Trace-class for an arbitrary $H\sp{\ast} $-algebra

A Bound for the Nilpotency Class of a Lie Algebra

In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.

String Junctions for Arbitrary Lie Algebra Representations

We consider string junctions with endpoints on a set of branes of IIB string theory defining an ADE-type gauge Lie algebra. We show how to characterize uniquely equivalence classes of junctions related by string/brane crossing through invariant charges that count the effective number of prongs ending on each brane. Each equivalence class defines a point on a lattice of junctions. We define a me...

The Extension of an Arbitrary Boolean Algebra to an Implicative Boolean Algebra

Class Algebra for Ontology Reasoning

Class algebra provides a natural framework for sharing of ISA hierarchies between users that may be unaware of each other’s definitions. This permits data from relational databases, objectoriented databases, and tagged XML documents to be unioned into one distributed ontology, sharable by all users without the need for prior negotiation or the development of a “standard” ontology for each field...

Subpolynomial trace reconstruction for random strings and arbitrary deletion probability

The deletion-insertion channel takes as input a bit string x ∈ {0, 1}, and outputs a string where bits have been deleted and inserted independently at random. The trace reconstruction problem is to recover x from many independent outputs (called “traces”) of the deletion-insertion channel applied to x. We show that if x is chosen uniformly at random, then exp(O(log n)) traces suffice to reconst...