A new family of linearly implicit fractional step methods is proposed for the efficient numerical solution of a class of nonlinear time-dependent reaction-diffusion equations. By using the method of lines, the original problem is first discretized in space via a mimetic finite difference technique. The resulting differential system of stiff nonlinear equations is locally decomposed by suitable ...

Problem 1. this needs to be fleshed out We will use 3 arrays A, B, and C. A will represent that actual array and hold the stored items in their stored positions. Arrays B and C will act as “checks” for which entries of A are truly initialized. B will contain a list, built up sequentially from position 0, of all entries of A that have been filled. We use a “length” variable i to keep track of th...

As usual, we are only guaranteed the attacks find a key consistent with the input-output examples rather than finding the target key itself, but empirically we estimate that with three input-output examples the target key will be the only one consistent with the input-output examples and hence will be the one found by the attack. The same attacks using only two input-output examples will also t...

We will remove vertices from a given graph G of treewidth k in a good elimination ordering, and we can assume w.l.o.g. that G is connected. Some cliques in a current graph will be active cliques. For each active clique C and for each subset S of vertices in C, we store information if there exists a vertex cover of the original graph G that chooses exactly vertices in S out of the vertices in C....

System splitting problem (SS problem) is to determine proper splitting points (or called splitting strategies) to split the entire interconnected transmission network into islands ensuring generation/load balance and satisfaction of transmission capacity constraints when islanding operation of system is unavoidable. For a large-scale power system, its SS problem is very complicated in general b...

n+k Let 23 be a hornotopy (n+k)-sphere and p : G)< ~E~-2] a smooth semi-free action of a finite group G on 23 with fixed-point set a manifold F n of dimension no A decomposition of 23 into two G-invariant disks will be called a splitting of the action and the induced splitting of 2] G denoted F = FI<9 F 2. We ask whether every such action has a splitting with Hi(F1) ~Hi(F2) for i> 0 (these are ...

We consider aspects of vertex splitting and connectivity augmentation in hypergraphs. In the splitting problem we are given a hypergraph G = (V + s, E) in which s is only incident with edges of size two and asked to “split” s in such a way that we preserve the local-connectivity in the set V . We develop results that lead to a characterisation of the hypergraphs in which there is no such split....

Solution. In a finite connected graph with n ≥ 2 vertices, the domain for the vertex degrees is the set {1, 2, . . . , n − 1} since each vertex can be adjacent to at most all of the remaining n−1 vertices and the existence of a degree 0 vertex would violate the assumption that the graph be connected. Therefore, treating the n vertices as the pigeons and the n−1 possible degrees as the pigeonhol...