What costs is it worth incurring to avoid the risk of climate change? People rarely think of this as a question amenable to a precise answer. Yet an answer can be calculated: it depends on the following four parameters (at least). These are (1) the probability distribution of the effects of...

In this paper it is shown how a general two-sided orthant probability for a quadrivariate normal distribution can be evaluated by a one-dimensional numerical integral calculation. The quadrivariate normal distribution can have any covariance matrix and any mean vector. This affords a practical...

A two-step infinite α-cuts fuzzy linear programming (TSIFP) method is developed in this study. The introduction of infinite α-cuts to conventional fuzzy linear programming frameworks makes it possible to generate more reliable optimal results than conventional fuzzy linear programming, where...

Eutrophication of surface water is a worldwide concern. Sediments may play an important role in buffering phosphorus (P) concentration in the overlying water column. However, information on the spatial variation of sediment P availability as affected by agricultural water discharge and...

In the past decade, the development of nanoelectronics and nano-optics has attracted much interest in surface nanostructuring of semiconductor materials. The irradiation of a microlens array by a laser beam generates many focused light spots, which can act as a direct writing tool on...