We prove Gaussian estimates from above of the fundamental solutions to a class of ultraparabolic equations. These estimates are independent of the modulus of continuity of the coefficients and generalize the classical upper bounds by Aronson for uniformly parabolic equations.  2003 Elsevier Science (USA). All rights reserved.

Estimating the degree of approximation in the uniform norm, of a convex function on a finite interval, by convex algebraic polynomials, has received wide attention over the last twenty years. However, while much progress has been made especially in recent years by, among others, the authors of this article, separately and jointly, there have been left some interesting open questions. In this pa...

This work aims at explaining the syntactical properties of continuous normalization, as introduced in proof theory by Mints, and further studied by Ruckert, Buchholz and Schwichtenberg. In an extension of the untyped coinductive λ-calculus by void constructors (so-called repetition rules), a primitive recursive normalization function is defined. Compared with other formulations of continuous no...

For each q ∈ N0, we construct positive linear polynomial approximation operators Mn that simultaneously preserve k-monotonicity for all 0 ≤ k ≤ q and yield the estimate |f(x)−Mn(f, x)| ≤ cω λ 2 ( f, nφ(x) (φ(x) + 1/n) ) , for x ∈ [0, 1] and λ ∈ [0, 2), where φ(x) := √ x(1− x) and ω 2 is the second Ditzian-Totik modulus of smoothness corresponding to the “step-weight function” ψ. In particular, ...

Abstract. Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials which are coconvex with it, namely, polynomials that change their convexity exactly at the points where f does. We discuss some Jackson type estimates where the constants involved depend on the location of the points of change of c...

The cosmological moduli problem for relatively heavy moduli fields is reinvestigated. For this purpose we examine the decay of a modulus field at a quantitative level. The modulus dominantly decays into gauge bosons and gauginos, provided that the couplings among them are not suppressed in the gauge kinetic function. Remarkably the modulus decay into a gravitino pair is unsuppressed generically...

Consider the Sturm-Liouville problem on a finite interval with Dirichlet boundary conditions. Let the elastic modulus and the density be of bounded variation. Results for both the forward problem and the inverse problem are established. For the forward problem, new bounds are established for the eigenfrequencies. The bounds are sharp. For the inverse problem, it is shown that the elastic modulu...

This paper proposes two nonlinear blind equalizers: the nonlinear constant modulus algorithm (NCMA) and the nonlinear modified constant modulus algorithm (NCMA) by applying a nonlinear transfer function (NTF) into constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA), respectively. The effect of the NTF on CMA and MCMA is theoretically analyzed, which implies that the ...

The elastic modulus of two varieties of Iranian pumpkin seed and its kernel (namely, Zaria and Gaboor) were evaluated as a function of size (large, medium, and small), loading rate (2, 5, 8, and 10 mm/min), and moisture content (4, 7.8, 14, and 20% d.b) under quasistatic compression loading. The results showed that elastic modulus of pumpkin seed and its kernel decreased with increasing moistur...

By using the particle swarm optimization algorithm for crystal structure prediction, we reveal a newly orthorhombic Cmcm structure of HfB4, which is more energetically superior to the previously proposed YB4-, ReP4-, FeB4-, CrB4-, and MnB4-type structures in the considered pressure range. The phonon dispersion and elastic constants calculations confirm that the new phase is dynamically and mech...