We characterize proximality of multidimensional \begin{document}$ \mathscr{B} $\end{document}-free systems in the case number fields and lattices id="M2">\begin{document}$ \mathbb{Z}^m $\end{document}, id="M3">\begin{document}$ m\geq2 $\end{document}.

The event of partly grain-free ear is a crucial problem which can result in severe reductions in corn yield. In a two year field investigation, during 2003-2004, an experiment was conducted to determine the effect of  boron (B) and zinc (Zn) application on yield and yield components of corn (Zea mays L.) plants grown in a B and Zn-deficient calcareous soil (fine, carbonatic, thermic, Typic Hapl...

in this paper we study the dynamics of hepatitis b virus (hbv) infection under administration of a vaccine and treatment, where the disease is transmitted directly from the parents to the offspring  and also through contact with infective individuals. stability of the disease-free steady state is investigated. the basic reproductive rate, $r_0$, is derived. the results show that the dynamics of...

The synthesis of cis-N-[a-carbobenzyloxy-b-(p-hydroxyphenyl)ethyl]-3-phthalimido-4-styryl-2-azetidinone is described. We have found that the electron-rich Schiff bases can afford the cis-b-lactam ring even in the presence of the free hydroxyl functions. The mechanisms of cis and trans-b-lactam ring formation are discuss...

[B(OH)3]0.78[B(OH)2(OSO3H)]0.22 or (BSA) was simply prepared by addition of chlorosulfonic acid to commercial boric acid at room temperature. This cheap and green solid acid was used as an efficient catalyst for synthesis of acylals from aldehydes under solvent-free conditions at room temperature.

[B(OH)3]0.78[B(OH)2(OSO3H)]0.22 or (BSA) was simply prepared by addition of chlorosulfonic acid to commercial boric acid at room temperature. This cheap and green solid acid was used as an efficient catalyst for synthesis of acylals from aldehydes under solvent-free conditions at room temperature.

the synthesis of cis-n-[a-carbobenzyloxy-b-(p-hydroxyphenyl)ethyl]-3-phthalimido-4-styryl-2-azetidinone is described. we have found that the electron-rich schiff bases can afford the cis-b-lactam ring even in the presence of the free hydroxyl functions. the mechanisms of cis and trans-b-lactam ring formation are discussed. the discussions are consistent with the recent publications.