Binomial Difference Ideal and Toric Difference Variety

In this paper, the concepts of binomial difference ideals and toric difference varieties are defined and their properties are proved. Two canonical representations for Laurent binomial difference ideals are given using the reduced Groebner basis of Z[x]-lattices and regular and coherent difference ascending chains, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, perfect, and toric are given in terms of their support lattices which are Z[x]-lattices. The reflexive, well-mixed, and perfect closures of a Laurent binomial difference ideal are shown to be binomial. Four equivalent definitions for toric difference varieties are presented. Finally, algorithms are given to check whether a given Laurent binomial difference ideal I is reflexive, prime, well-mixed, perfect, or toric, and in the negative case, to compute the reflexive, well-mixed, and perfect closures of I. An algorithm is given to decompose a finitely generated perfect binomial difference ideal as the intersection of reflexive prime binomial difference ideals.Comment: 72 page

Gene duplication and an accelerated evolutionary rate in 11S globulin genes are associated with higher protein synthesis in dicots as compared to monocots

Background: Seed storage proteins are a major source of dietary protein, and the content of such proteins determines both the quantity and quality of crop yield. Significantly, examination of the protein content in the seeds of crop plants shows a distinct difference between monocots and dicots. Thus, it is expected that there are different evolutionary patterns in the genes underlying protein synthesis in the seeds of these two groups of plants. Results: Gene duplication, evolutionary rate and positive selection of a major gene family of seed storage proteins (the 11S globulin genes), were compared in dicots and monocots. The results, obtained from five species in each group, show more gene duplications, a higher evolutionary rate and positive selections of this gene family in dicots, which are rich in 11S globulins, but not in the monocots. Conclusion: Our findings provide evidence to support the suggestion that gene duplication and an accelerated evolutionary rate may be associated with higher protein synthesis in dicots as compared to monocots

Hydrogen production by mixed culture of several facultative bacteria and anaerobic bacteria

AbstractThe characteristic of hydrogen production by facultative anaerobic bacteria, obligate anaerobic bacteria and their mixed culture was studied by the batch culture method. The results showed that, due to the synergistic effect between facultative bacteria and anaerobic bacteria, the ability of hydrogen production in the mixed culture was much better than that in the pure culture. Especially, the culture Scheme No.7 mixed up with three strains (Bacterium. E: Bacterium. B: Bacterium. P = 1:1:1) not only had the best hydrogen production capacity (1.885 mol H2/mol glucose) and maximum average hydrogen production rate (212.2 mL/(L·h)), but also had stable hydrogen production under continuous culture conditions, which was 1.968 mol H2/mol glucose

δ\delta meson effects on neutron stars in the modified quark-meson coupling model

The properties of neutron stars are investigated by including $\delta$ meson field in the Lagrangian density of modified quark-meson coupling model. The $\Sigma^-$ population with $\delta$ meson is larger than that without $\delta$ meson at the beginning, but it becomes smaller than that without $\delta$ meson as the appearance of $\Xi^-$. The $\delta$ meson has opposite effects on hadronic matter with or without hyperons: it softens the EOSes of hadronic matter with hyperons, while it stiffens the EOSes of pure nucleonic matter. Furthermore, the leptons and the hyperons have the similar influence on $\delta$ meson effects. The $\delta$ meson increases the maximum masses of neutron stars. The influence of $(\sigma^*,\phi)$ on the $\delta$ meson effects are also investigated.Comment: 10 pages, 6 figures, 4 table