Modules (also known as profunctors or distributors) and morphisms among them subsume categories and functors and provide more general and abstract framework to explore the theory of structures. In this book we generalize and redevelop the basic notions and results of category theory using this framework of modules. Topics Chapter 1 introduces modules and cells among them. A moduleM ∶ X⇢A from a...

Let LD8(1, 0) and LE8(1, 0) be the simple vertex operator algebras associated to untwisted affine Lie algebra ĝD8 and ĝE8 with level 1 respectively. In the 1980s by I. Frenkel, Lepowsky and Meurman as one of the many important preliminary steps toward their construction of the moonshine module vertex operator algebra, they use roots lattice showing that LD8(1, 0) can embed into LE8(1, 0) as a v...

We describe a concept to employ Trusted Computing technology to secure Conditional Access Systems (CAS) for DVB. Central is the embedding of a trust anchor, e.g. a trusted platform module (TPM) into the set-top box or Conditional Access Module. Various deployment scenarios exhibit possibilities of charging co-operation with mobile network operators (MNO) via trusted mobile devices, or with othe...

We prove that an arbitrary (not necessarily countably generated) Hilbert G −A module on a G − C∗ algebra A admits an equivariant embedding into a trivial G−A module, provided G is a compact Lie group and its action on A is ergodic.

ERRATUM: It has come to our attention that there was a flaw in our use of Socher et al. (2011)’s recursive auto-encoder (RAE). Whereas the original version of this paper used one and the same pair of compositional matrices W (1),W (2) for composing word vectors from all involved sources, in this corrected version we retrained the RAE’s compositional matrices for each word vector source. This so...

it has been proved that sphericity testing for digraphs is an np-complete problem. here, we investigate sphericity of 3-connected single source digraphs. we provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $o(n)$ time.

Starting university is challenging. Students require resilience to face the inevitable challenges of life, yet many may not be equipped with strategies they need. In this research, we explored changes in following delivery a building module within core first-year course. Psychology students at University South Australia completed adapted Resilience Work Scale two separate time points and undert...