where α > 0, β > 0 and p(t) and q(t) are continuous functions on an infinite interval [a,∞) satisfying p(t) > 0 and q(t) > 0 (t≥a). The growth bounds near t = ∞ of nonoscillatory solutions are obtained, and necessary and sufficient integral conditions
are established for the existence of nonoscillatory solutions having specific asymptotic growths as t→∞.
Authors:István Berkes, Lajos Horváth, Piotr Kokoszka and Qi-man Shao
We study the almost sure convergence of the Bartlett estimator for the asymptotic variance of the sample mean of a stationary
weekly dependent process. We also study the a.\ s.\ behavior of this estimator in the case of long-range dependent observations.
In the weakly dependent case, we establish conditions under which the estimator is strongly consistent. We also show that,
after appropriate normalization, the estimator converges a.s. in the long-range dependent case as well. In both cases, our
conditions involve fourth order cumulants and assumptions on the rate of growth of the truncation parameter appearing in the
definition of the Bartlett estimator.
A method has been developed for the correction of counting losses in NAA for the case of a mixture of short-lived radionuclides. It is applicable to systems with Ge detectors and Wilkinson or successive approximation ADC's and will correct losses from pulse pileup and ADC dead time up to 90%. The losses are modeled as a constant plus time-dependent terms expressed as a fourth order polynomial function of the count rates of the short-lived radionuclides. The correction factors are calculated iteratively using the peak areas of the short-lived radionuclides in the spectrum and the average losses as given by the difference between the live time and true time clocks of the MCA. To calibrate the system a measurement is performed for each short-lived nuclide. In a test where the dead time varied from 70% at the start of the measurement to 13% at the end, the measured activities were corrected with an accuracy of 1%.