We consider a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this family of meta-Fibonacci sequences and two families of related sequences we derive ordinary generating functions and recurrence relations. Included in these fami...

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in t...

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[Abstract] In this paper, we introduce a new type of high order shock capturing schemes – uniform weighted compact and non-compact scheme (UWCNC) or simply XJL scheme developed by Xie, Jiang and Liu. This new scheme is based on the feature of discrete data sets instead of the physics. The fundamental task of CFD is to provide an accurate approximation of derivatives for a given discrete data se...

We show the existence of a compact Kähler manifold which does not fit in proper flat family over an irreducible base with one projective (possibly singular) fiber. also give topological version this statement. This strengthens our earlier counterexamples to Kodaira algebraic approximation problem.