Sivakumar Nagarajan

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Preface In Spring 1994, we taught a course called Interactive Proof Systems at TIFR, Bombay. The class met once a week for three hours. The lecture notes supplied for this course are collected in this report. We had intended to provide an introduction to the area of computational complexity for an audience with no prior exposure to Theoretical Computer(More)
This paper proposes two different parallel genetic algorithms (PGAs) for constrained ordering problems. Constrained ordering problems are constraint optimization problems (COPs) for which it is possible represent a candidate solution as a permutation of objects. A decoder is used to decode this permutation into an instantiafion of the COP vm-iables. Two(More)
The fabrication of mesoporous silica films with well-defined morphologies [1] offers tremendous opportunity for device structures. In particular the generation of a mesoporous silica film with cylindrical nanochannels of prescribed diameters oriented normal to the substrate holds great promise for applications in catalysis, [2] bio-molecular separations,(More)
The Szeged index of a graph G, denoted by S z(G) = uv=e∈E(G) n G u (e)n G v (e). Similarly , the Weighted Szeged index of a graph G, denoted by S z w (G) = uv=e∈E(G) d G (u)+ d G (v) n G u (e)n G v (e), where d G (u) is the degree of the vertex u in G. In this paper, the exact formulae for the weighted Szeged indices of generalized hierarchical product and(More)
In the title compound, C18H15NO2, the dihedral angle between the mean planes of the quinoline ring system and the phenyl ring is 78.8 (1)°. The mean plane of the carboxyl-ate group is twisted from the mean planes of the quinoline ring system and phenyl ring by 1.5 (9) and 77.6 (4)°, respectively. In the crystal, mol-ecules are linked by weak C-H⋯O(More)
Preface In Spring 1994, we taught a course called Interactive Proof Systems at TIFR, Bombay. The class met once a week for three hours. The lecture notes supplied for this course are collected in this report. We had intended to provide an introduction to the area of computational complexity for an audience with no prior exposure to Theoretical Computer(More)