Pyranopyrazoles. II. Synthesis and reactions of 1H,6H-pyrano[2,3-c]pyrazol-6-ones

Various 1H,6H-pyrano[2,3-c]pyrazol-6-ones (III-XXIII) were obtained from β-keto esters and 1H-pyrazol-5-ones or hydrazines. Nitrations, chlorinations and brominations of these pyranopyrazoles were also carried out giving the corresponding derivatives (XXIV-LXIV). The pyrone ring is the more reactive one in these reactions and the preferred position of attack is the 5-position. The substitution products are formed by the addition-elimination route.     

Simulation model for shapiro time delay and light deflection experiments

The time delay experiment proposed by I.I. Shapiro in 1964 and conducted in the seventies was the most precise experiment of general relativity until that time. Further experimentation has improved the accuracy level of both the time delay and the light deflection experiments. A simulation model is proposed that involves only a simple mass and time transformation factor involving velocity of light. The light deflection and the time delay experiments are numerically simulated using this model that does not use the general relativistic equations. The computed values presented in this paper compare well with recent levels of accuracy of their respective experimental results.     

Min-cut clustering

We describe a decomposition framework and a column generation scheme for solving a min-cut clustering problem. The subproblem to generate additional columns is itself an NP-hard mixed integer programming problem. We discuss strong valid inequalities for the subproblem and describe some efficient solution strategies. Computational results on compiler construction problems are reported.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.This research was supported by NSF grants DMS-8719128 and DDM-9115768, and by an IBM grant to the Computational Optimization Center, Georgia Institute of Technology.