Topic
Product (mathematics)
About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.
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TL;DR: In this paper, it is shown that the standard binning method utilized in the classical study of scattering processes dealing with more than three atoms, which consists in rounding the product vibrational actions (the x i's) to their nearest (the n i ''s), is not appropriate when the total energy disposal in the products is too low for the classical and quantum densities of vibrational states to be equal.
228 citations
TL;DR: This work describes the work on extracting attribute and value pairs from textual product descriptions, and presents promising results on apparel and sporting goods products and shows that the system can accurately extract attribute-value pairs from product descriptions.
Abstract: We describe our work on extracting attribute and value pairs from textual product descriptions. The goal is to augment databases of products by representing each product as a set of attribute-value pairs. Such a representation is beneficial for tasks where treating the product as a set of attribute-value pairs is more useful than as an atomic entity. Examples of such applications include demand forecasting, assortment optimization, product recommendations, and assortment comparison across retailers and manufacturers. We deal with both implicit and explicit attributes and formulate both kinds of extractions as classification problems. Using single-view and multi-view semi-supervised learning algorithms, we are able to exploit large amounts of unlabeled data present in this domain while reducing the need for initial labeled data that is expensive to obtain. We present promising results on apparel and sporting goods products and show that our system can accurately extract attribute-value pairs from product descriptions. We describe a variety of application that are built on top of the results obtained by the attribute extraction system.
228 citations
227 citations
TL;DR: In this article, the authors investigate some properties of a class of higher order cohomology operations of several variables, the higher products, defined by Massey as a generalization of his triple product.
Abstract: In this paper, we shall investigate some properties of a class of higher order cohomology operations of several variables. These operations, the higher products, were defined by Massey as a generalization of his triple product. There is a correspondence between the higher products and iterated Whitehead products in homotopy groups [5], [11]. It has been noted that the differentials in certain spectral sequences involving the Ext and Tor functors are related to Massey higher products [6], [9]. In particular, the differentials in a spectral sequence relating the cohomology of a space with that of its space of loops are generalized higher products. In the first part we establish a number of properties of these higher products. These properties indicate the similarities between the higher products and the cup product. In the final section, the higher products are specialized to an operation of one variable. In certain cases, this operation may be evaluated in terms of primary Steenrod operations (Theorems 14, 19). These results are useful in the computation of the higher product structure of a space with coefficients in a field.
226 citations