72,809 research outputs found
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
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