Let R be a commutative ring with unity and let M be an R-module. In this paper we
study strongly (completely) hollow submodules and quasi-hollow submodules. We investigate
the basic properties of these submodules and the relationships between them. Also we study
the be behavior of these submodules under certain class of modules such as compultiplication,
distributive, multiplication and scalar modules. In part II we shall continue the study of these
submodules.

     Let  be an R-module, and let  be a submodule of . A submodule  is called -Small submodule () if for every submodule  of  such that  implies that . In our work we give the definition of -coclosed submodule and -hollow-lifiting modules with many properties.

In earthquake engineering problems, uncertainty exists not only in the seismic excitations but also in the structure's parameters. This study investigates the influence of structural geometry, elastic modulus, mass density, and section dimension uncertainty on the stochastic earthquake response of a multi-story moment resisting frame subjected to random ground motion. The North-south component of the Ali Gharbi earthquake in 2012, Iraq, is selected as ground excitation. Using the power spectral density function (PSD), the two-dimensional finite element model of the moment resisting frame's base motion is modified to account for random ground motion. The probabilistic study of the moment resisting frame structure using stochastic fin

This paper presents the non-linear finite element method to study the behavior of four reinforced rectangular concrete MD beams with web circular openings tested under two-point load. The numerical finite elements methods have been used in a much more practical way to achieve approximate solutions for more complex problems.  The ABAQUS /CAE is chosen to explore the behavior of MD beams. This paper also studies, the effect of both size and shape of the circular apertures of MD beams. The strengthening technique that used in this paper is externally strengthening using CFRP around the opening in the MD beams. The numerical results were compared to the experimental results in terms of ultimate load failure and displace

The construction of highly safe and durable buildings that can bear accident damage risks including fire, earthquake, impact, and more, can be considered to be the most important goal in civil engineering technology. An experimental investigation was prepared to study the influence of adding various percentages 0%, 1.0%, and 1.5% of micro steel fiber volume fraction (Vf) to reactive powder concrete (RPC)—whose properties are compressive strength, splitting tensile strength, flexural strength, and absorbed energy—after the exposure to fire flame of various burning temperatures 300, 400, and 500 °C using gradual-, foam-, and sudden-cooling methods. The outcomes of this research proved that the maximum reduction in mechanical prop

In Australia, most of the existing buildings were designed before the release of the Australian standard for earthquake actions in 2007. Therefore, many existing buildings in Australia lack adequate seismic design, and their seismic performance must be assessed. The recent earthquake that struck Mansfield, Victoria near Melbourne elevated the need to produce fragility curves for existing reinforced concrete (RC) buildings in Australia. Fragility curves are frequently utilized to assess buildings’ seismic performance and it is defined as the demand probability surpassing capacity at a given intensity level. Numerous factors can influence the results of the fragility assessment of RC buildings. Among the most important factors that can affe