Vacuum Polarization Effects in a System of Two Three-Phase Chiral Bags

In the model of three-phase chiral quark bags in 1+1 dimensions, we obtain self-consistent solutions describing the system of two interacting bags. Attention is focused on investigating the role played by the fermionic vacuum polarization inside the bags in the dynamics of the system; the bosonic field interrelating the bags is taken into account only at the one-meson exchange level. The renormalized total energy of the system is investigated as a function of parameters characterizing the geometry of the problem and of the additional bag characteristics arising in 1+1 dimensions. We show that in the system of two three-phase bags, vacuum polarization yields a strong nonlinear interaction at small distances, which can be either repulsive or attractive depending on the bag characteristics.     

Peeling Layers of an Onion: Inventory Model with Multiple Delivery Modes and Forecast Updates

This paper is concerned with a periodic review inventory system with fast and slow delivery modes and regular demand forecast updates. At the beginning of each period, on-hand inventory and demand information are updated. At the same time, decisions on how much to order using fast and slow delivery modes are made. Fast and slow orders are delivered at the end of the current and the next periods, respectively. It is shown that there exists an optimal Markov policy and that it is a modified base-stock policy.