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The authors show that the recently proposed pure-connection action for general relativity with a cosmological constant by Capovilla, Dell and Jacobson (1989) correctly yields the usual constraints of general relativity as given by Ashtekar (1986). They also point out alternative possibilities for the Capovilla-Dell-Jacobson action.

Analytic gravitational instanton solutions in a theory which includes a self-interacting scalar field are obtained. The relevant potential for the scalar field satisfying equations of motion is determined by developing a general technique. The corresponding actions are calculated exactly and the qualitative features of the solutions discussed.

Using the dynamic renormalization group (DRG) technique, we analyze general nonlinearities in a conservative nonlinear growth equation with non-conserved gaussian white noise. We show that they fall in two classes only: the Edwards-Wilkinson and Lai-Das Sarma types, by explicitly computing the associated amputated two and three point functions at the first order in perturbation parameter(s). We further generalize this analysis to higher order nonlinearities and also suggest a physically meaningful geometric interpretation of the same.