In the present study, the effect of banana peel and bagasse particle additives on the friction and wear behavior of multi-ingredient friction material nanocomposites have been investigated. In order to develop optimized properties of friction nanocomposite, the type and content of natural additives were changed beside the constant amount of other constituents such as alumina nanoparticle and ot...

We study smooth backfitting when there are errors-in-variables, which is motivated by functional additive models for a functional regression model with a scalar response and multiple functional predictors that are additive in the functional principal components of the predictor processes. The development of a new smooth backfitting technique for the estimation of the additive component function...

In this paper, we define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation: f (x 1 + · · · + x l) = (l – 1)f x 1 + · · · + x l–1 l – 1 + f (x l) for a fixed integer l with l > 1, and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.

(1.1) f(aq + b) = f(aq) + f(b) or f(aq + b) = f(aq)f(b) for all r ≥ 0, a ≥ 0 and 0 ≤ b < q. Note that these equations force f(0) = 0 or f(0) = 1 respectively. These functions are called q-additive and q-multiplicative, respectively. It is easy to see that the functional equations imply that these functions are defined for all integers, when the values f(aq) are known for 1 ≤ a ≤ q − 1 and all r...

We show how the Model-Free Prediction Principle of Politis (2013) can be applied to nonparametric regression with a univariate response and regressors that are high-dimensional or even infinite-dimensional, i.e., functional. Without assuming an additive model with i.i.d. errors, the Model-Free Principle is capable of yielding both consistent predictors as well as prediction intervals. 39.