Applied Mathematics

This manuscript deals with the Frattini Subgroups and some results based on frattini subgroups. In this paper we define the Frattini subgroup and then discuss some of its properties.We denote it by . We define nS, aS, aPNS, cS , aCS group. In this we show that nS group is a cS group and if any group G is an nS(cS) group then Fr(G)=E. thus we show that any normal subgroup of an nS-group is again an nS group and direct Product of two nS group is again an nS group. In this we show that if any nilpotent group G is nS then it is elementary abelian group.

The focus of this paper is to explore different types of matrix operations of fuzzy neutrosophic soft sets and composition method to construct the decision making for medical diagnosis.

In this paper, two different components and one repairman of with warm standby system priority is studied. Assume that two components of working time, standby time, the repair time after fault and the repair time after standby fault are subject to the different exponential distribution and the repair of the component 1 is geometry repair and the repair of the component 2 is as good as new. The component 1 has priority in use and repair. By using geometric process theory, the supplementary variable method and the Laplace transform, the reliability indices of the system are obtained.

In the classic Economic Order Quantity model the purchasing cost of an order is paid at the time of its receipt. In some cases sellers give their retailers a permissible for paments and some others aks buyers to pay all or a fraction of the purchasing cost in advance and may allow them to divide the prepayment into several equal-sized parts. We propose a generalized supplier–retailer inventory model under a given deterministic planning horizons which consists of n different periods using a trade credit policy that attracts more retailers. The trade credit policy adopted here is a demand dependent policy in which the supplier offers the retailer a permissible delay period as a non-decreasing function of the buyer demand. In addition, the demand rate is assumed to be a function of time and of the related period. During the given permissible period no interest is charged by the supplier on the retailer, but beyond that period an interest, with the conditions agreed upon, is charged on .However, during the permissible credit period, the retailer can accumulate the revenue of salls and earns an interest on that revenue.Hence, determin?ng such a trade credit period is recognized as an important strategy to increase seller’s profitability and minimize the retailer’s costs. Sufficient conditions on the existence and uniqueness of the optimal replenishment policy are provided.

Our aim in this paper is to investigate the commuting property of the Traces of a Symmetric Biderivations on prime and semiprime ring R. Furthermore, we look for the commutitivity of a ring R under some suitable conditions.

In this chapter, we introduce (1,2)*-fg-closed maps, (1,2)*-fg-open maps, (1,2)*-fg*-closed maps and (1,2)*-fg*-open maps in Fuzzy bitopological spaces and obtain certain characterizations of these classes of maps. In last section, we introduce (1,2)*-fg*-homeomorphisms and prove that the set of all (1,2)*-fg*-homeomorphisms forms a group under the operation composition of functions.

In this paper we analyse that how the firms manage carbon footprints in inventory management under the carbon emission trading scheme. Today’s modern world the carbon emission is one of the main sources for the global warming, so every mankind have the responsibility for reducing the carbon emission to mitigate global warming. It is generally accepted that carbon emission trading is one of the most effective market based mechanism to prohibit the amount of carbon emission. AmulyaGurtu, Mohammed Y.Jaber discussed the following result in their model paper “Impact of fuel price and carbon emission on inventory policies” [App.Mathematical Modelling, 39(2015) 1202-12016]. In that paper they mentioned that the order cost and lot sizes are affected by changes in fuel price, emission tax, fuel consumption, distance travelled. Now we expanded the above paper by introducing the emission minimizing policies such as a cap and trade system in the two level supply chain.Under the cap and trade system we explain about the carbon price and transfer quantity of carbon emission. We also provide the numerical example for better understanding.

The notion of closed set plays a fundamental role in the study of topological spaces. Levine[8], in 1970 introduced the concept of generalized closed sets in a topological space by comparing the closure of a subset with its open supersets. This has been studied extensively in recent years by many topologists. The investigation of generalized closed sets has led to several new and interesting concepts. New and interesting applications have been found in the field of Economics, Biology and Robotics etc. Generalized closed sets remain as an active and fascinating field within mathematicians.

In the changing market scenario, the study of the supply chain model in a fuzzy environment is gaining phenomenal importance around the globe. In such a scenario, it is the need of the hour that a real supply chain is operated in an uncertain environment and the omission of any effects of uncertainty leads to inferior supply chain designs. This work presents a fuzzy possibilistic linear programming approach to make strategic resource – planning decisions in multi-product and multi-time period two-echelon supply chains. In this model, demand rate, holding cost, transportation cost, packing charge and toll fees are considered as triangular fuzzy numbers. The objective of the proposed model is to provide an optimal inventory level for the warehouses and distribution centers and also, minimizing the total cost related to transportation, inventory carrying, packing and toll fees of the entire supply chain for a finite planning horizon. An industrial case demonstrates the feasibility of applying the proposed model to real world problem in a two-echelon supply chain under uncertain environment. In addition to that, if the efficiency of the transportation will be increased by using the light weight eco-friendly plastic pail rather than the traditional one, then the reduction of the total cost in the supply chain is also analyzed.

In this article, the problem of optimal control of time-invariant linear singular systems with quadratic performance index has been studied using Runge-Kutta (RK) method based on various means. The obtained discrete solutions are compared with the exact solutions of the time-invariant optimal control of linear singular systems. It is observed that the result obtained using Runge-Kutta arithmetic mean (RKAM) and RKCeM (Runge-Kutta Centroidal Mean) are closer to the true solutions of the problem. Error graphs for the simulated results and exact solutions are presented in a graphical form to highlight the efficiency of this RKAM and RKCeM. This RKAM and RKCeM can be easily implemented in a digital computer and the solution can be obtained for any length of time for this type of optimal control of time-invariant linear singular systems and it is an added advantage of this method.