let $m_r$ be a module with $s=end(m_r)$. we call a submodule $k$ of $m_r$ annihilator-small if $k+t=m$, $t$ a submodule of $m_r$, implies that $ell_s(t)=0$, where $ell_s$ indicates the left annihilator of $t$ over $s$. the sum $a_r(m)$ of all such submodules of $m_r$ contains the jacobson radical $rad(m)$ and the left singular submodule $z_s(m)$. if $m_r$ is cyclic, then $a_r(m)$ is the unique ...

Introduction Radiotherapy with small fields is used widely in newly developed techniques. Additionally, dose calculation accuracy of treatment planning systems in small fields plays a crucial role in treatment outcome. In the present study, dose calculation accuracy of two commercial treatment planning systems was evaluated against Monte Carlo method. Materials and Methods Siemens Once or linea...

The recent re-parametrization of the Martini coarse-grained force field, 3, improved accuracy model in predicting molecular packing and interactions dynamics simulations. Here, we describe how small molecules can be accurately parametrized within 3 framework present a database validated molecule models. We pay particular attention to description aliphatic aromatic ring-like structures, which ar...

Introduction: Accurate film dosimetry requires careful consideration of sources of uncertainty. Some of the sources of uncertainty are dependent on the size and location of region of interest (ROI), especially in small fields. Avoiding the penumbra is often a reason for using a small ROI. In contrast, choosing very small ROIs may increase uncertainty due to the reduction of th...