industrialization have countervailing effects on divorce. Urbanization and female employment are associated with higher levels of divorce, while age at first marriage and female education correspond to lower rates. These findings have implications for current and future family dynamics in sub‐Saharan Africa.