in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

Grade 1 open spiral fracture of left tibia in a 1.5 year-old horse was treated using a combination of 4.5 mm locking compression plate (LCP) and a dynamic compression plate applied in a neutralization manner. The open wound was managed postoperatively by regular dressing and lavage. Radiograph at 24 days post-treatment revealed callus formation and at two months complete bridging callus was obs...

let $r$ be an associative ring with identity. an element $x in r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if there exist $g in g$, $n in mathbb{z}$ and $r in r$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). a ring $r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if every element of $r$ is $mathbb{z}g$-regular (resp. strongly $...

We propose a natural subclass of regular languages (Alphabetic Pattern Constraints, APC) which is effectively closed under permutation rewriting, i.e., under iterative application of rules of the form ab ! ba. It is well-known that regular languages do not have this closure property, in general. Our result can be applied for example to regular model checking , for verifying properties of parame...

Graph theory and its applications attract several researchers from different areas of research. It is used to model wide range systems, for example in biological system studying chaotic systems. Decomposition complex graphs into simple small very helpful study that A complete classification given circulant degree 5 allow an Orthogonal Double Cover by some graphs. Whenever such a cover exists, o...