Probabilistic characterizations of some finite ring of matrices and its zero divisor graph

Let R be a finite ring. In this study, the probability that two random elements chosen from a finite ring have product zero is determined for some finite ring of matrices over Zn. Then, the results are used to construct the zero divisor graph which is defined as a graph whose vertices are the nonzero zero divisors of R and two distinct vertices x and y are adjacent if and only if xy = 0

On the probability and graph of some finite rings of matrices

The study on probability theory in finite rings has been an interest of various researchers. One of the probabilities that has caught their attention is the probability that two elements of a ring have product zero. In this study, the probability is determined for a finite ring R of matrices over integers modulo four. First, the annihilators of R are determined with the assistance of Groups, Algorithms and Programming (GAP) software and then the probability is calculated using the definition. Next, by using the results obtained, the zero divisor graph of the ring R is constructed. A zero divisor graph is defined as a graph in which the zero divisors of R are its vertices and two vertices are connected by an edge if their product is zero

ORIGINAL ARTICLE Undang-Undang Kedah Manuscript : A Law Canon Of An Early Malay State

ABSTRACT The manuscript under study is based on a microfilm copy of the original version found in the SOAS Library, with the reference number MS 40329. The manuscript was written in 1067 AH (1650 AD) and took several years to complete. The content was divided into five sections namely Port Laws, The Law of His Royal Highness, the Canon of Law of Datuk Kota Setar, The Method of making the "golden flowers (tribute)", and the Law of 1999 AH. On the whole, the Undang-Undang Kedah was a customary law which was beginning to be influenced by the Islamic law as practiced in an early Malay state. The study is aimed at discovering the historical evidence of the Malay legal system based on customary and Islamic canons of law in which became the basis of the life of the Malay traditional society. The Romanization from Jawi script and some description of the work has been done before, but analysis of the content of the work pertaining to the canon of law and the language used has not been studied thoroughly yet. This study is aimed at giving more detail description of the legal aspects besides describing the language used considered to be significant in understanding the work. However all aspects under study only focused on Port Laws to give more details in analyses. From a legal perspective, there was found much Islamic influence, however there were also Malay customary laws and inconsistencies with the requirements of Islamic law. It is also found that are many discrepancies between the vocabulary of MS 40329 and the other version of the manuscript. This study has an important implication for the philologist, historian and reader to understand the content and accurate reading of the manuscript under studied

Public Awareness and Practices Towards Self-Medication with Antibiotics Among Malaysian Population: Questionnaire Development and Pilot Testing

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