A Characterization of Chover-Type Law of Iterated Logarithm

Let $0 < \alpha \leq 2$ and $- \infty < \beta < \infty$. Let $\{X_{n}; n \geq 1 \}$ be a sequence of independent copies of a real-valued random variable $X$ and set $S_{n} = X_{1} + \cdots + X_{n}, ~n \geq 1$. We say $X$ satisfies the $(\alpha, \beta)$-Chover-type law of the iterated logarithm (and write $X \in CTLIL(\alpha, \beta)$) if $\limsup_{n \rightarrow \infty} \left| \frac{S_{n}}{n^{1/\alpha}} \right|^{(\log \log n)^{-1}} = e^{\beta}$ almost surely. This paper is devoted to a characterization of $X \in CTLIL(\alpha, \beta)$. We obtain sets of necessary and sufficient conditions for $X \in CTLIL(\alpha, \beta)$ for the five cases: $\alpha = 2$ and $0 < \beta < \infty$, $\alpha = 2$ and $\beta = 0$, $1 < \alpha < 2$ and $-\infty < \beta < \infty$, $\alpha = 1$ and $- \infty < \beta < \infty$, and $0 < \alpha < 1$ and $-\infty < \beta < \infty$. As for the case where $\alpha = 2$ and $-\infty < \beta < 0$, it is shown that $X \notin CTLIL(2, \beta)$ for any real-valued random variable $X$. As a special case of our results, a simple and precise characterization of the classical Chover law of the iterated logarithm (i.e., $X \in CTLIL(\alpha, 1/\alpha)$) is given; that is, $X \in CTLIL(\alpha, 1/\alpha)$ if and only if $\inf \left \{b:~ \mathbb{E} \left(\frac{|X|^{\alpha}}{(\log (e \vee |X|))^{b\alpha}} \right) < \infty \right\} = 1/\alpha$ where $\mathbb{E}X = 0$ whenever $1 < \alpha \leq 2$.Comment: 11 page

The Davis-Gut law for independent and identically distributed Banach space valued random elements

An analog of the Davis-Gut law for a sequence of independent and identically distributed Banach space valued random elements is obtained, which extends the result of Li and Rosalsky (A supplement to the Davis-Gut law. J. Math. Anal. Appl. 330 (2007), 1488-1493)

On Complete Convergence and Strong Law for Weighted Sums of i.i.d. Random Variables

We improve and generalize the result of Stout (1974, Theorem 4.1.3). In particular, the sharp moment conditions are obtained and some well-known results can be obtained as special cases of the main result. The method of the proof is completely different from that in Stout. We also improve and generalize Li et al. (1995) strong law for weighted sums of i.i.d. random variables

Acute and acute-on-chronic kidney injury of patients with decompensated heart failure: impact on outcomes

BACKGROUND: Acute worsening of renal function, an independent risk factor for adverse outcomes in acute decompensated heart failure (ADHF), occurs as a consequence of new onset kidney injury (AKI) or acute deterioration of pre-existed chronic kidney disease (CKD) (acute-on-chronic kidney injury, ACKI). However, the possible difference in prognostic implication between AKI and ACKI has not been well established. METHODS: We studied all consecutive patients hospitalized with ADHF from 2003 through 2010 in Nanfang Hospital. We classified patients as with or without pre-existed CKD based on the mean estimated glomerular filtration rate (eGFR) over a six-month period before hospitalization. AKI and ACKI were defined by RIFLE criteria according to the increase of the index serum creatinine. RESULTS: A total of 1,005 patients were enrolled. The incidence of ACKI was higher than that of AKI. The proportion of patients with diuretic resistance was higher among patients with pre-existed CKD than among those without CKD (16.9% vs. 9.9%, P = 0.002). Compared with AKI, ACKI was associated with higher risk for in-hospital mortality, long hospital stay, and failure in renal function recovery. Pre-existed CKD and development of acute worsening of renal function during hospitalization were the independent risk factors for in-hospital death after adjustment by the other risk factors. The RIFLE classification predicted all-cause and cardiac mortality in both AKI and ACKI. CONCLUSIONS: Patients with ACKI were at greatest risk of adverse short-term outcomes in ADHF. Monitoring eGFR and identifying CKD should not be ignored in patients with cardiovascular disease

Efficacy and safety of Ozone Therapy for patients with chronic hepatitis B : A multicenter, randomized clinical trial [abstract]

