The maximal Fejér operator on real Hardy spaces

We prove that the maximal Fej'er operator is not bounded on the real Hardy spaces H ¹, which may be considered over and . We also draw corollaries for the corresponding Hardy spaces over ² and ². This revised version was published online in August 2006 with corrections to the Cover Date.     

Unwinding of DNA polymerases by the antitumor drug,cis-diamminedichloroplatinum(II)

The helix-turn-helix motifs of the DNA binding domains of human polymerase-alpha and polymerase-kappa are dramatically perturbed upon binding to cisplatin with concomitant release of zinc.     

Development of chemically modified glass surfaces for nucleic acid,protein and small molecule microarrays

Microarrays have become a widely used tool to investigate the living cell at different levels. DNA microarrays enable the expression analysis of thousand of genes simultaneously, while protein arrays investigate the properties and interactions of proteins with other proteins and with non-proteinaceous molecules. One crucial step in producing such microarrays is the permanent immobilization of samples on a solid surface. Our goal was to develop diverse linker systems capable of anchoring different biological samples, especially DNA and drug-like small molecules. We developed 6 different chemical surfaces having a 3-D-like linker system for biomolecule immobilization, and compared them to previously described immobilization strategies. The attachment chemistry utilizes the amino reactive properties of acrylic and epoxy functions. The capacity of the support was increased by creating a branching structure holding the reactive functions. The method of anchoring was investigated through a model reaction. From HPLC and mass spectrometry measurements we concluded that the covalent binding of DNA occurs through nucleobases. The tested systems offer the capability to permanently immobilize several biomolecular species in an array format.     

(C,α) Summability of Walsh—Fourier Series

The one-dimensional dyadic martingale Hardy spaces H _p are introduced and it is proved that the maximal operator of the (C,) means of a Walsh—Fourier series is bounded from H _p to L _p (1/( + 1) < p < ) and is of weak type (L ₁,L ₁). As a consequence, we obtain the summability result due to Fine; more exactly, the (C,) means of the Walsh—Fourier series of a function f L ₁ converge a.e. to the function in question. Moreover, we prove that the (C,) means are uniformly bounded on H _p whenever 1/( + 1) < p < . We define the two-dimensional dyadic hybrid Hardy space H ₁ and verify that the maximal operator of the (C,,) means of a two-dimensional function is of weak type H ₁ ,L ₁). Consequence, the Walsh—Fourier series of every function f H ₁ is (C,,) summable to the function f.     

Extension of a theorem of Fejér to double Fourier-Stieltjes series

A theorem of Fejér states that if a periodic function F is of bounded variation on the closed interval [0, 2π], then the nth partial sum of its formally differentiated Fourier series divided by n converges to π^-1[F(x+0)-F(x-0)] at each point x. The generalization of this theorem for Fourier-Stieltjes series of (nonperiodic) functions of bounded variation is also well known. The aim of the present article is to extend these results to the (m, n)th rectangular partial sum of double Fourier or Fourier-Stieltjes series of a function F(x, y) of bounded variation over the closed square [0, 2π]×[0, 2π] in the sense of Hardy and Krause. As corollaries, we also obtain the following results:

Two-kaon correlations in central Pb+Pb collisions at 158 a GeV/c

Two-particle interferometry of positive kaons is studied in Pb+Pb collisions at mean transverse momenta approximately 0.25 and 0.91 GeV/c. A three-dimensional analysis was applied to the lower p(T) data, while a two-dimensional analysis was used for the higher p(T) data. We find that the source-size parameters are consistent with the m(T) scaling curve observed in pion-correlation measurements in the same collisions, and that the duration time of kaon emission is consistent with zero within the experimental sensitivity.     

The Two-Parameter Dyadic Derivative and Dyadic Hardy Spaces

It is shown that the maximal operator of the two-parameter dyadic derivative of the dyadic integral is bounded from the two-parameter dyadic Hardy-Lorentz space H _p,q to L _p,q (1/2 < p < , 0 < q L is dyadically differentiable and its derivative is f a.e.     

Cellular automata for the spreading of technologies in socio-economic systems

We introduce an agent-based model for the spreading of technological developments in socio-economic systems where the technology is mainly used for the collaboration/interaction of agents. Agents use products of different technologies to collaborate with each other which induce costs proportional to the difference of technological levels. Additional costs arise when technologies of different providers are used. Agents can adopt technologies and providers of their interacting partners in order to reduce their costs leading to microscopic rearrangements of the system. Analytical calculations and computer simulations revealed that starting from a random configuration of different technological levels a complex time evolution emerges where the spreading of advanced technologies and the overall technological progress of the system are determined by the amount of advantages more advanced technologies provide, and by the structure of the social environment of agents. We show that agents tend to form clusters of identical technological level with a power law size distribution. When technological progress arises, the spreading of technologies in the system can be described by extreme order statistics.     

Absolutely convergent Fourier series, classical function classes and Paley’s theorem

This is a survey paper on the recent progress in the study of the continuity and smoothness properties of a function f with absolutely convergent Fourier series. We give best possible sufficient conditions in terms of the Fourier coefficients of f which ensure the belonging of f either to one of the Lipschitz classes Lip(α) and lip(α) for some 0 < α ≤ 1, or to one of the Zygmund classes Zyg(α) and zyg(α) for some 0 < α ≤ 2. We also discuss the termwise differentiation of Fourier series. Our theorems generalize those by R. P. Boas Jr., J. Németh and R. E. A. C. Paley, and a number of them are first published in this paper or proved in a simpler way.