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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Patent•
07 Aug 2002
TL;DR: In this paper, a data management system for use in a consumer product development process comprises a computing device with a memory having a plurality of data bases including at least one database for each of the business units involved in the process.
Abstract: A data management system for use in a consumer product development process comprises a computing device with a memory having a plurality of data bases including at least one database for each of a plurality of business units involved in the product development process. An application program, for execution in the computing device, interfaces with at least one user to retrieve initial product information, to thereby produce a first product record in one of the plurality of databases. A sharing engine interacts with each of said databases to generate product records for each database using product information from said first product record, wherein each of said product records is organized by requirements from the database for which said product record is generated.
71 citations
TL;DR: A new randomized method for computing the min-plus product of two $n \times n$ matrices is presented, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense $n$-node directed graphs with arbitrary edge weights.
Abstract: We present a new randomized method for computing the min-plus product (a.k.a., tropical product) of two $n \times n$ matrices, yielding a faster algorithm for solving the all-pairs shortest path pr...
71 citations
01 Jan 1981
TL;DR: In this paper, the area-time product is used as a cost function for the design of a RAM-based system and an associative system, and it is shown that in each case an optimum design is possible using the area time product.
Abstract: Using VLSI technology, it will soon be possible to implement entire computing systems on one monolithic silicon chip. Conducting paths are required for communicating information throughout any integrated system. The length and organization of these communication paths place a lower bound on the area and time required for system operations. Optimal designs can be achieved in only a few of the many alternative structures. Two illustrative systems are analyzed in detail: a RAM-based system and an associative system. It is shown that in each case an optimum design is possible using the area-time product as a cost function.
71 citations
TL;DR: In this article, it was shown that the Mobius function is linearly disjoint from an analytic skew product on the 2 -torus, where the ergodic averages need not exist for all points.
Abstract: We prove that the Mobius function is linearly disjoint from an analytic skew product on the 2 -torus. These flows are distal and can be irregular in the sense that their ergodic averages need not exist for all points. The previous cases for which such disjointness has been proved are all regular. We also establish the linear disjointness of the Mobius function from various distal homogeneous flows.
71 citations