On the index of length four minimal zero-sum sequences

Let $G$ be a finite cyclic group. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\cdot\ldots\cdot(n_lg)$ where $g\in G$ and n_1, \ldots, n_l\in[1, \ord(g)], and the index \ind(S) of $S$ is defined to be the minimum of (n_1+\cdots+n_l)/\ord(g) over all possible $g\in G$ such that $\langle g \rangle =G$. A conjecture on the index of length four sequences says that every minimal zero-sum sequence of length 4 over a finite cyclic group $G$ with $\gcd(|G|, 6)=1$ has index 1. The conjecture was confirmed recently for the case when $|G|$ is a product of at most two prime powers. However, the general case is still open. In this paper, we make some progress towards solving the general case. Based on earlier work on this problem, we show that if $G=\langle g\rangle$ is a finite cyclic group of order $|G|=n$ such that $\gcd(n,6)=1$ and $S=(x_1g)(x_2g)(x_3g)(x_4g)$ is a minimal zero-sum sequence over $G$ such that $x_1,\cdots,x_4\in[1,n-1]$ with $\gcd(n,x_1,x_2,x_3,x_4)=1$, and $\gcd(n,x_i)>1$ for some $i\in[1,4]$, then \ind(S)=1. By using an innovative method developed in this paper, we are able to give a new (and much shorter) proof to the index conjecture for the case when $|G|$ is a product of two prime powers

Chlamydia trachomatis Serology in Women with and without Ovarian Cancer

Pelvic inflammation has been implicated in the genesis of ovarian cancer. We conducted serologic measurements of Chlamydia trachomatis antibodies as a surrogate marker of chlamydial pelvic inflammatory disease. Women with ovarian cancer (n = 521) and population-based controls (n = 766) were tested. IgG antibodies to serovar D of chlamydia elementary bodies (EBs) were detected using an ELISA assay. The odds of having ovarian cancer among women with the highest titers (≥0.40 OD units) were 0.6 (95% CI 0.4–0.9). These data do not support our earlier finding of elevated titers for antibodies to C. trachomatis among women with ovarian cancer

Two new flavonoids from Mosla soochouensis Matsuda

1078-108

Correlation of 3'-phosphoadenosine-5'-phosphosulfate synthase 1 (PAPSS1) expression with clinical parameters and prognosis in esophageal squamous cell carcinoma

Background. In recent years, 3'- phosphoadenosine-5'-phosphosulfate synthase 1 (PAPSS1) has been found to be highly expressed in some cancers and significantly associated with prognosis. Nevertheless, the role of PAPSS1 in esophageal squamous cell carcinoma (ESCC) is poorly understood. Methods. In this study, PAPSS1 expression in ESCC samples was researched through real-time quantitative polymerase chain reaction (qPCR), immunohistochemistry (IHC), and western blot (WB) techniques. siRNA technology was then used to inhibit PAPSS1 expression in ESCC cells, and cytologic tests were conducted to research gene affection on cell apoptosis, proliferation, and migration. Then, the expression of Bcl2, Ki67, and Snail was detected using qPCR and WB tests. These experimental data were analyzed by GraphPad software, where the P-value <0.05 was statistically significant. Results. The results showed that PAPSS1 expression level in ESCC tissues was higher than in the adjacent tissues. The data also showed that PAPSS1 was significantly correlated with N stage, and that the patients with high expressions had longer survival time. After transfection for 48 hours, the cell apoptosis rate of siRNA-PAPSS1 transfected groups decreased significantly, whereas the cell proliferation rate and migration ability increased relative to the control. At the same time, the expression levels of Bcl2, Ki67 and Snail were all upregulated by siRNA-PAPSS1. PAPSS1, however, was suppressed. Conclusions. PAPSS1 may be an ESCC suppressor gene, and its specific molecular mechanism in ESCC needs to be further studied