The goal of this research is to introduce the concepts of Large-small submodule and Large-hollow module and some properties of them are considered, such that a proper submodule N of an R-module M is said to be Large-small submodule, if N + K = M where K be a submodule of M, then K is essential submodule of M ( K ≤e M ). An R-module M is called Large-hollow module if every proper submodule of M is Large-small submodule in M.
Two grades of paving asphalt with penetration of 46 and 65 are studied for determining changes in their physical and chemical properties caused by ageing.
The ageing process has been conducted on two petroleum paving asphalt cement using thin film oven test at 150, 163 and 175 C, and ageing time 5, 10,15, 20, 25 and 30 hours. The effect of ageing time and temperature on penetration, kinematic viscosity, softening point, solubility in trichloroethylene, heat loss and changes in chemical composition are investigated. The results of thin film oven test process indicte that the asphaltenes concentration of all aged asphalt increases with increasing ageing time, while the opposite was observed for polar-aromatic and naphthene-aromatic. The
The research aims to study some of the human characteristics of the state of Singapore to know the impact of these characteristics on the strength of the state, its development and. The research included two aspects, theoretical and analytical, using the descriptive analytical method, force analysis method, as well as the historical method. The data was analyzed according to mathematical equations, including the size of the country's population, the extraction of the population growth rate and the concept of age structure, where some indicators related to this concept have been explained. The researcher reached a set of results, the most important of which were: that the population size of the state of Singapore in the period between (19
... Show MoreIn this work the effect of annealing temperature on the structure and the electrical properties of Bi thin films was studied, the Bi films were deposited on glass substrates at room temperature by thermal evaporation technique with thickness (0.4 µm) and rate of deposition equal to 6.66Å/sec, all samples are annealed in a vacuum for one hour. The X-ray diffraction analysis shows that the prepared samples are polycrystalline and it exhibits hexagonal structure. The electrical properties of these films were studied with different annealing temperatures, the d.c conductivity for films decreases from 16.42 ? 10-2 at 343K to 10.11?10-2 (?.cm)-1 at 363K. The electrical activation energies Ea1 and Ea2 increase from 0.031 to 0.049eV and
... Show MoreA high settlement may take place in shallow footing when resting on liquefiable soil if subjected to earthquake loading. In this study, a series of shaking table tests were carried out for shallow footing resting on sand soil. The input motion is three earthquake loadings (0.05g, 0.1g, and 0.2g). The study includes a reviewing of theoretical equations (available in literatures), which estimating settlement of footings due to earthquake loading, calibration, and verification of these equations with data from the shaking table test for improved soil by grouting and unimproved soil. It is worthy to note that the grouting materials considered in this study are the Bentonite and CKD slurries. A modification to the seismic set
... Show MoreThe main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit where linear operator from complete standard fuzzy normed space into a standard fuzzy normed space then belongs to the set of all fuzzy bounded linear operators