In this note we construct a poset map from a Boolean algebra to the Bruhat order which unveils an interesting connection between subword complexes, sorting orders, and certain totally nonnegative spaces. This relationship gives a simple new proof that the proper part of Bruhat order is homotopy equivalent to the proper part of a Boolean algebra — that is, to a sphere. We also obtain a geometric...

In a study of the word problem for groups, R. J. Thompson considered a certain group F of self-homeomorphisms of the Cantor set and showed, among other things, that F is nitely presented. Using results of K. that F is the fundamental group of a nite two-complex Z 2 having Euler characteristic one and which is Cockcroft, in the sense that each map of the two-sphere into Z 2 is homologically triv...

We introduce a notion of metric on a Lie groupoid, compatible with multiplication, and we study its properties. We show that many families of Lie groupoids admit such metrics, including the important class of proper Lie groupoids. The exponential map of these metrics allows us to establish a linearization theorem for Riemannian groupoids, obtaining both a simpler proof and a stronger version of...

Kawamata has shown that the quasi-Albanese map of a quasi-projective variety with log-irregularity equal to dimension and log-Kodaira 0 is birational. In this note, we show under these hypotheses proper in codimension 1 as conjectured by Iitaka.

Determination of the starter torque-speed diagram is a major task in the design or selection of a proper gas turbine starter. In this paper, the maximum power of the MGT-40 gas turbine starter was calculated based on the dynamics of the rotor, start-up logic, and compressor map. In a recent research, the pressure ratio was assumed as a linear function of the rotor speed and the required starter...

We prove that the norm-square of a moment map associated to a linear action of a compact group on an affine variety satisfies a certain gradient inequality. This allows us to bound the gradient flow, even if we do not assume that the moment map is proper. We describe how this inequality can be extended to hyperkähler moment maps in some cases, and use Morse theory with the norm-squares of hyper...

A liquid chromatography tandem-mass spectrometry method was developed to map the eleven disulfide bonds in Pfs25, a malaria transmission-blocking vaccine candidate. The compact and complex nature of Pfs25 has led to difficulties in prior peptide mapping efforts. Here, we report confirmation of proper disulfide pairing of a recombinant Pfs25, by optimizing denaturation and digestion with trypsin...