The number of cubic partitions modulo powers of 5

The notion of cubic partitions is introduced by Hei-Chi Chan and named by Byungchan Kim in connection with Ramanujan's cubic continued fractions. Chan proved that cubic partition function has Ramanujan Type congruences modulo powers of $3$. In a recent paper, William Y.C. Chen and Bernard L.S. Lin studied the congruent property of the cubic partition function modulo $5$. In this note, we give Ramanujan type congruences for cubic partition function modulo powers of $5$.Comment: 17 pages,Submitte

Survival Analysis for the Association between Anti-hypertensive Medication and Time to Dementia with Competing Risk

Indiana University-Purdue University Indianapolis (IUPUI)Background: High blood pressure (HBP) is a common risk factor for dementia in elder population. Anti-hypertensive medications have been reported to associate with lower incidence rate of dementia in elder African Americans. The Apolipoprotein E (ApoE) epsilon 4 allele has been shown to be associated with both increased dementia and hypertension risk. However, previous studies had not examined the association between anti-hypertensive medications by ApoE status accounting for the competing risk from death. Methods: This is a prospective observational cohort study in 1236 community-dwelling hypertensive African Americans aged 65 years and older without dementia at baseline, with follow-up cognitive assessment and clinical evaluation for dementia diagnosis. Dementia-free mortality was considered as the competing risk. Of these, 707 participants were genotyped for ApoE status. Anti-hypertensive medication use was obtained from prescription records in the electronic medical records of the Indiana Network for Patient Care (INPC). Cox proportional cause-specific hazard (CSH) regression models were applied to assess the association between anti-hypertensive medication use and CSHs for dementia and death in ApoE epsilon 4 carriers and non-carriers separately. Key results: In ApoE epsilon 4 carriers, participants using anti-hypertensive medications had lower CSH of dementia compared to those not on anti-hypertensive medications before adjusting for blood pressure (BP) (hazard ratio (HR), 0.365; 95% CI, 0.170 – 0.785; p = 0.0099). The HR was no longer significant once BP control was adjusted (HR, 0.784; 95% CI, 0.197 – 3.123; p = 0.7303). Anti-hypertensive medications were not associated with dementia rate in non-carriers. In ApoE epsilon 4 non-carriers, participants on anti-hypertensive treatment showed significantly lower CSH of death compared to those not on mediations adjusting for covariates and BP control (HR, 0.237; 95% CI, 0.149 – 0.375; p < 0.0001). There was no significant association between anti-hypertensive medication use and death in ApoE epsilon 4 carriers. Conclusions: Anti-hypertensive medication was associated with lower dementia rate in ApoE epsilon 4 carriers and that rate was primarily mediated through BP control. In non-carriers, anti-hypertensive medication was significantly associated with lower mortality rate and this association appears to be independent of BP control

An Evaluation of the Intermediation Role of Hong Kong in Chinese Foreign Trade

Two different data sources can be used to study Hong Kong's role in intermediating China's foreign trade. One is the bilateral trade statistics between Hong Kong and the Chinese Mainland reported by National Bureau of Statistics of China, and the other is the bilateral trade statistics published by Census and Statistics Department, Hong Kong. The corresponding statistics are not comparable to each other because of the different statistical criteria adopted by each source. Hong Kong's intermediation role has been declining since the mid-1990s. A major long-run factor contributing to the decline is the structural change in Hong Kong's industry led by Hong Kong direct investment in China. The Chinese currency appreciation will have a further negative effect on Hong Kong's intermediation role. Hong Kong's offshore trade has increased rapidly in recent years, but its impact is not strong enough to offset the declining share of Hong Kong in Chinese foreign trade.Bilateral trade statistics, Intermediation role, China and Hong Kong