Exact solutions have always played a central role in the investigation of physical theories whose content is encoded in a complicated set of di erential equations. The theory of general relativity is indeed an example of this. A number of exact solutions of Einstein's eld equations have been of key importance in the discussion of physical problems. Solutions have been found which describe black...

There are just five Fraı̈ssé classes of permutations (apart from the trivial class of permutations of a singleton set); these are the identity permutations, reversing permutations, composites (in either order) of these two classes, and all permutations. The paper also discusses infinite generalisations of permutations, and the connection with Fraı̈ssé’s theory of countable homogeneous structures,...

We consider the stabilization problem for three dimensional homogeneous polynomial systems, and derive an intrinsic suucient condition for stablizability. We show that this condition is satissed by an open set in the space of homogeneous systems of a xed degree.

Background: The purpose of this study is to fabricate inexpensive in-house low cost homogeneous and heterogeneous human equivalent thorax phantom and assess the dose accuracy of the Treatment Planning Systems (TPS) calculated values for different lung treatment dosimetery. It is compared with Thermoluminescent Dosimeter (TLD) measurement. Materials and Methods: Homogeneous and heterogeneous tho...

A relational first order structure is homogeneous if every isomorphism between finite substructures extends to an automorphism. Familiar examples of such structures include the rational numbers with the usual order relation, the countable random and so called Rado graph, and many others. Countable homogeneous structures arise as Fraı̈ssé limits of amalgamation classes of finite structures, and h...