A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm held the record by requiring just 4n log2 n−6n+8 arithmetic operations on real numbers for a size-n DFT, and was widely believed to be the best possible. Re...

GenVoca is a methodology and technology for generating product-lines, building variants of the same program. The primitive components from which applications are constructed are refinements or layers, which are modules that implement a feature that many programs of a product-line can share. Unlike conventional components (e.g., COM, CORBA, EJB), a layer encapsulates fragments of multiple classe...

This is an expository paper devoted to the Morse index of Chaperon’s generating families of Hamiltonian diffeomorphisms. After reviewing the construction of such generating families, we present Bott’s iteration theory in this setting: we study how the Morse index of a critical point corresponding to an iterated periodic orbit depends on the order of iteration of the orbit. We also investigate t...

The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. Such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. Strong covers for facets of Knapsack ploytope has been developed in the first pa...