Applied Mathematics

This paper introduces manufacturer consumer supply chain model to investigate pricing and advertising decision when price discounts and credit facilities for certain period are offered by the manufacturer. In this supply chain, the manufacturer is the supreme power to decide the level of price discount, advertising, brand name investment and has the power to introduce the credit period facility. For the first case when the manufacturer proposes price discount, we found that as there is no contribution of retailer in the supply chain, the manufacturer only utilises the entire profits and through the intensive marketing strategies, the manufacturer can equilibrium their consumers. For the second case, when the manufacturer introduces the credit period facilities to attract more number of consumers in wide range, we found that both the manufacturer and consumer have substantial benefits which lead to augment of profit margin and derive fulfilment respectively. Numerical examples were given to illustrate the optimal profit margins in the manufacturer consumer supply chain.

The knowledge of the structure of the boundary layer gives an idea to understand the capabilities of the atmosphere to dispose of pollutants. Finite difference technique with non-uniform grid is used to investigate the effect of various flow parameters on skin friction , heat transfer and other characteristics of two phase thermal boundary layer flow on a flat plate. Heat is diffused away from the heated surface for smaller values of Prandtl number Pr more rapidly than that of higher values of Pr. The particle density on the plate goes on increasing and attains a finite value of 3.5 at a far down stream station. The presence of coarser particles with high material density have an effect of increase in magnitude of particle velocity and particle phase density whereas to reduce the particle temperature. The increase in Prandtl number Pr is to increase the magnitude of carrier fluid velocity, particle velocity, particle phase density, coefficient of skin friction and Nusselt number where as to decrease the displacement thickness.

Given an arbitrary finite group , denote by the set of its element orders. The group is said to be recognizable by the set if the equality implies an isomorphism of and for each finite group . For a prime , the alternating groups are recognizable. But for are has not known. In this paper, we will give an example for not a prime, namely, that is characterizable.

In this paper, we study some of the properties of Q-fuzzy normal subgroups, cosets and prove some results on these.

Stock control is an act of stocking goods to satisfy expected future demand. This gives rise to the problem of “how much and when to place order for new goods when stock is going down. Decision regarding the quantity ordered and the time at which it is ordered is based on minimizing an appropriate cost function to balance the total cost function resulting from overstocking or under stocking. Quantity discount stimulates the interest of the distributor to stock more goods and hence the need for additional warehouse which may increase his holding cost. This work has considered inventory using two warehouses-owners and rented warehouses. A model similar to that of Tien Yu Lin (2011) is developed. It has been shown that optimal order quality that minimizes the expected total cost is obtained. The consequence of the limit of the holding cost of the rented warehouse on the optimal order size is also given.

Environment Pollution is assuming dangerous proportions all through the globe. This is the gift of modern living industrialization and urbanization. Transportation is a non-separable part of any society. It exhibits a very close relation to the style of life, the range and location of activities and the goods and services which will be available for consumption. Costs and benefits have mirror image relationship. A cost can be defined as a reduction in benefits and a benefit can be defined as a reduction in costs. Transportation benefits are often measured in terms reduced Transportation costs. Calculating costs is therefore the basis for calculating benefits. This paper deals with an Economic Order Quantity model (EOQ) which associates the vehicle cost, Damage cost, Parking cost, Environmental cost along with the costs of ordering, Purchasing and holding. This paper also investigates the attributing factors of the Environmental impacts which could be minimized to build a healthy society.

The purpose of present paper to study and introduces the concepts of fuzzy arw- super closed mappings and obtains some of their basic properties and characterizations in fuzzy topology.

The normal distribution is a very commonly occurring continuous probability distribution. Normal distributions are extremely important and are used in the natural and sciences related real valued random variables whose distributions are not really known. In this paper the Bivariate Normal distribution is used and the probability density functions for the exponent term q(x,y) are find out. Here Prolactin and Cortisol are considered as bivariate normal and the typical contour for the corresponding quadratic function q(x,y) for the Acupuncture- Prolactin and Cortisol, Control – Prolactin and Cortisol, Prolactin – Acupuncture and Control and Cortisol – Acupuncture and Control cases in the In Vitro Fertilization and Embryo Transfer Treatment days is given in the application part. The PDF obtained for the four cases in the In Vitro Fertilization and Embryo Transfer treatment is a part of an ellipse with the positive correlation.

In modern competitive business environment, it is essential to continuously work on improving the performance of their supply chains with high customer satisfaction. Inventory management is affected by the imperfect production process. So it is contemporary for the vendor to improve quality of the product/service where customer’s loyalty will be the by-product. In this paper vendor invests money to reduce the number of defective items produced. Also in many transactions regarding selling and buying, a specified delay of payment is offered or accepted by the vendor. This can be viewed as a kind of discount and has potential consequences for the order size. Differently from the existing literature this paper extends the model with the inclusion of stochastic demand, stock out cost and delay in payments. Numerical studies explore the beneficial of the vendor investment.

The study of fully developed mixed convection Couette flow of a nano fluid between two vertical parallel plates, with asymmetric thermal and nanoparticle concentration conditions at the walls, filled by a nanofluid has been studied. The nanofluid model used in this paper takes into account the lower plate moving velocity, Brownian diffusion and the thermophoresis effects and the analysis is based on analytical solutions. Analytical expressions for the fully developed velocity, temperature and nanoparticle concentration profiles as well as for the Nusselt and Sherwood numbers at the left wall of the channel are obtained and analysed.