An R-module M is called rationally extending if each submodule of M is rational in a direct summand of M. In this paper we study this class of modules which is contained in the class of extending modules, Also we consider the class of strongly quasi-monoform modules, an R-module M is called strongly quasi-monoform if every nonzero proper submodule of M is quasi-invertible relative to some direct summand of M. Conditions are investigated to identify between these classes. Several properties are considered for such modules
The concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies this concept and it is relationship to previous generalizationsm especially 2-Absorbing submodule and Quasi-2-Absorbing submodule, in addition to studying the most important Propositions, charactarizations and Examples. Now in this research, which is considered a continuation of the definition that was presented earlier, which is the Extend Nearly Pseudo Quasi-2-Absorbing submodules, we have completed the study of this concept in multiplication modules. And the relationship between the Extend Nearly Pseudo Quasi-2-Absorbing submodule and Extend Nearly Pseudo Quasi-2-Abs
... Show MoreThe concept of a 2-Absorbing submodule is considered as an essential feature in the field of module theory and has many generalizations. This articale discusses the concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules and their relationship to the 2-Absorbing submodule, Quasi-2-Absorbing submodule, Nearly-2-Absorbing submodule, Pseudo-2-Absorbing submodule, and the rest of the other concepts previously studied. The relationship between them has been studied, explaining that the opposite is not true and that under certain conditions the opposite becomes true. This article aims to study this concept and gives the most important propositions, characterizations, remarks, examples, lemmas, and observations related to it. In the en
... Show MoreSix isolates of A. pullulans were collected from many sources including Hibiscus sabdariffa (Roselle), old Roofs of houses and bathroom surface that referred as Ap ros1, Ap or2, 3, 4 and Ap bs5, 6 respectively, all these isolates were identified based on morphological characteristics and nutritional physiology profiles, all were able to utilize various carbon and nitrogen sources such as glucose, xylose, sucrose, maltose, ammonium sulfate, ammonium nitrate and ammonium chloride, also they showed positive test for starch and amylase, while α-cellulose, ethanol, and methanol were could not be ass
... Show MoreThe class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex
... Show MoreLower extremity exoskeletons can assist with performing particular functions such as gait assistance, and physical therapy support for subjects who have lost the ability to walk. This paper presents the analysis and evaluation of lightweight and adjustable two degrees of freedom, quasi-passive lower limb device to improve gait rehabilitation. The exoskeleton consists of a high torque DC motor mounted on a metal plate above the hip joint, and a link that transmits assistance torque from the motor to the thigh. The knee joint is passively actuated by spring installed parallel with the joint. The action of the passive component (spring) is combined with mechanical output of the motor to provide a good control on the designed exoskeleton whi
... Show MoreIn this article, we will present a quasi-contraction mapping approach for D iteration, and we will prove that this iteration with modified SP iteration has the same convergence rate. At the other hand, we prove that the D iteration approach for quasi-contraction maps is faster than certain current leading iteration methods such as, Mann and Ishikawa. We are giving a numerical example, too.
In this article, we recalled different types of iterations as Mann, Ishikawa, Noor, CR-iteration and, Modified SP_iteration of quasi δ-contraction mappings, and we proved that all these iterations equivalent to approximate fixed points of δ-contraction mappings in Banach spaces.
In this paper, we study some cases of a common fixed point theorem for classes of firmly nonexpansive and generalized nonexpansive maps. In addition, we establish that the Picard-Mann iteration is faster than Noor iteration and we used Noor iteration to find the solution of delay differential equation.