We discuss various properties of the new modulus of smoothness ω k,r (f, t)p := sup 0<h6t ‖W kh(·)∆khφ(·)(f , ·)‖Lp [−1,1], where φ(x) := √ 1− x2 and Wδ(x) = ( (1−x−δφ(x)/2)(1+x−δφ(x)/2) )1/2 . Related moduli with more general weights are also considered.

In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.

in gravity interpretation, inversion algorithms have been used widely over the years, but as the potential follows the gauss theorem, there are many equivalent source distributions that can produce the same known field. so to obtain a unique solution, suitable constraints should be introduced to the algorithm. during the last decades many authors have used several approaches to introduce a prio...

Using Fourier analysis, we prove that the limiting distribution of the standardized random number of comparisons used by Quicksort to sort an array of n numbers has an everywhere positive and infinitely differentiable density f , and that each derivative f (k) enjoys superpolynomial decay at ±∞. In particular, each f (k) is bounded. Our method is sufficiently computational to prove, for example...

We give direct approximation theorems for some linear operators in certain weighted spaces. The results are given in terms of some DitzianTotik moduli of smoothness.

This paper describes a method for melody detection in polyphonic musical signals. 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-sali...

We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval [0, 1] in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates.

Various authors have noted that in particular models, the upper bound on the axion decay constant may not hold. We point out that within supersymmetry, this is a generic issue. For large decay constants, the cosmological problems associated with the axion’s scalar partner are far more severe than those of the axion. We survey a variety of models, both for the axion multiplet and for cosmology, ...

The authors develop consistent nonparametric estimation techniques for the directional mixing density. Classical spherical harmonics are used to adapt Euclidean techniques to this directional environment. Minimax rates of convergence are obtained for rotationally invariant densities verifying various smoothness conditions. It is found that the difference in smoothness between the Laplace, the G...