The density functional theory (DFT) is a remarkably successful of electronic structure matter. At the foundation this lies Kohn-Sham (KS) equation. In paper, we describe long-time behaviour time-dependent KS Assuming weak self-interactions, prove global existence and scattering in (almost) full "short-range" regime. This achieved with new simple techniques, naturally compatible DFT involving co...

In this paper, we considered a deterministic inventory model with time-dependent demand and time-varying holding cost where deterioration is time proportional. The model considered here allows for shortages, and the demand is partially backlogged. The model is solved analytically by minimizing the total inventory cost. The result is illustrated with numerical example for the model. The model ca...

In this paper, an economic order quantity (EOQ) inventory model for a deteriorating item is developed with the following characteristics: (i) The demand rate is deterministic and two-staged, i.e., it is constant in first part of the cycle and linear function of time in the second part. (ii) Deterioration rate is time-proportional. (iii) Shortages are not allowed to occur. The o...

Periodontal ligament is a thin layer of soft tissue that connects root of a tooth to the surrounding alveolar bone. These ligaments play an important role in initiating tooth movement when loads are applied to teeth with orthodontic appliances. The majority of such soft tissues exhibit as viscoelastic bodies or have a time-dependent behavior. Due to the viscoelastic behavior of the periodontal ...

Effect of time dependent normal transpiration on the problem of unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder moving simultaneously with time-depended angular and axial velocities and with time-dependent wall temperature or wall heat flux are investigated. The impinging free stream is steady with a strain rate . A re...

Inventory models in which the demand rate dependents on the stock- dependent are based on the common real- life observation that greater product availability tends to stimulate more sales. In this study we develop an inventory model to determine an optimal ordering policy for quantity dependent demand rate and time dependent holding cost items with delay in payments permitted by the supplier un...