The minimum cut problem (or mincut problem) is to find a cut of minimum cost. If all costs are 1 then the problem becomes the problem of finding a cut with as few edges as possible. Cuts are often defined in a different, not completely equivalent, way. Define a cutset to be a set of edges whose removal disconnects the graph into at least two connected components. Minimal cutsets (a minimal cuts...

Abstact: Let B be a Brownian motion in R d , d = 2; 3. A time t 2 0; 1] is called a cut time for B0; 1] if B0; t) \ B(t; 1] = ;: We show that the Hausdorr dimension of the set of cut times equals 1 ? , where = d is the intersection exponent. The theorem, combined with known estimates on 3 , shows that the percolation dimension of Brownian motion (the minimal Hausdorr dimension of a subpath of a...

Since their introduction in form of a canonical representation logical functions, the Binary Decision Diagrams (BDDs) gained wide acceptance numerous industrial applications. This paper summarizes properties BDD Minimal Cut Sets (MCS) Fault Tree (FT) models most typically encountered nuclear energetics. sets from MCS are defined as paths top node to terminal nodes BDD, on which quantitative and...

investigation of reliability characteristics under fuzzy environments is proposed in this paper. fuzzy weibull distribution and lifetimes of components are using it described. formulas of a fuzzy reliability function, fuzzy hazard function and their α-cut set are presented. furthermore, the fuzzy functions of series systems and parallel systems are discussed, respectively. finally, some numeric...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.