Weosay thatotheosubmodules A, B ofoan R-module Moare µ-equivalent , AµB ifoand onlyoif <<µand <<µ. Weoshow thatoµ relationois anoequivalent relationoand hasegood behaviorywith respectyto additionmof submodules, homorphismsr, andydirectusums, weaapplyothese resultsotoointroduced theoclassoof H-µ-supplementedomodules. Weosay thatoa module Mmis H-µ-supplementedomodule ifofor everyosubmodule A of M, thereois a directosummand D ofoM suchothat AµD. Variousoproperties ofothese modulesoarepgiven.
In this article, we introduced a new concept of mappings called δZA - Quasi contractive mapping and we study the K*- iteration process for approximation of fixed points, and we proved that this iteration process is faster than the existing leading iteration processes like Noor iteration process, CR -iteration process, SP and Karahan Two- step iteration process for 𝛿𝒵𝒜 − quasi contraction mappings. We supported our analytic proof by a numerical example.
Computer vision is an emerging area with a huge number of applications. Identification of the fingertip is one of the major parts of those areas. Augmented reality and virtual reality are the most recent technological advancements that use fingertip identification. The interaction between computers and humans can be performed easily by this technique. Virtual reality, robotics, smart gaming are the main application domains of these fingertip detection techniques. Gesture recognition is one of the most fascinating fields of fingertip detection. Gestures are the easiest and productive methods of communication with regard to collaboration with the computer. This analysis examines the different studies done in the field of
... Show MoreStarting from 4, - Dimercaptobiphenyl, a variety of phenolic Schiff bases (methylolic, etheric, epoxy) derivatives have been synthesized. All proposed structure were supported by FTIR, 1H-NMR, 13C-NMR Elemental analysis all analysis were performed in center of consultation in Jordan Universty.
Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes app
... Show MoreThe effect of adding sand on clayey soil shear strength is investigated in this study. Five different percentage of clay-sand mixtures are used; 100% clay with 0% sand termed 100C, 60% clay with 40% sand termed 60C-40S, 30% clay with 70% sand termed 30C-70S, 15% clay with 85% sand termed 15C-85S, and as well as 100% sand termed 100S. The used clay was obtained from Baghdad city in Iraq and classified as CH soil, while the used sand was taken from Al-Khider area from Iraq and classified as SW soil. The initial dry unit weight for all mixtures is 16 kN/m3. The results show that the variations of the soil shear strength properties with soil components content changes