A submodule Ϝ of an R-module Ε is called small in Ε if whenever , for some submodule W of Ε , implies . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if , such that , then , where is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .
The one-dimensional, cylindrical coordinate, non-linear partial differential equation of transient heat conduction through a hollow cylindrical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical
function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant the
The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal con
... Show MoreBackground: Herbs are being widely explored to discover alternatives to synthetic antibacterial agents.Small Cardamom often referred to as queen of spices because of its very pleasant aroma and taste, have a history as old as human race. Most people use cardamom as a spice and are largely unaware of its numerous health benefits. The purpose of this study was to evaluate the effect of different concentrations of water and alcoholic cardamom extracts on sensitivities, growth, and adherence of Mutans streptococci in vitro. Materials and Methods: In this study, saliva was collected from ten volunteers (College students 18-22 years). Agar well technique was used to study the sensitivities of Mutans streptococci to different concentrations of s
... Show MoreExperimental investigation for small horizontal portable wind turbine (SHPWT) of NACA-44, BP-44, and NACA-63, BP-63 profiles under laboratory conditions at different wind velocity range of (3.7-5.8 m/s) achieved in present work. Experimental data tabulated for 2, 3, 4, and 6- bladed rotor of both profiles within range of blade pitch angles . A mathematical model formulated and computer Code for MATLAB software developed. The least-squares regression is used to fit experimental data. As the majority of previous works have been presented for large scale wind turbines, the aims were to present the performance of (SHPWT) and also to make a comparisons between both profiles to conclude which is the best performance. The overall efficiency and el
... Show MoreExperimental measurements were done for characterizing current-voltage and power-voltage of two types of photovoltaic (PV) solar modules; monocrystalline silicon (mc-Si) and copper indium gallium di-selenide (CIGS). The conversion efficiency depends on many factors, such as irradiation and temperature. The assembling measures as a rule cause contrast in electrical boundaries, even in cells of a similar kind. Additionally, if the misfortunes because of cell associations in a module are considered, it is hard to track down two indistinguishable photovoltaic modules. This way, just the I-V, and P-V bends' trial estimation permit knowing the electrical boundaries of a photovoltaic gadget with accuracy. This measure
... Show MoreBackground: Small cardamom or green cardamom is the dried fruit of the tall perennial herbaceous plant, Elettaria cardamomum Maton belonging to the family Zingiberaceae. The major use of small cardamom on world wide is for domestic culinary purpose and in medicine. This study was conducted to test the effect of small cardamom extracts on Mutans streptococci and Candida Albicans in comparison to 0.2% chlorhexidine gluconate and de-ionized water in vivo. Materials and Methods: Mutans streptococci and Candid Albicans were isolated, purified and diagnosed according to morphological characteristic and biochemical test. In this experiments, the effect of control agents and small cardamom extracts as a mouth rinses was tested on the saliva
... Show MoreThe current research aims to identify the contributions of small income-generating projects in theempowerment of rural women in Nineveh Governorate ,Al-Hamdaniya district, as a simplerandom sample was drawn from the research community of 280 respondents , according to theRobert Mason equation at the level of significance 0.05, so the sample size was 162 respondents,i.e. a percentage 58% collected the necessary data using a questionnaire prepared as a basic toolfor data collection consisting of 20 items distributed on two axes ,and the results of the researchwere analyzed and presented using the spss statistical program, as well as manual analysis usingrepetitions, the weighted mean, the standard deviation, and the percentage weight. And the
... Show More