We examined in which way gradual changes in the geometric structure of the illumination affect the perceived glossiness of a surface. The test stimuli were computer-generated three-dimensional scenes with a single test object that was illuminated by three point light sources, whose relative positions in space were systematically varied. In the first experiment, the subjects were asked to adjust...

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.

The many-to-one mapping from representations in the speech articulatory space to acoustic space renders the associated acoustic-to-articulatory inverse mapping non-unique. Among various techniques, imposing smoothness constraints on the articulator trajectories is one of the common approaches to handle the non-uniqueness in the acoustic-to-articulatory inversion problem. This is because, articu...

It has been understood for sometime that the classical smoothness spaces, such as the Sobolev and Besov classes, are not satisfactory for certain problems in image processing and nonlinear PDEs. Their deficiency lies in their isotropy. Functions in these smoothness spaces must be simultaneously smooth in all directions. The anisotropic generalizations of these spaces also have the deficiency th...

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...