This paper introduces a novel approach to conventional Photovoltaic (PV) modules that involves regulating the internal connections of PV strings (or submodules) using set switches isolate shaded submodules while leaving unshaded unaffected. By extending connection types include parallel or series via an external circuit, along with switches, output voltage and current can be adjusted without re...

Let N be a finitely generated module over a Noetherian local ring (R,m). We give criteria for the height of the order ideal N∗(x) of an element x ∈ N to be bounded by the rank of N . The Generalized Principal Ideal Theorem of Bruns, Eisenbud and Evans says that this inequality always holds if x ∈ mN . We show that the inequality even holds if the hypothesis becomes true after first extending sc...

The abilities of modern computers has provided immense power and flexibility for modeling things in the virtual realm. Yet the robotic systems through which computers can interact with the physical world are far more limited. Robots are often designed for limited, specific tasks with little chance of extending to different abilities. Self-reconfigurable robots are systems composed of many small...

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

we consider the class $mathfrak m$ of $bf r$--modules where $bf r$ is an associative ring. let $a$ be a module over a group ring $bf r$$g$, $g$ be a group and let $mathfrak l(g)$ be the set of all proper subgroups of $g$. we suppose that if $h in mathfrak l(g)$ then $a/c_{a}(h)$ belongs to $mathfrak m$. we investigate an $bf r$$g$--module $a$ such that $g not = g'$, $c_{g}(a) = 1$. we stud...

Problem statement: Algebraic K-theory of projective modules over commutative rings were introduced by Bass and central simple superalgebras, supercommutative super-rings were introduced by many researchers such as Knus, Racine and Zelmanov. In this research, we classified the projective supermodules over (torsion free) supercommutative super-rings and through out this study we forced our selves...

We introduce “virtual” crystals of the affine types g = D (2) n+1, A (2) 2n and C (1) n by naturally extending embeddings of crystals of types Bn and Cn into crystals of type A2n−1. Conjecturally, these virtual crystals are the crystal bases of finite dimensional U ′ q (g)-modules associated with multiples of fundamental weights. We provide evidence and in some cases proofs of this conjecture. ...

The combination of lithium ion battery (LIB) and organic (polymer) solar cells is expected to deliver versatile self-rechargeable portable energy sources, but less attention has been paid to the charging characteristics of LIB-using polymer solar cells. Here we demonstrate that the LIB packs, which were prepared by using lithium cobalt oxide (LiCoO2) and graphite as a cathode and an anode, resp...

This paper is a personal look at some issues in the representation theory of Lie groups having to do with the role of commutative hypergroups, bi-modules, and the construction of representations. We begin by considering Frobenius’ original approach to the character theory of a finite group and extending it to the Lie group setting, and then introduce bi-modules as objects intermediate between c...

In this article, we look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the non-homogeneous m-coprimary case in standard graded rings. Although our result does not depend upon dimension, the primary application is based on results known in dimension 2 due to the recent work of H. Brenner...