Search results for "algebraic properties"
showing 3 items of 3 documents
Solution for an arbitrary number of coupled identical oscillators.
1992
We propose a solution to the problem of solving the Schr\"odinger equation for an arbitrary number of identical one-dimensional harmonically coupled oscillators raised by Fan Hong-yi [Phys. Rev. A 42, 4377 (1990)]. The relationship between the Fock spaces associated with the uncoupled and coupled oscillators is given as well as the coordinate representation of the eigenstates. In view of further applications, the Lie algebraic properties of the model are examined, and the generalization to three spatial dimensions is made.
Algebraic Properties to Optimize kNN Queries
2011
International audience; New applications that are being required to employ Database Management Systems (DBMSs), such as storing and retrieving complex data (images, sound, temporal series, genetic data, etc.) and analytical data processing (data mining, social networks analysis, etc.), increasingly impose the need for new ways of expressing predicates. Among the new most studied predicates are the similarity-based ones, where the two commonest are the similarity range and the k-nearest neighbor predicates. The k-nearest neighbor predicate is surely the most interesting for several applications, including Content-Based Image Retrieval (CBIR) and Data Mining (DM) tasks, yet it is also the mos…
Identifying Algebraic Properties to Support Optimization of Unary Similarity Queries
2009
International audience; Abstract. Conventional operators for data retrieval are either based on exact matching or on total order relationship among elements. Neither ofthem is appropriate to manage complex data, such as multimedia data, time series and genetic sequences. In fact, the most meaningful way tocompare complex data is by similarity. However, the Relational Algebra, employed in the Relational Database Management Systems (RDBMS),cannot express similarity criteria. In order to address this issue, we provide here an extension of the Relational Algebra, aimed at representingsimilarity queries in algebraic expressions. This paper identies fundamental properties to allow the integration…