Global Optimization for a Class of Nonlinear Sum of Ratios Problem

We present a branch and bound algorithm for globally solving the sum of ratios problem. In this problem, each term in the objective function is a ratio of two functions which are the sums of the absolute values of affine functions with coefficients. This problem has an important application in financial optimization, but the global optimization algorithm for this problem is still rare in the literature so far. In the algorithm we presented, the branch and bound search undertaken by the algorithm uses rectangular partitioning and takes place in a space which typically has a much smaller dimension than the space to which the decision variables of this problem belong. Convergence of the algorithm is shown. At last, some numerical examples are given to vindicate our conclusions

Evidence of the side jump mechanism in the anomalous Hall effect in paramagnets

Persistent confusion has existed between the intrinsic (Berry curvature) and the side jump mechanisms of anomalous Hall effect (AHE) in ferromagnets. We provide unambiguous identification of the side jump mechanism, in addition to the skew scattering contribution in epitaxial paramagnetic Ni$_{34}$Cu$_{66}$ thin films, in which the intrinsic contribution is by definition excluded. Furthermore, the temperature dependence of the AHE further reveals that the side jump mechanism is dominated by the elastic scattering

A Review of Polypropylene and Polypropylene/Inorganic Nanocomposites for HVDC Cable Insulation

Due to its excellent electrical and thermal performance, as well as satisfying the needs for developing the environmentally friendly and recyclable cable insulation material, polypropylene has caused widespread concern. Nanodoping can effectively improve the electrical, thermal and mechanical properties of polypropylene nanocomposites, which provides a new method to solve the problems in its application in HVDC cable insulation. This chapter introduces research achievements on polypropylene and polypropylene/inorganic nanocomposites, which states the effects of nanodoping on the electrical properties, such as space charge behaviors, electrical tree aging, breakdown strength, etc. thermal conductivity and mechanical properties of the polypropylene and its multi-blends. The aging mechanism under different conditions is also discussed. The analysis shows that the surface treatment of nanoparticles can reduce the aggregation of nanoparticles and strengthen the interface effect, thus improving the comprehensive properties of polypropylene nanocomposites. This chapter also summarized the feasibility and future development of the polypropylene and its nanocomposites application in the insulation of HVDC cables