ON THE K-POWER PART RESIDUE FUNCTION

The main purpose of this paper is using the elementary and analytic methods to study the asymptotic properties of the k-power part residue, and give an interesting asymptotic formula for it

CONTEXT-BASED AUTOSUGGEST ON GRAPH DATA

Autosuggest is an important feature in any search applications. Currently, most applications only suggest a single term based on how frequent that term appears in the indexed documents or how often it is searched upon. These approaches might not provide the most relevant suggestions because users often enter a series of related query terms to answer a question they have in mind. In this project, we implemented the Smart Solr Suggester plugin using a context-based approach that takes into account the relationships among search keywords. In particular, we used the keywords that the user has chosen so far in the search text box as the context to autosuggest their next incomplete keyword. This context-based approach uses the relationships between entities in the graph data that the user is searching on and therefore would provide more meaningful suggestions

Kac-Moody Extensions of 3-Algebras and M2-branes

We study the 3-algebraic structure involved in the recently shown M2-branes worldvolume gauge theories. We first extend an arbitrary finite dimensional 3-algebra into an infinite dimensional 3-algebra by adding a mode number to each generator. A unique central charge in the algebra of gauge transformations appears naturally in this extension. We present an infinite dimensional extended 3-algebra with a general metric and also a different extension with a Lorentzian metric. We then study ordinary finite dimensional 3-algebras with different signatures of the metric, focusing on the cases with a negative eigenvalue and the cases with a zero eigenvalue. In the latter cases we present a new algebra, whose corresponding theory is a decoupled abelian gauge theory together with a free theory with global gauge symmetry, and there is no negative kinetic term from this algebra.Comment: v3: Appendix A added proving an identity; minor corrections and typos fixed. v4: slight refinement in section 2.1, no other change. 18 pages, Late