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SUMMARYAn adaptive refinement/derefinement algorithm of nested meshes is presented. Some definitions are introduced. The main properties of the derefinement algorithm are remarked upon and its efficiency is shown through two numerical examples: a time-dependent convection-diffusion problem with dominant convection and a quasistationary problem.

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In this paper, we apply the binomial, k-binomial, rising, and falling transforms to the k-Fibonacci sequence. Many formulas relating the so obtained new sequences are presented and proved. Finally, we define and find the inverse transforms of the sequences previously obtained.

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