for all x ∈ X, whereX denotes the dual space ofX and ⟨⋅, ⋅⟩ the generalized duality pairing between X and X. If X = H is a Hilbert space, then J becomes the identitymapping onH. A point x ∈ C is a fixed point of T : C ⊂ X → X provided Tx = x. Denote by F(T) the set of fixed points of T; that is, F(T) = {x ∈ C : Tx = x}. Let X be a normed linear space with dim X ≥ 2. The modulus of smoothness of...

Let f 2 C 1 ?1; 1] change its convexity nitely many times in the interval, say s times, at Y s : ?1 < y s < < y 1 < 1. We estimate the degree of simultaneous approximation of f and its derivative by polynomials of degree n, which change convexity exactly at the points Y s , and their derivatives. We show that provided n is suuciently large, depending on the location of the points Y s , the rate...

A cryptanalytic attack on the use of short RSA secret exponents is described. This attack makes use of an algorithm based on continued fractions which finds the numerator and denominator of a fraction in polynomial time when a close enough estimate of the fraction is known. The public exponent e and the modulus pq can be used to create an estimate of a fraction which involves the secret exponen...

This is a survey on best polynomial approximation on the unit sphere and the unit ball. The central problem is to describe the approximation behavior of a function by polynomials via smoothness of the function. A major effort is to identify a correct gadget that characterizes smoothness of functions, either a modulus of smoothness or a Kfunctional, the two of which are often equivalent. We will...

In this study four statistical grapheme-to-phoneme (G2P) conversion methods for canonical German are compared. The G2P models differ in terms of usage of morphologic information and of phoneme history (left context) information. In order to evaluate our models we introduce two measures, namely mean normalized Levenshtein distance for classification accuracy and conditional relative entropy for ...

Let F be a class of functions deened on a d-dimensional domain. Our task is to compute H m-norm "-approximations to solutions of 2mth-order elliptic boundary-value problems Lu = f for a xed L and for f 2 F. We assume that the only information we can compute about f 2 F is the value of a nite number of continuous linear functionals of f, each evaluation having cost c(d). Previous work has assume...

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...