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- Author or Editor: K. Fukuyama x
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Abstract
Takahashi [4] gave a concrete upper bound estimate of the law of the iterated logarithm for Σf(n k x). We extend this result and prove the best possibility of this bound.
Abstract
It is proved that two types of discrepancies of the sequence {θ n x} obey the law of the iterated logarithm with the same constant. The appearing constants are calculated explicitly for most of θ > 1.
Abstract
For any unbounded sequence {n k } of positive real numbers, there exists a permutation {n σ(k)} such that the discrepancies of {n σ(k) x} obey the law of the iterated logarithm exactly in the same way as the uniform i.i.d. sequence {U k }.
Abstract
An upper bound estimate in the law of the iterated logarithm for Σf(n k ω) where nk+1∫nk≧ 1 + ck -α (α≧0) is investigated. In the case α<1/2, an upper bound had been given by Takahashi [15], and the sharpness of the bound was proved in our previous paper [8]. In this paper it is proved that the upper bound is still valid in case α≧1/2 if some additional condition on {n k} is assumed. As an application, the law of the iterated logarithm is proved when {n k} is the arrangement in increasing order of the set B(τ)={1 i 1...qτ i τ|i1,...,iτ∈N 0}, where τ≧ 2, N 0=NU{0}, and q 1,...,q τ are integers greater than 1 and relatively prime to each others.
Kaufman and Philipp [6] and Dhompongsa [3] proved a uniform law of the iterated logarithm for ∑f(n k t). In this paper, we give a concrete upper bound for these results. Our bound is best possible in some cases.
Abstract
Some improvements of the detection sensitivity in pulse time interval analysis (TIA) based on selective extraction of successively 
- correlated decay events within millisecond order from random or background events, were established by the utilization of PSD, to reject 
/
-pulses from -ones and a simple chemical procedure of radium separation, together with the use of well resolved scintillator. By applying the PSD, the contribution of -decay events was completely eliminated in both the -spectra and the TIA distribution curves as well as the improvement into clear energy resolution and the enhancement of detection sensitivity for the TIA. As a result, the TIA and -spectrometric analysis of226Ra-extract showed the existence of223Ra (Ac-series) and /-correlated events with correlated life (due to 0.16 ms due to214Bi()
214Po()) along with a singly well resolved -peak to be useful for the determination of226Ra (U-series). The difference of half-lives (145 and 1.78 ms) due to216Po and215Po (direct daughters of224Ra for Th-series and223Ra for Ac-series, respectively) was also proven for the possibility of the simultaneous determination of both correlated events by using the TIA/PSD combined with chemical separation and liquid scintillation counting method. Finally, the simultaneous determination of three natural decay series, which include U-, Th- and Ac-series nuclides, have been conveniently carried out for some environmental samples using the present method combined with225Ra yield tracer (Np-series).
