Product (mathematics)

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

Web page annotation systems

Abstract: Methods and apparatus are provided for annotating web pages A data processing system (1), connectable to a user station (2), receives web page data retrieved from the Internet (3) in response to a user's request The web page data is analyzed to select, by subject matter, at least one product class to which the subject matter relates from a plurality of product classes represented in a product classification database (10) For each product class, the database (10) stores a set of product data items indicative of attributes of products in that class Annotations available for display are each associated with a display condition dependent on one or more product data items in the database (10) For each product class selected following analysis of the web page data, product data items are retrieved from the database (10) and used to evaluate the annotation display conditions If display conditions are satisfied, annotation data indicative of the annotations is supplied to the user station (2) for display

Apparatus, system, and method for optical verification of product information

Abstract: An apparatus, system, and method are disclosed for verifying product information. The apparatus includes an identification module configured to obtain a first set of data associated with a product. A database, in communication with the identification module, is configured to store data associated with the product in a database. An image module is configured to capture at least one image of a product. A recognition module, in communication with the image module, is configured to obtain a second set of data from at least one captured image of the product. A determination module configured to determine whether a match exists between the second set of data and the first set of data by comparing the second set of data with data in the database.

Method for relevancy ranking of products in online shopping

Abstract: A method, system and computer program product for ranking of products related to a product category in online shopping. A search query for one or more products is received from a user. A set of attributes and features of each attribute are extracted related to a product category for each of the one or more products. A score of each attribute is calculated based on the features. Further, the weights are assigned to each of the one or more attributes and a product rank is generated for each of the one or more products based on assigned weights and the score by using a predefined relevancy-ranking algorithm.

Seminormal forms and Gram determinants for cellular algebras

Abstract: This paper develops an abstract framework for constructing ``seminormal forms'' for cellular algebras. That is, given a cellular R-algebra A which is equipped with a family of JM-elements we give a general technique for constructing orthogonal bases for A, and for all of its irreducible representations, when the JM-elements separate A. The seminormal forms for A are defined over the field of fractions of R. Significantly, we show that the Gram determinant of each irreducible A-module is equal to a product of certain structure constants coming from the seminormal basis of A. In the non-separated case we use our seminormal forms to give an explicit basis for a block decomposition of A. The appendix, by Marcos Soriano, gives a general construction of a complete set of orthogonal idempotents for an algera starting from a set of elements which act on the algebra in an upper triangular fashion. The appendix shows that constructions with "Jucys-Murphy elements"depend, ultimately, on the Cayley-Hamilton theorem.