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The Hopkinson pressure bar was first suggested by Bertram Hopkinson in 1914 [1] as a way to measure stress pulse propagation in a metal bar. Later, in 1949 Herbert Kolsky [2] refined Hopkinson's technique by using two Hopkinson bars in series, now known as the split-Hopkinson bar, to measure stress and strain, incorporating advancements in the cathode ray oscilloscope in conjunction with ...
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Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
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Kernel density estimation of 100 normally distributed random numbers using different smoothing bandwidths.. In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights.
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where the average values (bars) and estimated standard deviations s are shown, as are the respective sample sizes. In principle, by using very large n the RE of the estimated g could be driven down to an arbitrarily small value. However, there are often constraints or practical reasons for relatively small numbers of measurements.