A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without the diagonals). A magilatin labelling is like a magic labelling but the values need be distinct only within each set. W...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

We show how high-resolution magic angle-spinning NMR spectroscopy can be used to characterize 13C-labeled saccharides that have been prepared using solid-phase synthesis techniques while they are still bound to a solid-support resin. With the use of 13C-labeled glucose as the starting material, we have successfully synthesized mono-, di- and trisaccharides with uniform 13C labeling of the sacch...

Introduction: Computed tomography (CT) has numerous applications in clinical procedures but its main problem is its high radiation dose to the patients compared to other imaging modalities using x-ray. CT delivers approximately high doses to the nearby tissues due to the scattering effect, fan beam (beam divergence) and limited collimator efficiency. The radiation dose from multi-slice scanners...

Model-generation based theorem provers such as SATCHMO and MGTP suffer from a combinatorial explosion of the search space caused by clauses irrelevant to the goal (negative clause) to be solved. To avoid this, two typical methods have been proposed. One is relevancy testing implemented in SATCHMORE by Loveland et al., and the other is non-Horn magic sets that are the extension of Horn magic set...

A magic square of order n is an n by n matrix with distinct nonnegative integer entries such that every row sum, column sum, and (two) diagonal sums equals to the same number m, the magic number. Adding 1 to every entry will give us a traditional magic square of positive integers. A magic square is pure if the entries are the consecutive numbers from 0 to n − 1, and hence it has magic number 3 ...

Introduction: In radiotherapy, treatment planning methods are evaluating and transforming every day, so precision in calculation and determination of dose delivery process is performing more important role in radiotherapy than past. In modern radiotherapy treatments, deramatically increase of small fields utilization, causes the polymeric gels has known as the most reliable dos...

Background: Accurate small radiation field dosimetry is essential in modern radiotherapy techniques such as stereotactic radiosurgery (SRS) and intensity modulated radiotherapy (IMRT). Precise measurement of dosimetric parameters such as beam profile, percentage depth doses and output factor of these beams are complicated due to the electron disequilibrium and the steep dose gradients. In the p...