Our main observation concerns closed geodesics on surfaces M with a smooth Finsler metric, i.e. a function F : TM → [0,∞) which is a norm on each tangent space TpM , p ∈ M , which is smooth outside of the zero section in TM , and which is strictly convex in the sense that Hess(F ) is positive definite on TpM \ {0}. One calls a Finsler metric F symmetric if F (p,−v) = F (p, v) for all v ∈ TpM . ...

In 2009, Jonoska, Seeman and Wu showed that every graph admits a route for a DNA reporter strand, that is, a closed walk covering every edge either once or twice, in opposite directions if twice, and passing through each vertex in a particular way. This corresponds to showing that every graph has an edge-outer embedding, that is, an orientable embedding with some face that is incident with ever...

Achieving an admission control strategy for CoS networks covering both intra-domain and end-to-end operation is still an open issue. This paper discusses how AC can be carried out without adding significant complexity to the network control plane and proposes a distributed service-oriented AC model for these networks. The model only involves the network edge nodes leaving the network core uncha...

The spatial structure and phase velocity of tropopause disturbances localized around the subpolar jet in the Southern Hemisphere are investigated using 6-hourly European Centre for Medium-Range Weather Forecasts reanalysis data covering 15 yr (1979–93). The phase velocity and phase structure of the tropopause disturbances are in good agreement with those of an edge wave vertically trapped at th...

In this paper, we present a method for the numerical minimization of the Mumford–Shah functional that is based on the idea of topological asymptotic expansions. The basic idea is to cover the expected edge set with balls of radius ε > 0 and use the number of balls, multiplied with 2ε, as an estimate for the length of the edge set. We introduce a functional based on this idea and prove that it c...

Let us shortly remind the main constructions of works [1], [2], [4]. Let there be given the universal covering of an oriented three-dimensional manifold, considered as a simplicial complex, in which every simplex is mapped into the three-dimensional Euclidean space (so that the intersections of their images in R are possible). To each edge is assigned thus a Euclidean length, and each tetrahedr...

Let ν(G) denote the maximum number of edge-disjoint triangles in a graph G and τ(G) denote the minimum total weight of a fractional covering of its triangles by edges. Krivelevich proved that τ(G) ≤ 2ν(G) for every graph G. This is sharp, since for the complete graphK4 we have ν(K4) = 1 and τ (K4) = 2. We refine this result by showing that if a graph G has τ(G) ≥ 2ν(G) − x, then G contains ν(G)...

Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

Much uncertainty exists about the history of the Greenland Ice Sheet (GIS), particularly as to the frequency of extreme shelf edge glaciations. Because the last glaciation removed most of the record of earlier GIS extent on land and shelf exploration of the older GIS glacial record requires the use of deeper marine archives. Here we present seismic evidence for the frequency of extreme shelf ed...

We examine the general problem of covering graphs by graphs: given a graph G, a collection P of graphs each on at most p vertices, and an integer r, is there a collection C of subgraphs of G, each belonging to P , such that the removal of the graphs in C from G creates a graph none of whose components have more than r vertices? We can also require that the graphs in C be disjoint (forming a “ma...