An efficient linearization technique for mixed 0-1 polynomial problem

This paper addresses a new and efficient linearization technique to solve mixed 0-1 polynomial problems to achieve a global optimal solution. Given a mixed 0-1 polynomial term z=c_tx₁x₂…x_ny, where x₁,x₂,…,x_n are binary (0-1) variables and y is a continuous variable. Also, c_t can be either a positive or a negative parameter. We transform z into a set of auxiliary constraints which are linear and can be solved by exact methods such as branch and bound algorithms. For this purpose, we will introduce a method in which the number of additional constraints is decreased significantly rather than the previous methods proposed in the literature. As is known in any operations research problem decreasing the number of constraints leads to decreasing the mathematical computations, extensively. Thus, research on the reducing number of constraints in mathematical problems in complicated situations have high priority for decision makers. In this method, each n-auxiliary constraints proposed in the last method in the literature for the linearization problem will be replaced by only 3 novel constraints. In other words, previous methods were dependent on the number of 0-1 variables and therefore, one auxiliary constraint was considered per 0-1 variable, but this method is completely independent of the number of 0-1 variables and this illustrates the high performance of this method in computation considerations. The analysis of this method illustrates the efficiency of the proposed algorithm.     

Some polishing experiments on copper in a hyperbolic cell

Some polishing experiments have been carried out on copper anodes in a hyperbolic cell designed by Gilmont and Walton, using orthophosphoric acid as the electrolyte. The results obtained have been compared to those obtained in similar experiments in a Hull cell. It has been found that very similar bands of different reflectivity and polishes are found to form in both the cells. These bands shift with time and a study of such displacements has been made. The results are briefly discussed.     

Size effect study in magnetoelectric BiFeO3 system

In this paper, we report for the first time finite size effects on Néel temperature (T _N) of magnetoelectric BiFeO₃ system. Novel wet chemical route has been developed to produce fine particles of BiFeO₃ with controlled size and size distribution. Unlike other oxide systems, lattice volume contraction has been observed with decrease in particle size. The decrease in T _N is co-related to unit cell volume contraction occurring with reduction in particle size.     

Polarisation and polishing studies on copper in a Hull cell

In continuation of our previous work,^1–2 the effects of polishing time, sp. gr. of the electrolyte, addition of EDTA, electrolyte level, etc., on the position, size and shape of the variously polished bands obtained in a Hull cell have now been studied. I–V measurement when carried out showed that total cell voltage increases regularly with total cell current, thereby affording no explanation for the variously polished bands. However, with a specially designed probe electrode,³ it has been possible to study the current distribution as existing during polarisation at different points of the anode surface and thus offer some explanation for the appearance of variously polished bands which could not be interpreted earlier in terms of electrode potentials.