In a previous paper Smallwood and Paez (1991) showed how to generate realizations of partially coherent stationary normal time histories with a specified cross-spectral density matrix. This procedure is generalized for the case of multiple inputs with a specified cross-spectral density function and a specified marginal probability density function (pdf) for each of the inputs. The specified pdfs are not required to be Gaussian. A zero memory nonlinear (ZMNL) function is developed for each input to transform a Gaussian or normal time history into a time history with a specified non-Gaussian distribution. The transformation functions have the property that a transformed time history will have nearly the same auto spectral density as the original time history. A vector of Gaussian time histories are then generated with the specified cross-spectral density matrix. These waveforms are then transformed into the required time history realizations using the ZMNL function.

Without the social will, no city can successfully Undertake the planning and programs necessary for meaningful progress toward sustainability. Social will derives from wellsprings of vital societal health. This paper presents an approach to helping cities in APEC member economies initiate a program for developing indicators of sustainability. Representative indicators of social capital and other aspects of civic engagement, as proxies for societal health, are presented.