In this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over Noetherian rings are proved. More...

desired physical form of cities has been noticeable since the beginning of urbanization, from old patterns of early civilizations to the latest urbanism’s theories, which offered to build better cities. the opinions in recent decades have expressed that compact physical form of cities is a better form than sprawl form to achieve urban sustainability. the form of the city is the embodiment of it...

‎let $g$ be a group with identity $e.$ let $r$ be a $g$-graded‎ ‎commutative ring and $m$ a graded $r$-module‎. ‎in this paper‎, ‎we‎ ‎introduce several results concerning graded classical prime‎ ‎submodules‎. ‎for example‎, ‎we give a characterization of graded‎ ‎classical prime submodules‎. ‎also‎, ‎the relations between graded‎ ‎classical prime and graded prime submodules of $m$ are studied‎.‎

AIM To compare the classical and simplified form of the continuity equation in small Trifecta valves. METHODS This is a retrospective analysis of post-operative echocardiograms performed for clinical reasons after implantation of Trifecta bioprosthetic valves. RESULTS There were 60 patients aged 74 (range 38-89) years. For the valves of size 19, 21 and 23mm, the mean gradient was 11.3, 10.7...

‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ ...

To use soil hydrology processe (SHP) models, which have increasingly extended during the last years, comprehensive knowledge about these models and their modeling approaches seems to be necessary. The modeling approaches can be categorized as either classical or non-classical. Classical approaches mainly model the SHP through solving the general unsaturated flow (Richards) equation, numerically...

To use soil hydrology processes (SHP) models, which have increasingly extended during the last years, comprehensive knowledge about these models and their modeling approaches seems to be necessary. The modeling approaches can be categorized as either classical or non-classical. Classical approaches mainly model the SHP through solving the general unsaturated flow (Richards) equation, numericall...

This is a report of the form of uterine anomaly involving a dual cervical canal in a side-by-side disposition with normal uterine cavity and normal vagina. It portrays a form of congenital uterine anomaly not explicable by the existing classical theory of mullerian anomalies. However, there has been a proposed reclassification of mullerian anomalies, which includes this type of anomaly under Ty...