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...

A magic square of order n consists of the numbers 1 to n placed such that the sum of each row, column and principal diagonal equals the magic sum n(n +1)/2. In addition, an odd ordered magic square is associative or self-complementary if diagonally opposite elements have the same sum (n +1)/2. The magic square is said to be regular Greco-Latin if it can be decomposed as a sum of a pair of Latin...

Physics interpretation of the " magic " baseline, L magic , that can play important role in future oscillation experiments is given. The " magic " baseline coincides with the refraction length, l 0. The latter, in turn, approximately equals the oscillation length in matter at high energies. Therefore at the baseline L = l 0 the oscillation phase is 2π, and consequently, the " solar " amplitude ...

We report on an evaluation of MAGIC, a system that automatically generates briefings of patient status after coronary bypass surgery, completed in the Cardio Thoracic Intensive Care Unit at New York Presbyterian Hospital. Through enhancements in system design, robustness and speed, we compared information obtained by nurses against two briefings, one automatically generated by MAGIC and one pro...

A total labelling of a graph over an abelian group is a bijection from the set of vertices and edges onto the set of group elements. A labelling can be used to define a weight for each edge and for each vertex of finite degree. A labelling is edge-magic if all the edges have the same weight and vertex-magic if all the vertices are finite degree and have the same weight. We exhibit magic labelli...

Our purpose is to introduce a linear-algebraic construction for magic rectangles of size pr × ps, where p is prime and 1 ≤ r ≤ s. For fixed p, r, and s, this method allows for the production of many different magic rectangles. It follows that, for many non-coprime dimensions, this construction will significantly augment the sparse collection of “known” magic rectangles. A magic rectangle of siz...

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. a graph $g$ is said to be $a$-magic graph if there exists a labeling$l:e(g)rightarrow a^{*}$ such that the induced vertex labeling$l^{+}:v(g)rightarrow a$, define by $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,where $n(v)$ denotes the s...

In this paper, we consider special class of trees called uniform k-distant trees, which have many interesting properties. We show that they have an edge-magic total labeling, a super edge-magic total labeling, a (a, d)-edge-antimagic vertex labeling, an (a, d)-edgeantimagic total labeling, a super (a, d)edge-antimagic total labeling. Also we introduce a new labeling called edge bi-magic vertex ...

Associated to any complex simple Lie algebra is a non-reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square and the magic triangle to give an additional row and column. The extra row and column in the magic square correspond to the sextonions. This is a six-dimensional subalgebra of the split octonions w...

ABSTRACT Magic labelings of graphs are studied in great detail by Stanley in [18] and [19], and Stewart in [20] and [21]. In this article, we construct and enumerate magic labelings of graphs using Hilbert bases of polyhedral cones and Ehrhart quasi-polynomials of polytopes. We define polytopes of magic labelings of graphs and digraphs. We give a description of the faces of the Birkhoff polytop...