The Atiyah–Singer index theorem, a landmark achievement of the early 1960s, brings together ideas in analysis, geometry, and topology. We recount some antecedents motivations, various forms its implications, which extend to present.

JCB • VOLUME 170 • NUMBER 1 • 2005 12 Spectrin is peripheral n 1971, “next to nothing was known about the organization of membrane proteins,” says S. Jonathan Singer (University of California, San Diego, CA). Singer had proposed that there were two kinds of membrane proteins— integral and peripheral—but the idea was, at the time, largely speculative (Singer, 1971). It was a collaborative study ...

We investigate blow-up manifolds of ${T}^{2}/{\mathbb{Z}}_{N}(N=2,3,4,6)$ orbifolds with magnetic flux. First, we construct the and zero-mode wave functions on them more precisely. In particular, through an appropriate singular gauge transformation, winding numbers ${T}^{2}/{\mathbb{Z}}_{N}$ can be replaced localized curvature flux at orbifold fixed points. addition, since have no singularities...

The Chinese musical idol show, Dimension Nova, (produced by entertainment company IQIYI) follows the same formula as other shows where a panel of judges choose from pool hopefuls to find best singer. However, contestants for Nova are virtual beings. way these characters presented, and show is edited, intends creations be focus audience, not creators behind them. Thus, augmented reality cameras ...

The Agaricales are the largest clade of mushroom-forming fungi, in Colombia, with 544 species approximately 16,000 currently recognized worldwide phylum Basidiomycota. We document seven Agaricaceae for first time from Colombian Caribbean region. Two these newly recorded country: Leucoagaricus lilaceus Singer and roseilividus (Murrill) E. Ludw. Five reported time: Agaricus griseorimosus Pegler, ...

Helga Kuhse and Peter Singer recently examined the view expressed by John Lorber that whereas at times it is permissible to allow severely handicapped infants to die, killing them must never be allowed. In attempting to demonstrate the mistaken nature of Lorber's fear that allowing active infanticide would lead us onto a slippery slope Kuhse and Singer make much use of John Harris's paper in th...

This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison–Singer problem. The result shows that every unitnorm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the res...

These notes cover various topics in C*-algebras and functional analysis related to the Kadison-Singer Problem[13]. They are intended for an audience that is familiar with some of the basic results in the theory of Banach and C*-algebras, but have sufficient references that they can be read with somewhat less preparation. These notes are based on a course taught in the Fall 2007 at the Universit...

We give a very simple derivation of the Atiyah-Patodi-Singer (APS) index theorem and its small generalization by using path integral massless Dirac fermions. It is based on Fujikawa's argument for relation between axial anomaly Atiyah-Singer theorem, only minor modification that sufficient to show APS theorem. The key ingredient identification boundary condition as physical state vectors in Hil...

The significant increase in the numbers of students with autism combined with the need for better trained teachers (National Research Council, 2001) call for research on the effectiveness of alternative methods, such as consultation, that have the potential to improve service delivery. Data from 2 randomized controlled single-blind trials indicate that an autism-specific consultation planning f...