Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...

In this paper we propose a method for the estimation of time-varying autoregressive processes. The approach is essentially to regularize the heavily underdetermined unconstrained prediction equations with a smoothness priors type side constraint. The implementation of nonhomogenous smoothness properties is straightforward. The method is compared to the usual determistic regression approach (TVA...

We consider Dirichlet series on convex polygons and their rate of approximation in AC(D). We show that the substitution of the respective Leont’ev coefficients by appropriate interpolating sums preserves the order of approximation up to a factor lnn. The estimates are given for moduli of smoothness of arbitrary order. This extends a result of Yu. I. Mel’nik in [4]. AMS Subject Classification (2...

In this paper severely ill-posed problems are studied which are represented in the form of linear operator equations with innnitely smoothing operators but with solutions having only a nite smoothness. It is well known, that the combination of Morozov's discrepancy principle and a nite dimensional version of the ordinary Tikhonov regularization is not always optimal because of its saturation pr...

In the present paper, we prove a global direct theorem for the modified Baskakov type operators in terms of so called DitzianTotik modulus of smoothness.

Many factors influence a vehicle’s rate of fuel consumption. Among them are engine efficiency, speed, aerodynamics, and rolling resistance. When it comes to the influence that pavement characteristics have on fuel consumption, one of the major contributors is surface roughness which impacts rolling resistance; more energy is required to propel a vehicle over a rough surface than over a smooth s...

The traditional concept of smoothness concerns differentiability, and we consider a function to be smooth if it is k-times differentiable. This concept is important in many aspects of numerical analysis, and the quality of reconstructions of signals from certain given observations depend on this information. For instance, a k-times differentiable function on the unit cube [0, 1] can be approxim...

In this paper the smoothness properties of Green’s operator-function an exponentially dichotomous bilinear matrix system and the smoothness properties the invariant torus of nonhomogeneus matrix system of equations have been considered. It hHave been proved that if some conditions, concerning the properties of coefficient of the system hold this operator-function has smoothness index which depe...

The Indiana Department of Transportation (INDOT) is currently utilizing a profilograph and the profile index for measuring smoothness assurance for newly constructed pavements. However, there are benefits to implementing a new International Roughness Index (IRI)–based smoothness specification utilizing road profiles measured using inertial profilers. Technological advancements have improved the...