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Mapping the B1 Field Distribution with Nonideal Gradients in a High-Resolution NMR Spectrometer

Geoffrey Bodenhausen
1999
Journal Articles

Abstract

To understand the behavior of many NMR expts., it is important to det. the spatial distribution of the B1 field. In this paper, we show how this distribution can be mapped independently of spin d., coil responsiveness, and nonlinearities of the B0 field gradients. As a byproduct we obtain a map of the (possibly nonlinear) spatial variation of the B0 field gradients used in the imaging procedure. (c) 1999 Academic Press. [on SciFinder (R)]

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Geoffrey Bodenhausen
1999
Journal Articles

Abstract

Official source

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In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

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In probability theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other F-tests. The F-distribution with d1 and d2 degrees of freedom is the distribution of where and are independent random variables with chi-square distributions with respective degrees of freedom and .

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Spatial analysis is any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures.

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