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...

In this paper we define a new class of partially filled arrays, called λ-fold relative Heffter that are generalization the arrays introduced by Archdeacon in 2015. After showing connection concept with several other ones, such as signed magic graph decompositions and difference families, determine some necessary conditions present existence results for infinite classes these arrays. last part a...

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 vertex magic total labeling of a graph with v vertices and e edges is de ned as a one to one map taking the vertices and edges onto the integers v e with the property that the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex Properties of these labelings are studied It is shown how to construct labelings for several families o...

For a given graph G, let V be the number of vertices and E be the number of edges. Consider a labeling of the vertices and edges which is a one-to-one mapping of the set of integers {1, 2, . . . , V + E} onto the vertices and edges of the graph, with the property that for every vertex the sum of the labels assigned to that vertex and all edges incident with it is some constant k. Although work ...

Let G(V,E) be a graph and λ be a bijection from the set V ∪E to the set of the first |V |+ |E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say λ is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say λ is an (s, d) -vertex antimagic total (VAT) labeling if the vertex weights form an arithmetic pro...