2-irreducible and strongly 2-irreducible ideals of commutative rings

An ideal I of a commutative ring R is said to be irreducible if it cannot be written as the intersection of two larger ideals. A proper ideal I of a ring R is said to be strongly irreducible if for each ideals J, K of R, J\cap K\subseteq I implies that J\subset I or K\subset I. In this paper, we introduce the concepts of 2-irreducible and strongly 2-irreducible ideals which are generalizations of irreducible and strongly irreducible ideals, respectively. We say that a proper ideal I of a ring R is 2-irreducible if for each ideals J, K and L of R, I= J\cap K\cap L implies that either I=J\cap K or I=J\cap L or I=K\cap L. A proper ideal I of a ring R is called strongly 2-irreducible if for each ideals J, K and L of R, J\cap K\cap L\subseteq I implies that either J\cap K\subseteq I or J\cap L\subseteq I or K\cap L\subseteq I.Comment: 15 page

Kewajiban Menuntut Ilmu dalam Perspektif Hadis

The purpose of this study is to discuss how the explanation of the hadith about the obligation to study. This research method uses a qualitative type through literature study with content analysis. The results and discussion of this study include the meaning of studying, takhrij hadith about the obligation to study, and how the ethics of a student in studying. The conclusion of this study shows that the command to study is an obligation and the hadith that explains the obligation to study is a saheeh hadith. This study recommends the importance of understanding among Muslims about their obligations in studying

System Architecture Optimization Using Hidden Genes Genetic Algorithms with Applications in Space Trajectory Optimization

In this dissertation, the concept of hidden genes genetic algorithms is developed. In system architecture optimization problems, the topology of the solution is unknown and hence, the number of design variables is variable. Hidden genes genetic algorithms are genetic algorithm based methods that are developed to handle such problems by hiding some genes in the chromosomes. The genes in the hidden genes genetic algorithms evolve through selection, mutation, and crossover operations. To determine if a gene is hidden or not, binary tags are assigned to them. The value of the tags determine the status of the genes. Different mechanisms are proposed for the evolution of the tags. Some mechanisms utilize stochastic operations while others are based on deterministic operations. All the proposed mechanisms are tested on mathematical and space trajectory optimization problems. Moreover, Markov chain models of the mechanisms are derived and their convergence is investigated analytically. The results show that the proposed concept are capable to search for the optimal solution by autonomously enabling the algorithms to assign the hidden genes

Carbon Nanotube-Based UV-Curable Nanocomposite Coatings

This chapter covers the preparation and properties of ultraviolet (UV)-curable nanocomposite containing carbon nanotubes as fillers. UV-curing technology is of particular interest due to its unique properties such as rapid curing process and solvent-free formulation. Alongside with the advantages of utilizing this curing method, carbon nanotubes undergo benefits including high aspect ratio, high transparency, and good mechanical properties. Carbon nanotubes (CNTs) are hollow cylindrical shaped configuration; consist of one, two, or more walls with an interlayer of non-covalent van der Waals force acting among the carbon atoms of various walls. Besides influencing the UV curing process, the CNTs loaded UV-curable nanocomposites sustain modified surface, thermal, mechanical, physical, and conductive properties which are discussed in this chapter. The health and safety concerns of using these classes of nanocomposite are further discussed

Evaluation of In-House and Global ESP Textbooks: A Genre-Based Approach

In the present article, five ESP textbooks on computer engineering, both in-house and global, have been evaluated using Swales’ (1990) ESP-based genre theory. The rationale behind such study was to investigate into features of the global textbooks that make them distinctive from their Iranian in-house counterparts. To achieve this goal, drawing on genre analysis as a theoretical framework, a systematic evaluation of the five textbooks based on an approach proposed by McDonough and Shaw (2003) with modifications in its suitability to the specific situation was conducted and the results tabulated through an assortment of grids for comparability purpose. The findings indicated that, despite a tendency to widen the scope of contemporary computer engineering environments as claimed by the Iranian authors, the dominance of traditional frameworks and textbooks persists and is not responsive to students’ needs and advances in genre theory in this field