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

Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities

In this paper, we give a conjecture, which generalises Euler's partition theorem involving odd parts and different parts for all moduli. We prove this conjecture for two family partitions. We give $q$-difference equations for the related generating function if the moduli is three. We provide new companions to Rogers-Ramanujan-Andrews-Gordon identities under this conjecture.Comment: 12 pages, revised versio

Screening of oleaginous yeast with xylose assimilating capacity for lipid and bio-ethanol production

Microbial oil is a promising new biodiesel resource, which have great potential in industrial-scale production. In our preliminary study, 57 oleaginous yeast with xylose assimilating capacity were isolated from 13 soil samples, 16 strains were identified as potential lipid biomass producer. Four strains which showed higher lipid content were used for further ethanol fermentation at different conditions. Strain 9-44 belonging to Pichia guillermondii showed the highest ethanol production (21.91 g/l), and the theoretical ethanol yield was 85.90%. Our study will be of great significance for coupling of lipid and bio-ethanol production, and also provide a choice of cellulocis biomass utilization.Key words: Microbial oil, oleaginous yeast, Pichia guillermondii, bio-ethanol, cellulocis biomass

Genetic polymorphisms of MDM2 and TP53 genes are associated with risk of nasopharyngeal carcinoma in a Chinese population

<p>Abstract</p> <p>Background</p> <p>The tumor suppressor TP53 and its negative regulator MDM2 play crucial roles in carcinogenesis. Previous case-control studies also revealed <it>TP53 </it>72Arg>Pro and <it>MDM2 </it>309T>G polymorphisms contribute to the risk of common cancers. However, the relationship between these two functional polymorphisms and nasopharyngeal carcinoma (NPC) susceptibility has not been explored.</p> <p>Methods</p> <p>In this study, we performed a case-control study between 522 NPC patients and 722 healthy controls in a Chinese population by using PCR-RFLP.</p> <p>Results</p> <p>We found an increased NPC risk associated with the <it>MDM2 </it>GG (odds ratio [OR] = 2.83, 95% confidence interval [CI] = 2.08-3.96) and TG (OR = 1.49, 95% CI = 1.16-2.06) genotypes. An increased risk was also associated with the <it>TP53 </it>Pro/Pro genotype (OR = 2.22, 95% CI = 1.58-3.10) compared to the Arg/Arg genotype. The gene-gene interaction of <it>MDM2 </it>and <it>TP53 </it>polymorphisms increased adult NPC risk in a more than multiplicative manner (OR for the presence of both <it>MDM2 </it>GG and <it>TP53 </it>Pro/Pro genotypes = 7.75, 95% CI = 3.53-17.58).</p> <p>Conclusion</p> <p>The findings suggest that polymorphisms of <it>MDM2 </it>and <it>TP53 </it>genes may be genetic modifier for developing NPC.</p