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Product (mathematics)

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


Papers
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Journal ArticleDOI
TL;DR: The exclusion principle of Maldacena and Strominger is seen to follow from deformed Heisenberg algebras associated with the chiral rings of S_N orbifold CFTs as mentioned in this paper.
Abstract: The exclusion principle of Maldacena and Strominger is seen to follow from deformed Heisenberg algebras associated with the chiral rings of S_N orbifold CFTs. These deformed algebras are related to quantum groups at roots of unity, and are interpreted as algebras of space-time field creation and annihilation operators. We also propose, as space-time origin of the stringy exclusion principle, that the $ADS_3 \times S^3$ space-time of the associated six-dimensional supergravity theory acquires, when quantum effects are taken into account, a non-commutative structure given by $SU_q(1,1) \times SU_q (2)$. Both remarks imply that finite N effects are captured by quantum groups $SL_q(2)$ with $q= e^{{i \pi \over {N + 1}}}$. This implies that a proper framework for the theories in question is given by gravity on a non-commutative spacetime with a q-deformation of field oscillators. An interesting consequence of this framework is a holographic interpretation for a product structure in the space of all unitary representations of the non-compact quantum group $SU_q(1,1)$ at roots of unity.

74 citations

Book ChapterDOI
Qi Su1, Kun Xiang1, Houfeng Wang1, Bin Sun1, Shiwen Yu1 
17 Dec 2006
TL;DR: In this article, a polarity lexicon is used to identify implicit product features expressed in product reviews in the context of opinion question answering, and each adjective in the lexicon was mapped to a set of predefined product features.
Abstract: This paper is concerned with automatic identification of implicit product features expressed in product reviews in the context of opinion question answering. Utilizing a polarity lexicon, we map each adjectives in the lexicon to a set of predefined product features. According to the relationship between those opinion-oriented words and product features, we could identify what feature a review is regarding without the appearance of explicit feature nouns or phrases. The results of our experiments proved the validity of this method.

74 citations

Journal ArticleDOI
TL;DR: Experiments indicate that the retrieving-and-filtering mechanism outperforms the prior retrieving-only mechanism in terms of generating a higher ratio of valuable product ideas.
Abstract: This paper presents a fuzzy CBR (case-based reasoning) technique for generating new product ideas from a product database for enhancing the functions of a given product (called the baseline product). In the database, a product is modeled by a 100-attribute vector, 87 of which are used to model the use-scenario and 13 are used to describe the manufacturing/recycling features. Based on the use-scenario attributes and their relative weights - determined by a fuzzy AHP technique, a fuzzy CBR retrieving mechanism is developed to retrieve product-ideas that tend to enhance the functions of the baseline product. Based on the manufacturing/recycling features, a fuzzy CBR mechanism is developed to screen the retrieved product ideas in order to obtain a higher ratio of valuable product ideas. Experiments indicate that the retrieving-and-filtering mechanism outperforms the prior retrieving-only mechanism in terms of generating a higher ratio of valuable product ideas.

73 citations

Patent
05 Jun 2007
TL;DR: In this article, a method and system for automatically creating an image product based on assets stored in a user database is presented, where a number of stored digital media files are analyzed to determine their semantic relationship to an event and are classified according to requirements and semantic rules.
Abstract: A method and system for automatically creating an image product based on assets stored in a user database. A number of stored digital media files are analyzed to determine their semantic relationship to an event and are classified according to requirements and semantic rules for generating the image product. These requirements and rules refine the association between the assets and the event for which the image product is generated. The assets which best meet the requirements and rules of the image product are ranked and the highest ranking ones are included in the image product.

73 citations

Journal ArticleDOI
TL;DR: In this article, the relationship between the scalar curvature of a warped product M Xf N of Riemann manifolds and those ones of M and N was established and the weights f were found to obtain constant curvatures on M X f N when M is compact.
Abstract: We establish the relationship between the scalar curvature of a warped product M Xf N of Riemann manifolds and those ones of M and N. Then we search for weights f to obtain constant scalar curvature on M Xf N when M is compact.

73 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
20244
20239,015
202219,171
20212,013
20202,263