Thermal treatment of supersaturated Ti1!xAlxN films (x " 0.67) with a dominant ternary cubic-phase were performed in the 700– 1000 !C range. Grazing incidence X-ray diffraction (GIXRD) shows that, for annealing temperatures up to 800 !C, the film structure undergoes the formation of coherent cubic AlN (c-AlN) and TiN (c-TiN) nanocrystallites via spinodal decomposition and, at higher temperature...

‎A tree containing exactly two non-pendant vertices is called a double-star‎. ‎Let $k_1$ and $k_2$ be two positive integers‎. ‎The double-star with degree sequence $(k_1+1‎, ‎k_2+1‎, ‎1‎, ‎ldots‎, ‎1)$ is denoted by $S_{k_1‎, ‎k_2}$‎. ‎It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching‎. ‎In this paper‎, ‎we study the $S_{1,2}$-decomposit...

We propose a new filtering algorithm for the cumulative constraint. It applies the Edge-Finding, the Extended-Edge-Finding and the Time-Tabling rules in O(kn logn) where k is the number of distinct task heights. By a proper use of tasks decomposition, it enforces the Time-Tabling rule and the Time-Table Extended-Edge-Finding rule. Thus our algorithm improves upon the best known Extended-Edge-Fi...

In 2006 Barát and Thomassen conjectured that every planar 4-edge-connected 4-regular simple graph of size divisible by three admits a claw-decomposition. Later, Lai (2007) disproved this conjecture family graphs with edge-connectivity 4 which the smallest one contains 24 vertices. note, we first give smaller counterexample having only 18 vertices next construct 4-connected essentially 6-edge-co...

In 1994 S. McGuinness showed that any greedy clique decomposition of an n-vertex graph has at most ⌊n2/4⌋ cliques (The greedy clique decomposition of a graph, J. Graph Theory 18 (1994) 427-430), where a clique decomposition means a clique partition of the edge set and a greedy clique decomposition of a graph is obtained by removing maximal cliques from a graph one by one until the graph is empt...