Dynamics of McMullen maps

In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to a question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that the boundary is a quasi-circle if it contains neither a parabolic point nor a recurrent critical point. For the whole Julia set, we show that the McMullen maps have locally connected Julia sets except in some special cases.Comment: Complex dynamics, 51 pages, 13 figure

Rigidity of non-renormalizable Newton maps

Non-renormalizable Newton maps are rigid. More precisely, we prove that their Julia set carries no invariant line fields and that the topological conjugacy is equivalent to quasi-conformal conjugacy in this case

Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps

We give three families of parabolic rational maps and show that every Cantor set of circles as the Julia set of a non-hyperbolic rational map must be quasisymmetrically equivalent to the Julia set of one map in these families for suitable parameters. Combining a result obtained before, we give a complete classification of the Cantor circles Julia sets in the sense of quasisymmetric equivalence. Moreover, we study the regularity of the components of the Cantor circles Julia sets and establish a sufficient and necessary condition when a component of a Cantor circles Julia set is a quasicircle.Comment: 39 pages, 10 figures and 1 table, to appear in Discrete and Continous Dynamical Systems-

"half-electron (e/2)" -- free electron fractional charge induced by twisted light

Recent advances in ultrafast electron emission, microscopy, and diffraction reveal our capacity to manipulate free electrons with remarkable quantum coherence using light beams. Here, we present a framework for exploring free electron fractional charge in ultrafast electron-light interactions. An explicit Jackiw-Rebbi solution of free electron is constructed by a spatiotemporally twisted laser field, showcasing a flying topological quantum number with a fractional charge of e/2 (we call it "half-electron"), which is dispersion-free due to its topological nature. We also propose an Aharonov-Bohm interferometry for detecting these half-electrons. The half-electron is a topologically protected bound state in free-space propagation, expands its realm beyond quasiparticles with fractional charges in materials, enabling to advance our understanding of exotic quantum and topological effects of free electron wavefunction.Comment: 23 pages, 4 figures, supplementary materia

Secular trend of the leading causes of death in China from 2003 to 2013

Background: To analyze the epidemiological characteristics and secular trends of the leading causes of death in China.Methods: Data on the leading causes of death was collected from the Statistical Yearbook of China. Data for 11 years, from 2003 to 2013, was analyzed by regression analysis and chi-square test.Results: The top 3 causes of death from 2009 to 2013 were cancer, cerebrovascular disease, and cardiopathy, with the role of cardiopathy increasing over time (P<0.01). The proportion of deaths related to cardio-cerebrovascular diseases in urban and rural areas increased to 41.9% and 44.8%, respectively, in 2013, and was significantly higher than that for cancer, 25.5% and 22.4% (both P<0.01). Injury and poisoning in urban or rural areas represented the fifth leading cause of death. In 2006, endocrine, nutritional, and metabolic diseases were the sixth main cause of death, with 3.3% in urban areas. The role of genito-urinary,respiratory, and digestive system diseases in urban areas and genito-urinary system diseases in rural areas decreased during this period (all P<0.05).Conclusion: Cancer, cerebrovascular disease, and cardiopathy accounted for more than 67% of all deaths from 2007 to 2013 in China, and significantly increased in proportion from 2003 to 2013.Keywords: Causes of death; China; cancer; cardiovascular diseas