We study the one-dimensional conservation law. We use a characteristic surface to define a class of functions, within which the integral version of the conservation law is solved in a simple and direct way. We develop a simple algorithm for computing the unique solution. The method uses the equal-area principle and gives the solution for any given time directly.

No abstract

We study the one-dimensional conservation law. We use a characteristic surface to define a class of functions, within which the integral version of the conservation law is solved in a simple and direct way. A simple algorithm for computing the unique solution is developed. The method uses the equal-area principle and yields the solution for any given time directly.2010 Mathematics subject classification: primary 35L65; secondary 65M25.

The article presents the results of precipitation and aerosol (PM10) data analyses in Slovenia. Analyses of rainfall data for some areas of Slovenia, such as the Ljubljana Basin, Zasavje, Šalek Valley, Celje Basin, and the coastal area, suggest that rain on the weekend is more frequent than on weekdays; nevertheless, these deviations are not statistically significant. A comparison of three separate decades showed that the pattern of weekly rainfall in the 21st century is different than that in the last period of the 20th century. The weekly cycle of PM10 for the considered stations is quite similar to that of some of the more contaminated regions of the world. Furthermore, the connection between PM10 and precipitation in most of the analyzed cases was statistically significant.