Product (mathematics)

About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.

Content aggregation method and apparatus for an on-line product catalog

Abstract: The method comprises processing plural product information records from the product information sources into one or more groups based on which product information records are likely to correspond to the same product, correlating a unique product ID corresponding to the product associated with each of said groups to identify the product, comparing each identified product to categories of a taxonomy to determine a category for the identified products in the taxonomy, and determining attributes for each categorized product based on the product information records corresponding to each group, creating product specifications based on the determined attributes and storing the product specification in the corresponding determined categories of the taxonomy.

Coherent state induced star product on R λ 3 and the fuzzy sphere

Abstract: Using the Hopf fibration and starting from a four-dimensional noncommutative Moyal plane ${R}_{\ensuremath{\theta}}^{2}\ifmmode\times\else\texttimes\fi{}{R}_{\ensuremath{\theta}}^{2}$ we obtain a star product for the noncommutative (fuzzy) ${R}_{\ensuremath{\lambda}}^{3}$ defined by $[{x}^{i}{,x}^{j}]=i\ensuremath{\lambda}{\ensuremath{\epsilon}}_{\mathrm{ijk}}{x}^{k}.$ Furthermore, we show that there is a projection function which allows us to reduce the functions on ${R}_{\ensuremath{\lambda}}^{3}$ to that of the fuzzy sphere, and hence we introduce a new star product on the fuzzy sphere. We will then briefly discuss how using our method one can extract information about the field theory on the fuzzy sphere and ${R}_{\ensuremath{\lambda}}^{3}$ from the corresponding field theories on ${R}_{\ensuremath{\theta}}^{2}\ifmmode\times\else\texttimes\fi{}{R}_{\ensuremath{\theta}}^{2}$ space.

Technical Note: Mathematical Properties of the Optimal Product Line Selection Problem Using Choice-Based Conjoint Analysis

Abstract: Selecting and pricing product lines is an essential activity in many businesses. In recent years, quantitative approaches for such tasks have been gaining in popularity. One often-employed method is to use data from traditional rankings/ratings-based conjoint analysis and attack the product line selection problem with enumeration or heuristics. In this note, we employ a relatively new methodology known as choice-based conjoint analysis (to model customer preferences) and investigate its mathematical properties when used to model the product line selection problem. Despite some inherent limitations resulting from its aggregated formulation, we show that this more parsimonious conjoint approach has some special mathematical properties that lead to an efficient optimal algorithm to tackle the product line/price selection problem. As a result, problems of realistic size can be solved efficiently using standard, commercially available mathematical programming codes.

A Fedosov Star Product of Wick Type for Kähler Manifolds

Abstract: In this Letter we compute some elementary properties of the Fedosov star product of Weyl type, such as symmetry and order of differentiation. Moreover, we define the notion of a star product of the Wick type on every Kahler manifold by a straightforward generalization of the corresponding star product in Cn: the corresponding sequence of bidifferential operators differentiates its first argument in holomorphic directions and its second argument in antiholomorphic directions. By a Fedosov type procedure, we give an existence proof of such star products for any Kahler manifold.