May [4] estimated some direct and inverse results for certain combinations of these operators. Very recently Finta and Gupta [1] studied some direct and inverse results for the second-order Ditzian-Totik modulus of smoothness. The rates of convergence in ordinary approximation for function of bounded variation for these operators and similar types of operators were estimated in [2, 3, 7]. Very ...

Supersymmetry breaking via gaugino condensation is studied in vacua of heterotic M–theory with five–branes. We show that supersymmetry is still broken by a global mechanism and that the non–perturbative superpotential takes the standard form. When expressed in terms of low energy fields, a modification arises due to a threshold correction in the gauge kinetic function that depends on five–brane...

We present a characterization of the approximation errors of the PostWidder and the Gamma operators in Lp(0,∞), 1 ≤ p ≤ ∞, with a weight x for any real γ. Two types of characteristics are used – weighted Kfunctionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it. AMS classification: 41A25, 41A27, 41A35, 41A36.

In this paper we answer a question raised in [25], Sec. 4, by showing that the genus zero moduli operad {M0,n+1} can be endowed with natural descent data that allow it to be considered as the lift to SpecZ of an operad over F1. The relevant descent data are based on a notion of constructible sets and constructible functions over F1, which describes suitable differences of torifications with a p...

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...

We investigate slope distributions in the northern hemisphere of Mars from topographic profiles collected by the Mars Orbiter Laser Altimeter. Analysis of the region from about 12øS to 82øN, over diverse geologic units, indicates that the range of regional-scale slopes is small, generally < 3 ø. Surface smoothness is most distinctive in the vast northern hemisphere plains, where slopes are typi...

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.