Investigation of Masked N-Acyl-N-isocyanates: Support for Oxadiazolones as Blocked N-Isocyanate Precursors

In contrast to carbon-substituted isocyanates that are common building blocks, N-substituted isocyanates remain underdeveloped and reports on their N-acyl derivatives (i. e. amido-isocyanates) are exceedingly rare. Herein, amido-isocyanates were investigated in the context of syntheses of aza-tripeptide and hydantoins subunits starting from simple bench-stable precursors. A key finding is that the amido-isocyanate formed in situ cyclized to yield an oxadiazolone, and that under suitable reaction conditions this heterocycle is a traceless blocked (masked) N-isocyanate. Using organic bases as catalysts and upon heating, oxadiazolone formation is observed, and various nucleophiles to provide the desired aza-dipeptides or hydantoins in moderate to high yields. Further support for an amido-isocyanate intermediate was obtained using carboxylic acids as nucleophiles, affording N-acylhydrazide products.     

Trispectrum for the response of a non-linear oscillator

Simulation is used to obtain information about non-Gaussian aspects of the absolute response acceleration of a bi-linear hysteretic oscillator with an excitation which is Gaussian white noise. Attention is focused on the frequency content of the fourth cumulant of the response. This frequency content is studied by consideration of the trispectrum and also by the simplified technique of looking at the coefficient of excess for the response of a narrowband linear system mounted on the non-linear oscillator. Attempts are also made to model the non-Gaussian response of the non-linear oscillator by a filtered delta correlated (FDC) process, but it is shown that no process of this type can exhibit some of the significant characteristics of the non-linear response. In particular, the trispectrum of the non-linear response appears to be more narrowband than the power spectral density, and also it sometimes does not have the same sign at every point in the three-dimensional frequency space, and this behavior is distinctly different from that of any FDC process. Modifications of the FDC model are suggested in order to obtain improved approximations of the non-linear response.     

Integral Representations of Increments of Stochastic Processes

A formulation is presented in which the increment of a stochastic process is represented as an integral of the derivative of the process. It is shown that this representation is an alternative to the more common approach of writing equations for the differentials of stochastic processes. A possible advantage of the integral formulation is that its reliance on derivatives, rather than differentials, makes the operations of stochastic calculus more closely resemble those of ordinary deterministic calculus. This similarity to well-known mathematics may serve to make stochastic calculus accessible to a broader audience than in the past. The integral formulation is herein shown to be compatible with the Itô differential rule for non-Gaussian processes and is used to describe the increment of the nonstationary response of a system governed by a vector stochastic equation with parametric delta-correlated excitation.