Annals of Optimization Theory and Practice
Volume:3 Issue: 1, Autumn 2020

This paper investigate some characteristics of the age replacement model with minimal repair, of series-parallel system with non-uniform failure rates and are subjected to two different types of failures, which are Type I and Type II failures. The six units of the system formed three subsystems, which are subsystems A, B and C. Subsystem A is having three parallel units, subsystem B is having a single unit and subsystem C is having two parallel units. We constructed age replacement model with minimal repair that will determine the optimal replacement time of the series-parallel system. Furthermore, we also considered some modifications of the age replacement model with minimal repair constructed. Finally, some numerical examples are given to illustrate the characteristics of the age replacement models with minimal repair constructed. From the results obtained, it was observed that the optimal replacement time of the system when the three units of A are in parallel is higher than when the three units of A are in series. It was also observed that, the optimal replacement time obtained from the standard age replacement model is higher than the optimal replacement time obtained from standard age replacement model with minimal repair.

In this paper, we introduce the concept strong algebrability of certain C^* algebras generated by finite generators. In fact, using Gelfand theorem, we identify the members of the C^* algebra generated by one element, with the continuous functions on its spectrum, and use some recent result for strong algebrability for functions spaces. Moreover, we introduce the new concept unitable elements in unital C^* algebras, and then we express our main result for this kind of elements. In fact, the C^* subalgebra generated by a non unitable element in a C^* algebra is strongly c algebrable. As the last result in this paper, we show 2^c strong algebrability of direct sums of C^* algebras, using non unitable elements of them.

Today, with the advancement of sciences in various fields, mathematics is being optimally used in all sciences, mathematics is therefore widely used in other sciences, and Islamic and military sciences are no exception, and mathematics can be used to design various offensive and defensive operations in battlefields and solve battlefield equations in order to gain absolute or relative superiority over the enemy as in the game theory of war, the application of mathematics can be clearly seen. This practical research, conducted through a library method, has modeled the challenges between the two armies of Imam ʿAlī ibn Abī Ṭālib (AS) and a group called the Māriqīn or Khawārij in the battle of Nahrawān using Game Theory and analyzed each army’s strategies against each other, and finally explore the war utility to find the strategic equilibrium point between them. Therefore, we calculate the utility function for the set of strategies of each of the two armies including the army of Amir al-Mu’minin, ʿAlī ibn Abī Ṭālib (AS) and the Khawārij of Nahrawān and analyze it.

Groundwater quality plays an important role in human, animal, and plant health. Measurements of water quality are random variables that need a probabilistic model. The interest in fitting probability distribution in modeling water quality data remains strong in hydrology and engineering. This paper has been designed to find the best fitting probability distribution of calcium concentration of groundwater collected from 28 sampling sites in Gwale area, Kano state, Northwestern Nigeria. The parameter estimates for the groundwater data are analyzed using gamma, logistic, lognormal, normal, and Weibull distributions. The statistics measure such as the Akaike information criterion (AIC), Bayesian information criterion, log-likelihood, and Kolmogorov-Smirnov (K-S) test are computed to compare the fitted distributions. The most suitable distribution has been selected using these statistics measures. The result indicates that the logistic distribution with the highest log-likelihood value, and the smallest AIC and BIC values were found to fit the calcium concentration of groundwater data than other competing distributions. This research describes the use of probability distribution in modeling groundwater quality data and could be used to describe groundwater quality data in any other location.

The paper aims to give some new kinds of operational laws named as neutrality addition and scalar multiplication for the pairs of linguistic interval-valued intuitionistic neutrosophic fuzzy number. The main idea behind these operations is to include the linguistic interval-valued intuitionistic neutrosophic fuzzy number of the decision-maker and score function. We define the linguistic interval-valued intuitionistic neutrosophic fuzzy number and operational laws. We introduce the three geometric operators including, linguistic interval-valued intuitionistic neutrosophic fuzzy weighted geometric operator, linguistic interval-valued intuitionistic neutrosophic fuzzy ordered weighted geometric operator and linguistic interval-valued intuitionistic neutrosophic fuzzy weighted hybrid geometric operatorl. Finally, a multiattribute group decision-making approach based on the proposed operators is presented and investigated with numerous numerical examples.