Spatially resolved electronic structure inside and outside the vortex cores of a high-temperature superconductor

Puzzling aspects of high-transition-temperature (high-Tc) superconductors include the prevalence of magnetism in the normal state and the persistence of superconductivity in high magnetic fields. Superconductivity and magnetism generally are thought to be incompatible, based on what is known about conventional superconductors. Recent results, however, indicate that antiferromagnetism can appear in the superconducting state of a high-Tc superconductor in the presence of an applied magnetic field. Magnetic fields penetrate a superconductor in the form of quantized flux lines, each of which represents a vortex of supercurrents. Superconductivity is suppressed in the core of the vortex and it has been suggested that antiferromagnetism might develop there. Here we report the results of a high-field nuclear-magnetic-resonance (NMR) imaging experiment in which we spatially resolve the electronic structure of near-optimally doped YBa2Cu3O7-delta inside and outside vortex cores. Outside the cores, we find strong antiferromagnetic fluctuations, whereas inside we detect electronic states that are rather different from those found in conventional superconductors.     

Gorenstein平坦预包络和预解式

我们在［７］中引进了Ｇｏｒｅｎｓｔｅｉｎ平坦模。本文将这类模的刻画推广到任意ｎ－Ｇｏｒｅｎｓｔｅｉｎ环上，并利用这类模刻画了ｎ－Ｇｏｒｅｓｔｅｉｎ环。而且，我们证明了任意ｎ－Ｇｏｒｅｎｓｔｅｉｎ环上Ｇｏｒｅｎｓｔｅｉｎ平坦预包络的存在性，并证得得这种环关于Ｇｏｒｅｎｓｔｅｉｎ平坦模的内射类的整体维数至多为ｎ－２，当ｎ≤１时，该整体维数为零。     

Evolution of indirect reciprocity

Natural selection is conventionally assumed to favour the strong and selfish who maximize their own resources at the expense of others. But many biological systems, and especially human societies, are organized around altruistic, cooperative interactions. How can natural selection promote unselfish behaviour? Various mechanisms have been proposed, and a rich analysis of indirect reciprocity has recently emerged: I help you and somebody else helps me. The evolution of cooperation by indirect reciprocity leads to reputation building, morality judgement and complex social interactions with ever-increasing cognitive demands.