‎we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel‎, ‎that is‎, ‎every simple right $r$-module has a flat $b$-cover‎. ‎we give some properties of such rings along with examples‎. ‎we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...

‎We call a ring $R$ right generalized semiperfect if every simple right $R$-module is an epimorphic image of a flat right $R$-module with small kernel‎, ‎that is‎, ‎every simple right $R$-module has a flat $B$-cover‎. ‎We give some properties of such rings along with examples‎. ‎We introduce flat strong covers as flat covers which are also flat $B$-covers and give characterizations of $A$-perfe...

A prototype concentrating photovoltaic (CPV) module was designed and constructed with a low concentrating dielectric compound parabolic concentrator (DiACPC) for outdoor characterisation. The designed concentrator has acceptance half angles of 0 & 55 with a concentration ratio of 2.8. This concentrator design is suitable for building facade integration in higher latitude (>55 ) locations. A sma...

This paper is a sequel of [ER]. Specifically, letW be a Coxeter group, generated by si, i ∈ I. Then, following [ER], one can define a new deformation A+ = A+(W ) of the group algebra Z[W+] of the group W+ of even elements in W . This deformation is an algebra over the ring R = Z[t±1 ijk] = Z[T] of regular functions on a certain torus T of deformation parameters. The main result of [ER] implies ...

let r be a right gf-closed ring with finite left and right gorenstein global dimension. we prove that if i is an ideal of r such that r/i is a semi-simple ring, then the gorensntein flat dimensnion of r/i as a right r-module and the gorensntein injective dimensnnion of r/i as a left r-module are identical. in particular, we show that for a simple module s over a commutative gorensntein ring r, ...

Let R be a right GF-closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, ...

Because of the associativity of fusion products ⊠, the above hypothesis is equivalent to the condition that for each irreducible module W , there is an irreducible module W̃ such that HomV (W̃ ⊠ W,V ) 6= 0. In the previous paper [6], we have introduced a concept of ”Semi-Rigidity” and then proved that if W is semi-rigid, then W is flat for the fusion products ⊠, that is, 0 → W ⊠ A → W ⊠ B → W ⊠ C...

Let $R$ be a commutative ring. An $R$-module $M$ is called semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ $\GV$-torsion for any finitely generated ideal $I$. In this article, we show that the class of modules covering class. Moreover, introduce dimensions $R$-modules and $sr$-$w$-weak global ring $R$. Utilizing these notions, give some homological characterizations $\WQ$-rings $Q_0$-\PvMR s.

‎Let $C$ be a semidualizing module‎. ‎We first investigate the properties of‎ ‎finitely generated $G_C$-projective modules‎. ‎Then‎, ‎relative to $C$‎, ‎we introduce and study the rings over which‎ ‎every submodule of a projective (flat) module is $G_C$-projective (flat)‎, ‎which we call $C$-Gorenstein (semi)hereditary rings‎. ‎It is proved that every $C$-Gorenstein hereditary ring is both cohe...

sheet metal components design and manufacture need a great deal of experience and know-how. strip layout design is usually done with trial and error until best design for strip layout is finally achieved. knowledge for the system is formulated from plasticity theories, experimental results, and the empirical knowledge of field experts. in this paper, an algorithm which can automatically design ...