Background. Ozone therapy has a long history. Some studies proved that ozone therapy was useful in treatment of virus hepatitis.Objective: To evaluate the efficacy and safety of new medical ozone therapy system for the treatment of chronic hepatitis B. Method. One hundred eighty-nine patients with chronic hepatitis B were included in this open-label, phase 3 study, and randomly assigned to receive ozone autohemotherapy with experimental ozone generator TianYi (group 1) or with ozone generator Humares (group 2) or oral diammonium glycyrrhizinate capsules (group 3) in a 1:1:1 ratio for 12 weeks. The primary efficacy end point was sera HBV DNA level of less than 1×103 IU/ml or having a more than 2 log10 reduction in HBV DNA level at the end of 12 weeks treatment as compared to baseline HBV DNA level. Secondary end points included HBeAg seroconversion, biochemical response, and combined response. Results. At the end of 12 weeks treatment, the proportion of patients reached the primary end point of virologic response in group 1, group 2, and group 3 were 22.4% (13/58, 95% CI, 12.5 to 35.3), 14.7 (9/61, 95% CI, 7.0 to 26.2) and 3.9% (2/51, 95% CI, 0.5 to 13.5), respectively (p=0.021) in the pre-protocol population. Virologic response occurred in more patients receiving ozone therapy with experimental device than patients receiving oral diammonium glycyrrhizinate capsules (mean difference 18.5%, 95% CI 6.3 to 31.5, p=0.005). However, there was no statistical difference in VR12 rates between the treatment of medical ozone therapy system with experimental device (group 1) and with Humares (group 2) (mean difference 7.7%, 95% CI -6.5 to 22.0, p=0.282). More HBeAg seroconversion in patients treated by Tianyi ozone therapy system than those treated by Humares ozone therapy device and oral diammonium glycyrrhizinate capsules (14.8%, 5.1% and 7.3%, respectively, P = 0.272). Higher biochemical response rate was observes in patients receiving ozone therapy than oral diammonium glycyrrhizinate capsules (31.6%, 36.7% and 24.0%, respectively, p = 0.359). The safety profile was similar for the three treatment groups and adverse events were .scare infrequent and mild. Conclusions. Ozone therapy had superior antiviral efficacy with a similar safety profile as compared with oral diammonium glycyrrhizinate capsules through week 12 treatment. Ozone therapy is also associated with normalized ALT and AST levels, demonstrating that ozone therapy could benefit the patients with chronic hepatitis B

Perbandingan Perhitungan Trafik Jam Sibuk CDMA 2000 1x Pada BTS Inner City Dan BTS Outer City Dengan Mempergunakan Metode ADPH, TCBH, FDMH Dan FDMP

Cellular communication system is a wireless communication system where the subscriber can move within a wide network coverage. Code Division Multiple Access (CDMA) is a multiuser access technology that is each user uses a unique code contained in the access channel in the system. Calculation and determination of peak hours can be done by several methods such as: Average Daily Peak Hour (ADPH), Time Consistent Busy Hour (TCBH), Fixed Daily Measurement Hour (FDMH), Fixed Daily Measurement Period (FDMP). The effectiveness of the channel should be determined by occupancy both at inner city territory and outer city &nbsp;territory location. Using design Erlang (Erl) for supply channel at Base Transceiver Station (BTS) that provided, BTS has a design Erlang of 369,83 Erl at inner city and it has a design Erlang of 241,8 Erl at outer city. Peak hour on the inner city occurred at 12:00 to 15:00, whereas the outer city of peak hour occurred at 18:00 to 21:00. Effectiveness value that determined by operator are : &lt;20% = low occupancy (not effective), 21% to 69% = normal occupancy (effective), and &gt; 70% = high occupancy (very effective). In this case occupancy values obtained in each method is between 21% to 69% which means effectiv

Predicting Progression of IgA Nephropathy: New Clinical Progression Risk Score

IgA nephropathy (IgAN) is a common cause of end-stage renal disease (ESRD) in Asia. In this study, based on a large cohort of Chinese patients with IgAN, we aim to identify independent predictive factors associated with disease progression to ESRD. We collected retrospective clinical data and renal outcomes on 619 biopsy-diagnosed IgAN patients with a mean follow-up time of 41.3 months. In total, 67 individuals reached the study endpoint defined by occurrence of ESRD necessitating renal replacement therapy. In the fully adjusted Cox proportional hazards model, there were four baseline variables with a significant independent effect on the risk of ESRD. These included: eGFR [HR = 0.96(0.95–0.97)], serum albumin [HR = 0.47(0.32–0.68)], hemoglobin [HR = 0.79(0.72–0.88)], and SBP [HR = 1.02(1.00–1.03)]. Based on these observations, we developed a 4-variable equation of a clinical risk score for disease progression. Our risk score explained nearly 22% of the total variance in the primary outcome. Survival ROC curves revealed that the risk score provided improved prediction of ESRD at 24th, 60th and 120th month of follow-up compared to the three previously proposed risk scores. In summary, our data indicate that IgAN patients with higher systolic blood pressure, lower eGFR, hemoglobin, and albumin levels at baseline are at a greatest risk of progression to ESRD. The new progression risk score calculated based on these four baseline variables offers a simple clinical tool for risk stratification