If a class of nitely generated groups G is closed under isometric amalgamations along free subgroups, then every G 2 G can be quasi-isometrically embedded in a group Ĝ 2 G that has no proper subgroups of nite index. Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space X such that X has no non-trivial nite-sh...

We present a countably infinite number of new explicit co-homogeneity one Sasaki–Einstein metrics on S × S, in both the quasi-regular and irregular classes. These give rise to new solutions of type IIB supergravity which are expected to be dual to N = 1 superconformal field theories in four dimensions with compact or non-compact R-symmetry and rational or irrational central charges, respectivel...

We study cocoverings of triangulated categories, in the sense of Rouquier, and prove that for any regular cardinal α the condition of α-compactness, in the sense of Neeman, is local with respect to such cocoverings. This was established for ordinary compactness by Rouquier. Our result yields a new technique for proving that a given triangulated category is well-generated. As an application we d...

We present a countably infinite number of new explicit co-homogeneity one Sasaki–Einstein metrics on S × S, in both the quasi-regular and irregular classes. These give rise to new solutions of type IIB supergravity which are expected to be dual to N = 1 superconformal field theories in four dimensions with compact or non-compact R-symmetry and rational or irrational central charges, respectivel...

If a class of finitely generated groups G is closed under isometric amalgamations along free subgroups, then every G ∈ G can be quasi-isometrically embedded in a group Ĝ ∈ G that has no proper subgroups of finite index. Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space X such that X has no non-trivial fin...

In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique uppercontinuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinite...

Recent progress in the development of compact models for high speed bipolar transistors with quasi ballistic base widths on the order of a mean free path length is summarized The correctness of basing such models on the drift di usion equation is examined by comparing results with solutions to the Boltzmann transport equation Use ful and well founded compact expressions are presented for import...