• Korean Journal of Mathematics
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• v.26 no.2
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• pp.155-166
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• 2018

Consider FARIMA time series with innovations that have infinite variances. We are interested in the estimation of self-similarities $H_n$ of FARIMA(0, d, 0) by using modified R/S statistic. We can confirm that the $H_n$ converges to Hurst parameter $H=d+\frac{1}{2}$. Finally, we figure out ARMA and minimum variance power spectrum density of FARIMA processes.

• The Korean Journal of Nuclear Medicine Technology
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• v.14 no.2
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• pp.150-154
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• 2010

Purpose: Ejection fraction (EF) is one of the most important factors that evaluate heart function. Recently, according to echocardiography and myocardial perfusion SPECT, the number of gated blood pool scan (planar GBP) is declining. Measurement of left ventricular ejection fraction using gated blood pool SPECT (GBPS) is known as relatively correspond with echocardiography. We compared EF derived from plnar GBP, GBPS and echocadiography using modified simpson method to determine the accuracy. Materials and Methods: From January 2007 to June 2010, planar GBP and GBPS were performed on 34 patients who admitted to Pusan National University Hospital (men 23, women 11, mean age $52.6{\pm}27.2$). Each patient was injected with $^{99m}{TcO_4}^-$ of 20 mCi after pyrophosphate injection and then scanned using both planar GBP and GBPS techniques. For image analysis, we use ADAC Laboratories, Ver. 4.20 software. The result analyzed was processed by SPSS 17.0 Win statistic program and statistical method applied in data analysis is one-way anova, Tukey's post hoc test, pearson correlation test. Results: One-way anova test show no significant difference (planar GBP $56.3{\pm}13.9%$; GBPS $60.4{\pm}16.0%$; echocardiography $59.1{\pm}14.4%$, p=0.486, p>0.05). Tukey's post hoc test show no significant difference (planar GBP-echocardiography p=0.697; GBPS-echocardiography p=0.928; planar GBP-GBPS p=0.469, p>0.05). Values for EF obtained with planar GBP and GBPS correlated well with those obtained with echocardiography (planar-echocardiography r=0.697; GBPS-echocardiography r=0.928; planar GBP-GBPS r=0.469). Conclusion: The problems of accuracy and reproducibility for planar GBP still remain. But planar GBP is a safe and non-invasive method. In addition, planar GBP is useful to evaluate patient with low resolution echocardiography images. GBPS is not appicated clinically. but GBPS can be obtain various left ventricular functional parameters. planar GBP, GBPS and echocardiography show a good correlation between each other. Therefore, planar GBP and GBPS are useful for evaluating left ventricular ejection fraction.