In this work, we get a combinatorial characterization for maximal generalized outerplanar graphs (mgo graphs). This result yields a recursive algorithm testing whether a graph is a mgo graph or not.
The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical comparisons...
Let V be a finite set and 𝓜 a collection of subsets of V. Then 𝓜 is an alignment of V if and only if 𝓜 is closed under taking intersections and contains both V and the empty set. If 𝓜 is an alignment of V, then the elements of 𝓜 are called convex sets and the pair (V,𝓜 ) is called an alignment or a convexity. If S ⊆ V, then the convex hull of S is the smallest convex set that contains S. Suppose X ∈ ℳ. Then x ∈ X is an extreme point for X if X∖{x} ∈ ℳ. A convex geometry on a finite set is...
The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical...
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