Let g ≥ 3 and n ≥ 0, and let Mg,n be the mapping class group of a surface of genus g with n boundary components. We prove that Mg,n contains a unique subgroup of index 2g−1(2g − 1) up to conjugation, a unique subgroup of index 2g−1(2g + 1) up to conjugation, and the other proper subgroups ofMg,n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of Mg,n...

1.1. Overview. In this paper, we prove a curvature-type result about Teichmüller space, in the style of synthetic geometry. We show that, in the Teichmüller metric, “thin-framed triangles are thin”—that is, under suitable hypotheses, the variation of geodesics obeys a hyperbolic-like inequality. This theorem has applications to the study of random walks on Teichmüller space. In particular, an a...

At present the most general algebraic and algorithmic frame for discussing the problem of indefinite summation is provided by the work of Karr (1981, 1985). His method, working over ΠΣ-fields which are certain difference field extensions of a constant field K, can be viewed as a summation analogue to Risch’s integration method. A difference field simply is a field F together with an automorphis...

The auto-oxidation of trans-1,2-disiloxybenzocyclobutene was found to be very efficient, giving endo-peroxide in quantitative yield. Each step of the mechanism of spin-forbidden addition of triplet oxygen O2((3)Σg) was studied by both EPR/spin trapping and theoretical studies.

Let G be an affine group scheme of finite type over a global field F . (We do not assume G to be reductive or smooth or connected.) Let AF denote the locally compact adele ring of F , S be a finite non-empty set of places of F that contains the archimedean places, and AF the factor ring of adeles with vanishing component along S; for FS = ∏ v∈S Fv, we have AF = FS ×AF . Recall that if X is a fi...

By using the path integral method , we calculate the Green functions of field strength of Yang-Mills theories on arbitrary nonorientable surfaces in Schwinger-Fock gauge. We show that the non-gauge invariant correlators consist of a free part and an almost x-independent part. We also show that the gauge invariant n-point functions are those corresponding to the free part , as in the case of ori...

We consider the structural similarity of small gallium clusters to the bulk structure of α-gallium, which has been previously described as a molecular metal, via density functional theory-based computations. Previous calculations have shown that the tetramer, the hexamer, and the octamer of gallium are all structurally similar to the α-phase. We perform an analysis of the bonding in these clust...