the largest class of algebraic hyper structures satisfying the module like axioms is the v h -module. in this paper, we consider the category of v h -modules and prove that the direct limit alwaysexists in this category. direct limits are defined by a universal property, and so are unique. the mostpowerful tool in order to obtain a module from a given v h - module is the quotient out procedure....

This paper proposes a hybrid switching technique for a domestic PV system with AC-module architecture. In this PV system, independent control of PV modules, which are directly connected to DC terminals of a single-phase cascaded multilevel inverter, makes module-level MPPT possible to extract maximum available solar energy, especially in partial shading conditions. As one of the main contributi...

Homotopy categorical groups of any pointed space are defined via the fundamental groupoid of iterated loop spaces. This notion allows, paralleling the group case, to introduce the notion of K-categorical groups KiR of any ring R. We also show the existence of a fundamental categorical crossed module associated to any fibre homotopy sequence and then, K1R and K2R are characterized, respectively,...

The largest class of algebraic hyper structures satisfying the module like axioms is the v H module. In this paper, we consider the category of v H -modules and prove that the direct limit always exists in this category. Direct limits are defined by a universal property, and so are unique. The most powerful tool in order to obtain a module from a given v H module is the quotient out procedure. ...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.