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Now we extend one method into a sequence of binomial
data, propose a stepwise confidence interval method for toxic-ity
study, and also in our paper, two methods of constructing intervals for the
risk difference are proposed. The first one is based on the well-known
conditional confidence intervals for odds ratio, and the other one comes from
Santner“small-sample confidence intervals for the difference of two success
probabilities”, and it produces exact intervals, through employing our method.
This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or a localized function. This study finds that wavelet’s dual can be a harmonic which is not local. This finding leads to new CWT inversion formulas. It also justifies the concept of normal wavelet transform which is useful in time-frequency analysis and time-frequency filtering. This study also proves a law for CWT inversion: either wavelet or its dual must integrate to zero.
Shockwave detection is critical in
analyzing shockwave structure and location. High speed video imaging systems
are commonly used to obtain image frames during shockwave control experiments.
Image edge detection algorithms become natural choices in detecting shockwaves. In this paper, a computer
software system designed for shockwave detection is introduced. Different image
edge detection algorithms, including Roberts, Prewitt, Sobel, Canny, and Laplacian of Gaussian, are implemented and
can be chosen by the users to easily and accurately detect the shockwaves. Experimental results show that the
system meets the design requirements and can accurately detect shockwave for
further analysis and applications.