Uniform estimates on paraproducts

We prove uniformL ^p estimates (Theorem 1.1) for a family of paraproducts and corresponding maximal operators.     

Darstellung und Eigenschaften von 1-Norbornylkupfer

Preparation and Properties of 1-Norbornyl Copper 1-Norbornyl copper was synthesized from copper(II) acetylacetonate and 1-norbornyl lithium. The compound shows an unexpected stability and decomposes only at ca. 80°C with precipitation of copper and formation of norbornyl radicals which were proved by spin-trap experiments. A further characterization was performed by the IR and ¹³C-NMR spectra.     

Strict estimation of the maximum of a function of one variable

We describe an algorithm for the strict estimation of max _xI f(x) whenf is analytic onI. If roundoff is neglected the error bound can be made arbitrarily small by an adaptive implementation. A majorant concept is utilized and an Algol program is given. Finally we outline the special application to the strict estimation of the range of a polynomial without any determination of the zeros of the derivative.     

Monotonicity and error bounds in schemes of Romberg type for the computation off(n) (0) by central differences and extrapolation

Summary An integral form of the remainder terms of the entries in the extrapolation scheme is shown to have kernels of constant sign within columns. Monotonicity of one or more derivatives of the function to be differentiated is transformed into certain monotonicity properties of the scheme. For functions of this kind the extrapolation scheme also provides for strict inclusions off(ⁿ) (0). This property may be extended to a larger class of functions through a majorant concept.     

Die Kristallstrukturen und Phasentransformationen des tetramorphen RbGel3

Crystal Structures and Phase Transitions of the Tetramorphic RbGeI₃ The thermal behaviour of RbGeI₃ has been studied by X-ray diffraction, Raman spectroscopy, and DTA/DSC. The compound is tetramorphic. Yellow crystals of the LT-form have been obtained by crystallization from aqueous HI solutions. The orthorhombic crystal structure of LT? RbGeI₃ (space group P2₁2₁2₁; a = 10.1441(8) Å; b = 4.5460(5) Å; c = 16.8438(9) Å) shows a distorted NH₄CdCl₃ type structure with pyramidal GeI₃ anions. Three reversible phase transformations were found by heating. In a first step at 181°C LT? RbGeI₃ is transferred into the orthorhombic perovskite MT1—RbGeI₃ (red, space group Pn2₁a; a = 8.566(3) Å; b = 11.868(6) Å; c = 8.018(4) Å; RbGeBr₃ type structure) by a reconstructive phase transition. Subsequently at 221°C the phase MT2—RbGeBr₃ with a rhombohedrically deformed perovskite type structure (black, space group R3m; a = 5.990(2) Å; α = 88,89(3)°; CsGeCl₃ type structure) is formed. The high temperature modification HT? RbGeI₃ shows the cubic perovskite type structure (space group Pm3m; a = 5.994(3) (Å) and is stable above 244°C until decomposition occurs at 334°C.     

Uniform estimates on multi-linear operators with modulation symmetry

In a previous paper [20] in this series, we gaveL ^p estimates for multi-linear operators given by multipliers which are singular on a non-degenerate subspace of some dimensionk. In this paper, we give uniform estimates when the subspace approaches a degenerate region in the casek = 1, and when all the exponentsp are between 2 and ∞. In particular, we recover the non-endpoint uniform estimates for the bilinear Hubert transform in [12]. Dedicated to Tom Wolff     

Lower Bounds for Shellsort

We show lower bounds on the worst-case complexity of Shellsort. In particular, we give a fairly simple proof of an Ω(n (lg² n)/(lg lg n)²) lower bound for the size of Shellsort sorting networks for arbitrary increment sequences. We also show an identical lower bound for the running time of Shellsort algorithms, again for arbitrary increment sequences. Our lower bounds establish an almost tight trade-off between the running time of a Shellsort algorithm and the length of the underlying increment sequence.     

Lipschitz Linearization of the Maximal Hyperbolic Cross Multiplier

Journal of Fourier Analysis and Applications - We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition...