introduction the use of cut-outs in electron applicators make changes on output, isodose, and percentage depth dose (pdd) curves. these changes and electron beam dose distribution in the form of three-dimensional (3d) can be measured by gel dosimeters. materials and methods dosimetry was performed with and without a square shield (6×6 cm2 field). the energies were 4, 9, and 16 mev and phantom w...

A distance magic labeling of a graph G = (V, E) of order n is a bijection l : V → {1, 2, . . . , n} with the property that there is a positive integer k (called magic constant) such that w(x) = k for every x ∈ V . If a graph G admits a distance magic labeling, then we say that G is a distance magic graph. In the case of non-regular graph G, the problem of determining whether there is a distance...

Magic is “a concept used to describe a mode of rationality or way of thinking that looks to invisible forces to influence events, effect change in material conditions, or present the illusion of change” (Encyclopedia Britannica s.v. magic). “Magic and sorcery are the influencing of events, objects, people, and physical phenomena by mystical, paranormal or supernatural means. The terms can also ...

The rapidly increasing rate at which biological data is being produced requires a corresponding growth in relational databases and associated tools that can help laboratories contend with that data. With this need in mind, we describe here a Modular Approach to a Genomic, Integrated and Comprehensive (MAGIC) Database. This Oracle 9i database derives from an initial focus in our laboratory on ge...

Today's application is to magic! Not the friendship kind, though 1 ; instead, we're going to talk about magic squares, an incredibly old piece of mathematics that we can study using Latin squares. Definition. A magic square is a n × n grid filled with the integers {0, 1,. .. n 2 − 1}, such that • each number is used exactly once in our entire grid, and • the sum of all of the entries along any ...

We define a simple algorithm for creating large numbers of semi-magic n× n squares when n is odd. Special cases of the algorithm can also be used to easily create magic and extra magic (or panmagic) n× n squares when n is odd. The algorithm can also create extremely magic n × n squares when n ≥ 5 is prime. These extremely magic n × n squares have n! standard magic n-element subsets, and these n...

A (p,q) graph G is total edge-magic if there exits a bijection f: Vu E ~ {1.2,. .. ,p+q} such that for each e=(u,v) in E, we have feu) + fee) + f(v) as a constant. For a graph G, denote M(G) the set of all total edge-magic labelings. The magic strength of G is the minimum of all constants among all labelings in M(G), and denoted by emt(G). The maximum of all constants among M(G) is called the m...

Let $A$ be an abelian group. A graph $G=(V,E)$ is said to be $A$-barycentric-magic if there exists a labeling $l:E(G)longrightarrow Asetminuslbrace{0}rbrace$ such that the induced vertex set labeling $l^{+}:V(G)longrightarrow A$ defined by $l^{+}(v)=sum_{uvin E(G)}l(uv)$ is a constant map and also satisfies that $l^{+}(v)=deg(v)l(u_{v}v)$ for all $v in V$, and for some vertex $u_{v}$ adjacent t...