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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: This article presents a language independent theory of product line refinement, establishing refinement properties that justify stepwise and compositional product line evolution.

68 citations

Patent
29 Dec 2001
TL;DR: In this paper, the authors describe a configuration creation embodiment that includes receiving data corresponding to product or service options, identifying a solution space corresponding to the data, setting rules for evaluating constraint relationships of the data and for navigating the solution space, and generating cross-domain logical response engines corresponding to a navigation of the problem space.
Abstract: Aspects of the invention provide for creating, operating and updating product configurators. A configuration creation embodiment includes receiving data corresponding to product or service options, identifying a solution space corresponding to the data, setting rules for evaluating constraint relationships of the data and for navigating the solution space, and generating cross-domain logical response engines corresponding to a navigation of the solution space.

68 citations

Journal Article
TL;DR: In this paper, the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state was considered.
Abstract: We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability. Our proofs employ a novel kind of quantum reduction from a quantum information theory problem to the problem of computing the inner product. The communication required for the former problem can then be bounded by an application of Holevo's theorem. We also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit.

68 citations

Book ChapterDOI
01 Jan 2016
TL;DR: In this article, a wavelet expansion theory for positive definite distributions over the real line and a fractional derivative operator for complex functions in the distribution sense are defined. But the authors do not define a fraction operator for real distributions in the sense of a convolutional product.
Abstract: In this chapter we describe a wavelet expansion theory for positive definite distributions over the real line and define a fractional derivative operator for complex functions in the distribution sense. In order to obtain a characterization of the complex fractional derivative through the distribution theory, the Ortigueira-Caputo fractional derivative operator \(_{\text {C}}\text {D}^{\alpha }\) [13] is rewritten as a convolution product according to the fractional calculus of real distributions [8]. In particular, the fractional derivative of the Gabor–Morlet wavelet is computed together with its plots and main properties.

68 citations

01 Jan 1993
TL;DR: It is recommended that with the adoption of PCR technology in clinical laboratories, primers should be designed to produce amplicons of at least 240 to 350 bp (depending on G + C content) and that at least one effective method of controlling carryover contamination should be incorporated into each PCR protocol.

68 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