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 direct and inverse theorems are established for the best approximation in the weighted L space on the unit sphere of R, in which the weight functions are invariant under finite reflection groups. The theorems are stated using a modulus of smoothness of higher order, which is proved to be equivalent to a K-functional defined using the power of the spherical h-Laplacian. Furthermore, similar ...

This brief provides findings on the observed effect of initial pavement smoothness (also known as initial roughness, or as-constructed roughness) on the long-term pavement roughness progression of asphalt overlays. The relationship can be used as a measure for estimating the long-term effect of pavement smoothness and for consideration when developing smoothness specifications and/or payment ad...

We present a characterization of the approximation errors of the PostWidder and the Gamma operators in Lp(0,∞), 1 ≤ p ≤ ∞, with a weight x0(1 + x)γ∞−γ0 with arbitrary real γ0, γ∞. Two types of characteristics are used – weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on simple modifications of it. 2000 Mathematics Subject Classi...

In this work we investigate the approximation problems in the Smirnov-Orlicz spaces in terms of the fractional modulus of smoothness. We prove the direct and inverse theorems in these spaces and obtain a constructive descriptions of the Lipschitz classes of functions defined by the fractional order modulus of smoothness, in particular. 1. Preliminaries and introduction A function M (u) : R → R ...

For rather general moduli of smoothness ρ, like ρ(h)=h ln(c/h), we consider the Hölder spaces Hρ(B) of functions [0, 1] → B where B is a separable Banach space. We establish an isomorphism between Hρ(B) and some sequence Banach space. With this analytical tool, we follow a very natural way to study, in terms of second differences, the existence of a version in Hρ(B) for a given random field. 20...

In this paper, we propose a general algorithmic framework for the first-order methods in optimization broad sense, including minimization problems, saddle-point problems and variational inequalities (VIs). This allows obtaining many known as special case, list accelerated gradient method, composite methods, level-set Bregman proximal methods. The idea of is based on constructing an inexact mode...

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.