We establish quantitative results for the approximation properties of the q-analogue of the Bernstein operator defined by Lupaş in 1987 and for the approximation properties of the limit Lupaş operator introduced by Ostrovska in 2006, via Ditzian-Totik modulus of smoothness. Our results are local and global approximation theorems. 2000 Mathematics Subject Classification. 41A25, 41A36.

We investigate a rearrangement inequality for pairs of n × n matrices: Let ‖A‖p denote (Tr(A∗A)p/2)1/p, the C trace norm of an n×n matrix A. Consider the quantity ‖A+B‖p+‖A−B‖p. Under certain positivity conditions, we show that this is nonincreasing for a natural “rearrangement” of the matrices A and B when 1 ≤ p ≤ 2. We conjecture that this is true in general, without any restrictions on A and...

Size matters. Human perception most naturally relates relative extent, area or volume to importance, nearness and weight. Reversely, conveying importance of something by depicting it at a different size is a classic artistic principle, in particular when importance varies across a domain. One striking example is the neuronal homunculus; a human figure where the size of each body part is proport...

There are two kinds of estimates of the degree of approximation of continuous functions on [−1, 1] by algebraic polynomials, Nikolskii-type pointwise estimates and Jackson-type uniform estimates, involving either ordinary moduli of smoothness, or the DitzianTotik (DT) ones, or the recent estimates involving the weighted DTmoduli of smoothness. The purpose of this paper is to complete the table ...

In this paper we obtain some limit cases of inequalities of Ul’yanov-type for modulus of smoothness between Lorentz-Zygmund spaces on Tn . Corresponding embedding theorems for the Besov spaces are investigated. Mathematics subject classification (2010): 41A17, 46E30, 46E35, 46M35.

This paper describes an algorithm for melody detection in polyphonic recordings. Our approach starts by obtaining a set of pitch candidates for each time frame, with recourse to an auditory model. Trajectories of the most salient pitches are then constructed. Next, note candidates are obtained by trajectory segmentation (in terms of frequency and pitch salience variations). Too short, low-salie...

We study the effect of inflation on gaugino condensation in supergravity. Unless the Hubble scale H is significantly below the gaugino condensation scale, the gaugino condensate is a dynamical variable which cannot be integrated out. For a sufficiently high H, the gaugino condensate evolves to zero which in turn leads to dilaton/moduli destabilization. In practice, this often occurs at the Hubb...

We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space Rn. In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is (n − 2)-rectifiable. In this paper, we ...

In this study, we investigated the effect of viewpoint density and speed of motion on perceived smoothness of viewpoint transitions. The effect of viewpoint density was examined for two types of viewer motion: forward and lateral motion. In both cases, we found that perceived smoothness varies with viewpoint density. We also found the number of viewpoints required to maintain a certain level of...