The object ive was to determine the ef fect iveness of a regular prescribed burning programfor reducing tree mortal i ty in southern pine forests burned by wi ldf ire . This s tudy was conducted on publ ic and industry lands in northeast Florida. On the Osceola National Forest, mean mortality was 3.5% in natural stands and 43% in plantations two growing seasons after u June 1998 wildfire. Burn ...

Let P be a graph property which is preserved by removal of edges, and consider the random graph process that starts with the empty n-vertex graph and then adds edges one-by-one, each chosen uniformly at random subject to the constraint that P is not violated. These types of random processes have been the subject of extensive research over the last 20 years, having striking applications in extre...

A 2-matching in an undirected graph G = (V G,EG) is a function x : EG → {0, 1, 2} such that for each node v ∈ V G the sum of values x(e) on all edges e incident to v does not exceed 2. The size of x is the sum ∑ e x(e). If {e ∈ EG | x(e) 6= 0} contains no triangles then x is called triangle-free. Cornuéjols and Pulleyblank devised a combinatorial O(mn)-algorithm that finds a triangle free 2-mat...

We prove some sufficient conditions for a directed graph to have the property of a conjecture of J. (1982): "Every directed graph contains an independent set which meets every longest directed path". Let G be a directed graph, and denote by V(G) its vertex-set, by A(G) its arc-set, X(G) denotes its chromatic number, and A(G) the length of the longest directed path. Independently, B. Roy and T. ...

We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(ĝln). We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand–Tsetlin character (or q-character). We also apply the qu...

We consider moments of the normalized volume of a symmetric or nonsymmetric random polytope in a fixed symmetric convex body. We investigate for which bodies these moments are extremized, and calculate exact values in some of the extreme cases. We show that these moments are maximized among planar convex bodies by parallelograms.

Let 7(G) denote the minimum cardinality of a dominating set of a graph G = (V,E). A longstanding upper bound for 7(G) is attributed to Berge: For any graph G with n vertices and maximum degree A(G), 7(G) <~ n A(G). We eharacterise connected bipartite graphs which achieve this upper bound. For an arbitrary graph G we furnish two conditions which are necessary if 7(G) + A(G) = n and are sufficien...