Dobinski-type relations: Some properties and physical applications

We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the Kerr Hamiltonian.Comment: 7 pages, 1 figur

Differences in Human versus Lightning Fires between Urban and Rural Areas of the Boreal Forest in Interior Alaska

In western North America, the carbon-rich boreal forest is experiencing warmer temperatures, drier conditions and larger and more frequent wildfires. However, the fire regime is also affected by direct human activities through suppression, ignition, and land use changes. Models are important predictive tools for understanding future conditions but they are based on regional generalizations of wildfire behavior and weather that do not adequately account for the complexity of human–fire interactions. To achieve a better understanding of the intensity of human influence on fires in this sparsely populated area and to quantify differences between human and lightning fires, we analyzed fires by both ignition types in regard to human proximity in urban (the Fairbanks subregion) and rural areas of interior Alaska using spatial (Geographic Information Systems) and quantitative analysis methods. We found substantial differences in drivers of wildfire: while increases in fire ignitions and area burned were caused by lightning in rural interior Alaska, in the Fairbanks subregion these increases were due to human fires, especially in the wildland urban interface. Lightning fires are starting earlier and fires are burning longer, which is much more pronounced in the Fairbanks subregion than in rural areas. Human fires differed from lightning fires in several ways: they started closer to settlements and highways, burned for a shorter duration, were concentrated in the Fairbanks subregion, and often occurred outside the brief seasonal window for lightning fires. This study provides important insights that improve our understanding of the direct human influence on recently observed changes in wildfire regime with implications for both fire modeling and fire management