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...

We construct orthonormal bases compatible with bi-variate homogeneous $$\alpha $$ -modulation spaces and the associated of Triebel–Lizorkin type. The construction is based on generating a separable -covering using carefully selected tensor products univariate brushlet functions regard to this covering. show that systems form an unconditional for -spaces

We present a new algorithm for exact two-level logic optimization. It diiers from the classical approach; rather than generating the set of all prime implicants of a function, and then deriving a covering problem, we derive the covering problem directly and implicitly , and then generate only those primes involved in the covering problem. We represent a set of primes by the cube of their inters...

Generating functions have long been used to analyze properties of sequences of numbers. In this note, we use generating functions to analyze a class of combinatorial objects, called interconnection networks. In particular, we prove that two families of interconnection networks are isomorphic by showing that the corresponding generating functions are isomorphic.

In this work, we introduce a novel network synthesis model that can generate families of evolutionarily related synthetic protein-protein interaction (PPI) networks. Given an ancestral network, the proposed model generates the network family according to a hypothetical phylogenetic tree, where the descendant networks are obtained through duplication and divergence of their ancestors, followed b...

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomialpositivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include, for example, genera...

Finding suitable non-supersingular elliptic curves becomes an important issue for the growing area of pairing-based cryptosystems. For this purpose, many methods have been proposed when embedding degree k and cofactor h are taken different values. In this paper we propose a new method to find pairing-friendly elliptic curves without restrictions on embedding degree k and cofactor h. We propose ...

Generating families of linear models from nonlinear parameter-dependent equations requires explicit analytical characterization of the equilibrium surface. Doing so in terms of the original system parameters is generally not possible. Introducing an alternative parameterization, we propose an efficient method for computing local linear parameter-dependent families. Although local, these familie...