Making MathWorld

Weisstein, Eric W.

doi:10.3888/tmj.10.3-3

Cited by 805 publications

(1,168 citation statements)

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“…It displayed on an oscilloscope can be used to give a quick estimate of the relative phase of two signals at the same frequency. The plots presented here represent X cos tY cos t Ø (6) Where the phase angle Ø is indicated in degrees by the number the top right of each plot. To use this catalogue, adjust the oscilloscope so that the X and Y signals have exactly the same amplitude (8 division's peak-to-peak) the pattern is accurately centred on the screen.…”

Section: Discussionmentioning

confidence: 99%

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Geometrical and Graphical Representations Analysis of Lissajous Figures in Rotor Dynamic System

Al-Khazali¹,

Askari²

2012

IOSRJEN

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This paper provides a broad review of the state of the art in Lissajous curve techniques, with particular regard to rotating machinery. Lissajous figure is a subject too wide-ranging to allow a comprehensive coverage of all of the areas associated with this field to be undertaken, and it is not the authors' intention to do so. However, a general overview of the broader issues of Lissajous curve is provided, it tells us about the phase difference between the two signals and the ratio of their frequencies, and several of the various methodologies are discussed. The experimental technique used Oscilloscopic with Rotor Rig; the display is usually a CRT or LCD panel which is laid out with both horizontal and vertical reference lines we can demonstrate the waveform images on an oscilloscope. The objective of this paper is to provide the reader with an insight into recent developments in the field of Lissajous curve, with particular regard to rotating machines. The subject of it in rotating machinery is vast, including the diagnosis of items such as rotating shafts, gears and pumps.

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Section: Discussionmentioning

confidence: 99%

“…Lissajous' setup was similar to the apparatus which is used today to project laser lightshows [6,7].…”

Section: Introductionmentioning

confidence: 99%

Geometrical and Graphical Representations Analysis of Lissajous Figures in Rotor Dynamic System

Al-Khazali¹,

Askari²

2012

IOSRJEN

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“…For spheres just 4 are necessary, as for planes. For more details, we refer the reader to [31]. Another vertex coloring result is given by Groetzsch's theorem [12].…”

Section: Graph Coloringmentioning

confidence: 99%

Efficient Loopy Belief Propagation Using the Four Color Theorem

Timofte

Gool

2013

Advanced Topics in Computer Vision

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Summary. Recent work on early vision such as image segmentation, image denoising, stereo matching, and optical flow uses Markov Random Fields. Although this formulation yields an NP-hard energy minimization problem, good heuristics have been developed based on graph cuts and belief propagation. Nevertheless both approaches still require tens of seconds to solve stereo problems on recent PCs. Such running times are impractical for optical flow and many image segmentation and denoising problems and we review recent techniques for speeding them up. Moreover, we show how to reduce the computational complexity of belief propagation by applying the Four Color Theorem to limit the maximum number of labels in the underlying image segmentation to at most four. We show that this provides substantial speed improvements for large inputs, and this for a variety of vision problems, while maintaining competitive result quality.

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“…In general, the distance between points and in a Euclidean space is given by Weisstein (Weisstein, 1999) …”

Section: Euclidean Distance Matrix Analysis (Edma)mentioning

confidence: 99%