The new techniques in seismic design of structures are usually attributed to high damping ratios. In such systems, the assumption of classical (i.e. proportional) damping is not valid and in most cases they should be considered as Non-classical systems. Since the analytical tools for studying the behavior of such structures are not easily available, the present work attempts to find the limits,...

primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. in fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  in this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...

let r be a commutative ring and m be an r-module. we say that m is fully primary, if every proper submodule of m is primary. in this paper, we state some characterizations of fully primary modules. we also give some characterizations of rings over which every module is fully primary, and of those rings over which there exists a faithful fully primary module. furthermore, we will introduce some ...

Survival of patients with multiple myeloma has improved substantially because of availability of new therapies including autotransplants, immunomodulating drugs and proteasome-inhibitors. Second primary cancers have emerged as an important determinant of morbidity and mortality among cancer survivors. Even though there is an increased risk of new cancers of the lymphoreticular and haematopoetic...

‎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.‎

the vehicle routing problem with backhauls (vrpb) as an extension of the classical vehicle routing prob-lem (vrp) attempts to define a set of routes which services both linehaul customers whom product are to be delivered and backhaul customers whom goods need to be collected. a primary objective for the problem usually is minimizing the total distribution cost. most real-life problems have othe...

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...