Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper we compute powers of the genearlized mixed product ideals and show that Lk  have a linear resolution if and only if Ik have a linear resolution for all k. We also introduce the generalized mixed polymatroidal ideals and prove that powers and monomial localizations of a generalized mixed polymatroidal ideal...

In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexi...

Curado and Rego-Monteiro introduced in [2] a new algebraic structure generalizing the Heisenberg algebra and containing also the q-deformed oscillator as a particular case. This algebra, called generalized Heisenberg algebra, depends on an analytical function f and the eigenvalues αn of the Hamiltonian are given by the one-step recurrence αn+1 = f(αn). This structure has been used in different ...