Overall 10389 snails were collected from four study areas of Punjab from November 2005 to October2006. The highest prevalence (38%) was found for Indoplanorbis followed by Physa (17%), Bellamaya(10.3%), Gyraulus (10%), Lymnaea (9.2%), Oncomelania (9%) and the lowest was found for Bulinus (6.7%).Only Indoplanorbis snails were found to be positive for Schistosoma bovis cercaria. Correlation betwe...

Unprovability Theory started with Kurt Gödel’s incompleteness theorems in 1931 but only gained mathematical significance since the late 1970s when Jeff Paris and Harvey Friedman discovered the first few families of interesting combinatorial statements that cannot be proved using the axioms of Peano Arithmetic or even some stronger axiomatic systems. In this survey article we briefly introduce t...

Many graph properties and graph transformations can be formalized inMonadic Second-Order logic. This language is the extension of First-Order logic allowing variables denoting sets of elements. In the case of graphs, these elements can be vertices, and in some cases edges. Monadic second-order graph properties can be checked in linear time on the class of graphs of tree-width at most k for any ...