Global perinormality in a generalized D + M construction

Abstract

An integral domain R is perinormal if every local going-down overring is a localization of R and globally perinormal if every going-down overring is a localization of R. In this paper, I introduce notions of graded perinormal and graded globally perinormal domains and show that many results obtained for perinormal and globally perinormal domains have graded analogs. I also give some results for descent of properties between a graded domain and its 0th graded component.

Weather, Vol. 79, no. 6, June 2024, pp. 174‐204

“…This function assumes damage only occurs when the value of the given meteorological variable exceeds u X . For wind gust speeds the threshold u X = 20ms −1 is often used, however Klawa and Ulbrich (2003) note this threshold may be Box 1. Definition of Aggregate Severity Index (ASI) Suppose that N storms impact a given location over a specified time period, and let {X 1 , X 2 , …, X N } be the values of a meteorological hazard variable (e.g.…”

“…Such functions are often designed to be well correlated with insured losses. For example, Klawa and Ulbrich (2003), and many subsequent studies, have represented wind storm severity using the conceptual loss function of form with k = 3 and where threshold u X is chosen to be high (e.g. 20ms −1 or a local high percentile of near surface instantaneous wind gusts).…”

“…As a result, use of percentile based thresholds better reflects the climatology of regions. The severity index (SI) used by Klawa and Ulbrich (2003) used the 98th percentile of wind gust speeds alongside the population of an area. This study will use different threshold combinations and only consider meteorological variables for our SIs to focus only on the impact of the hazard.…”

“…This study will use different threshold combinations and only consider meteorological variables for our SIs to focus only on the impact of the hazard. While introducing exposure can improve a SI (Klawa and Ulbrich, 2003), this study chooses to focus on the relationships between hazards.…”

“…Correlation is more positive over the ocean and more negative over land. As 20ms −1 is a widely used wind threshold (Klawa and Ulbrich, 2003;Hillier and Dixon, 2020), the existence of negative correlation is important for the consideration of compound hazards. Regional patterns of correlation can be observed in Figure 5(c).…”