Convergence of the Poincare Constant

The Poincare constant R(Y) of a random variable Y relates the L2 norm of a function g and its derivative g'. Since R(Y) - Var(Y) is positive, with equality if and only if Y is normal, it can be seen as a distance from the normal distribution. In this paper we establish a best possible rate of convergence of this distance in the Central Limit Theorem. Furthermore, we show that R(Y) is finite for discrete mixtures of normals, allowing us to add rates to the proof of the Central Limit Theorem in the sense of relative entropy.Comment: 11 page

Dirac Line-nodes and Effect of Spin-orbit Coupling in Non-symmorphic Critical Semimetal MSiS (M=Hf, Zr)

Topological Dirac semimetals (TDSs) represent a new state of quantum matter recently discovered that offers a platform for realizing many exotic physical phenomena. A TDS is characterized by the linear touching of bulk (conduction and valance) bands at discrete points in the momentum space (i.e. 3D Dirac points), such as in Na3Bi and Cd3As2. More recently, new types of Dirac semimetals with robust Dirac line-nodes (with non-trivial topology or near the critical point between topological phase transitions) have been proposed that extends the bulk linear touching from discrete points to 1D lines. In this work, using angle-resolved photoemission spectroscopy (ARPES), we explored the electronic structure of the non-symmorphic crystals MSiS (M=Hf, Zr). Remarkably, by mapping out the band structure in the full 3D Brillouin Zone (BZ), we observed two sets of Dirac line-nodes in parallel with the kz-axis and their dispersions. Interestingly, along directions other than the line-nodes in the 3D BZ, the bulk degeneracy is lifted by spin-orbit coupling (SOC) in both compounds with larger magnitude in HfSiS. Our work not only experimentally confirms a new Dirac line-node semimetal family protected by non-symmorphic symmetry, but also helps understanding and further exploring the exotic properties as well as practical applications of the MSiS family of compounds.Comment: 5 figure

An Improved NSGA-II and its Application for Reconfigurable Pixel Antenna Design

Based on the elitist non-dominated sorting genetic algorithm (NSGA-II) for multi-objective optimization problems, an improved scheme with self-adaptive crossover and mutation operators is proposed to obtain good optimization performance in this paper. The performance of the improved NSGA-II is demonstrated with a set of test functions and metrics taken from the standard literature on multi-objective optimization. Combined with the HFSS solver, one pixel antenna with reconfigurable radiation patterns, which can steer its beam into six different directions (θDOA = ± 15°, ± 30°, ± 50°) with a 5 % overlapping impedance bandwidth (S11 < − 10 dB) and a realized gain over 6 dB, is designed by the proposed self-adaptive NSGA-II