On the square-free number sequence

The main purpose of this paper is to study the number of the square-free number sequence, and give two interesting asymptotic formulas for it. At last, give another asymptotic formula and a corollary

Bem1p contributes to secretory pathway polarization through a direct interaction with Exo70p.

The exocyst serves to tether secretory vesicles to cortical sites specified by polarity determinants, in preparation for fusion with the plasma membrane. Although most exocyst components are brought to these sites by riding on secretory vesicles as they are actively transported along actin cables, Exo70p displays actin-independent localization to these sites, implying an interaction with a polarity determinant. Here we show that Exo70p directly and specifically binds to the polarity determinant scaffold protein Bem1p. The interaction involves multiple domains of both Exo70p and Bem1p. Mutations in Exo70p that disrupt its interaction with Bem1, without impairing its interactions with other known binding partners, lead to the loss of actin-independent localization. Synthetic genetic interactions confirm the importance of the Exo70p-Bem1p interaction, although there is some possible redundancy with Sec3p and Sec15p, other exocyst components that also interact with polarity determinants. Similar to Sec3p, the actin-independent localization of Exo70p requires a synergistic interaction with the phosphoinositide PI(4,5)P2

Bowen entropy for actions of amenable groups

Bowen introduced a definition of topological entropy of subset inspired by Hausdorff dimension in 1973 \cite{B}. In this paper we consider the Bowen's entropy for amenable group action dynamical systems and show that under the tempered condition, the Bowen entropy of the whole compact space for a given F{\o}lner sequence equals to the topological entropy. For the proof of this result, we establish a variational principle related to the Bowen entropy and the Brin-Katok's local entropy formula for dynamical systems with amenable group actions.Comment: 13 page

Nitrate sources and dynamics in a salinized river and estuary : a δ15N-NO₃⁻ and δ18O-NO₃⁻ isotope approach

To trace NO3- sources and assess NO3- dynamics in salinized rivers and estuaries, three rivers (Haihe River: HH River, Chaobaixin River: CB River and Jiyun River: JY River) and two estuaries (HH Estuary and CJ Estuary) along the Bohai Bay (China) have been selected to determine dissolved inorganic nitrogen (DIN: NH4+, NO2- and NO3-. Upstream of the HH River, NO3- was removed 30.9 +/- 22.1% by denitrification, resulting from effects of the floodgate: limiting water exchange with downstream and prolonging water residence time to remove NO3-. Downstream of the HH River NO3- was removed 2.5 +/- 13.3% by NO3- turnover processes. Conversely, NO3- was increased 36.6 +/- 25.2% by external N source addition in the CB River and 34.6 +/- 35.1% by instream nitrification in the JY River. The HH and CY Estuaries behaved mostly conservatively excluding the sewage input in the CJ Estuary. Hydrodynamics in estuaries has been changed by the ongoing reclamation projects, aggravating the loss of the attenuation function of NO3- in the estuary