Resolving a question of Banero, we show that for every integer K > 1, there exists a word with additive complexity identically K. This result is perhaps surprising in light of the rather strong restriction on the existence of words with constant abelian complexity, given in the work of Currie and Rampersad. To prove our result we generalize the notion of a sturmian word. We also pose some quest...

In this paper we rigorously derive stochastic amplitude equations for a rather general class of SPDEs with quadratic nonlinearities forced by small additive noise. Near a change of stability we use the natural separation of time-scales to show that the solution of the original SPDE is approximated by the solution of an amplitude equation, which describes the evolution of dominant modes. Our res...

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation f(2x+ y) + f(2x− y) = 4(f(x+ y) + f(x− y))− 3 7 (f(2y)− 2f(y)) + 2f(2x) − 8f(x).

In this paper, we prove the generalized Hyers–Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x− 2y) = 4f(x + y) + 4f(x− y)− 6f(x) + f(2y) + f(−2y)− 4f(y)− 4f(−y) in non-Archimedean Banach spaces.

We develop a non-parametric cost function using generalized additive models and demonstrate how to test for input separability. Our empirical example focuses on Canadian cable television (CATV) provision. We estimate a new non-parametric cost function for this industry using financial and operating data collected between 1990 and 1996. This period is of particular importance from a policy persp...

This paper introduces the ―min-additive‖ (also called ―min-average‖) utility function. This function is a weighted combination of an additive utility function and a minimization over a set of single attribute utility functions. The weighting is accomplished by exploiting information already contained in the additive and minimization models. Four forms of the min-additive (MA) model are presente...