Topic
Division (mathematics)
About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.
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Journal Article•
TL;DR: In this article, the authors proposed an energy-efficient approach for the design of a low-complexity, low-energy particle filter for the U.S. Department of Energy's Office of Basic Energy Science.
Abstract: United States. Department of Energy. Office of Basic Energy Science. Division of Materials Sciences and Engineering. (award DE-SC0010526)
72 citations
01 Jan 2009
72 citations
TL;DR: In this article, the authors present an analytical approach for the partitioning of the flow cross-sectional area in steady and uniform three-dimensional channels based on the availability of surplus energy from the main flow.
Abstract: This paper presents an analytical approach for the partitioning of the flow cross-sectional area in steady and uniform three-dimensional channels. The mechanism and direction of energy transport from the main flow are analyzed first. Based on the availability of surplus energy from the main flow, a concept of energy transportation through a minimum relative distance toward a unit area on the wetted perimeter is proposed. This leads to a novel method to analytically divide the flow area into various parts corresponding to the channel shape and roughness composition of its wetted perimeter. The demarcated boundary or “division line” can be evaluated using a presented equation. The existence of the division lines, which are lines of zero Reynolds shear stress within the flow region, has been proven through comparison with turbulence characteristics measurements. The method is illustrated in a study of the shear stress distribution in smooth rectangular open channels. Analytical solutions, valid for all aspec...
71 citations
Patent•
06 Aug 1998
TL;DR: In this article, a dense wavelength division multiplexer for separating an optical signal into optical channels is proposed, which provides an ease in alignment and a higher tolerance to drifts due to the increase in the width of the pass band.
Abstract: A dense wavelength division multiplexer for separating an optical signal into optical channels is provided. The dense wavelength division multiplexer of the present invention includes a manner for inputting an optical signal where the optical signal comprises a plurality of optical channels; a manner for separating one or more of the plurality of optical channels by introducing a phase difference between at least two of the plurality of optical channels, where the manner of separation includes a polarization beam splitter; and a manner for outputting the separated plurality of optical channels along a plurality of optical paths. The dense wavelength division multiplexer of the present invention provides an ease in alignment and a higher tolerance to drifts due to the increase in the width of the pass band. Its separators may also be placed in a multi-stage parallel cascade configuration to provide for a lower insertion loss. It may also be easily modified to perform the add/drop function as it separates channels. The material required to manufacture and implement the dense wavelength division multiplexer is readily available and do not require special or expensive materials or processes. It is thus cost effective.
70 citations
01 Jan 2008
TL;DR: The case of compact convex sets is examined, and the results are applied to generalize the Hukuhara difference of fuzzy numbers, using their compact and convex level-cuts.
Abstract: We propose a generalization of the Hukuhara difference. First, the case of compact convex sets is examined; then, the results are applied to generalize the Hukuhara difference of fuzzy numbers, using their compact and convex level-cuts. Finally, a similar approach is seggested to attempt a generalization of division for real intervals and fuzzy numbers.
70 citations