We generalize the Hermite-Korkin-Zolotarev (HKZ) reduction theory of positive definite quadratic forms over $\mathbb Q$ and its balanced version introduced recently by Beli-Chan-Icaza-Liu to a totally real number field $K$. apply HKZ-reduction study growth

Let  be a local Cohen-Macaulay ring with infinite residue field,  an Cohen - Macaulay module and  an ideal of  Consider  and , respectively, the Rees Algebra and associated graded ring of , and denote by  the analytic spread of  Burch’s inequality says that  and equality holds if  is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of  as  In this paper we ...

In this paper, a new cascaded multilevel inverter by capability of increasing the number of output voltage levels with reduced number of power switches is proposed. The proposed topology consists of series connection of a number of proposed basic multilevel units. In order to generate all voltage levels at the output, five different algorithms are proposed to determine the magnitude of DC volta...