Applicability of the BioArena System to Investigation of the Mechanisms of Biological Effects

JPC – Journal of Planar Chromatography – Modern TLC - Bioautography can be extended to a complex system called BioArena by linking different steps to it, for example dissolving a...     

Absolutely convergent Fourier integrals and classical function spaces

We study the continuity and smoothness properties of functions whose Fourier transforms. belong to , and give sufficient conditions in terms of to ensure that f belongs 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. These sufficient conditions are also necessary under an additional positivity assumption. Our theorems extend known results from periodic to nonperiodic functions. This research was supported by the Hungarian National Foundation for Scientific Research under Grant T 046 192.     

On the absolute convergence of multiple fourier series

Let f: R ^N → C be a periodic function with period 2π in each variable. We prove suffcient conditions for the absolute convergence of the multiple Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative in case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to multiple Fourier series. This research was started while the first author was a visiting professor at the Department of Mathematics, Texas A&M University, College Station during the fall semester in 2005; and it was also supported by the Hungarian National Foundation for Scientific Research under Grant T 046 192.     

Multiple beneficial effects of resveratrol and their chemical-biochemical basis

On the basis of in vitro and in vivo investigations trans-resveratrol (RV) is a natural, concentration-dependent formaldehyde (HCHO) mobilizer, scavenger, capture and carrier molecule. The capturing and mobilization of HCHO from a given biological unit (e.g. tissue) with RV (first step) generates a chemopreventive effect. The reaction products between endogenous HCHO and RV (second step) may exert killing/inhibiting effects on pathogens and/or cancer cells. These two steps result in the double effect of RV. From the model reaction mixture of RV and HCHO in diluted formalin solution, different reaction products were detected, separated and identified. Similar reactions can be observed between RV and endogenous HCHO in plant and animal tissues as well. Capturing the HCHO molecules in model experiments with HCHO-capture molecules (in vitro conditions) the antibacterial activity of RV decreased substantially. The in vitro investigations were extended to in vivo conditions. The discovery of a quadruple immune response of plants to pathogens resulting from pretreatment with RV opens new horizons in the confirmation of the diverse beneficial effects of RV.     

Raman spectroscopic evaluation of the influence of Pseudomonas bacteria on aflatoxin B1 in the BioArena complex bioautographic system

The mechanism of the antibacterial‐toxic effect of aflatoxin B1 (AFB1) was investigated in the BioArena complex bioautographic system that consists of planar liquid chromatographic development and biological detection. In this system, the killing‐inhibiting activity of AFB1 against Pseudomonas savastanoi (Psm) bacterial cells was visualised. The role of formaldehyde (HCHO) was suggested in the antibacterial‐toxic action of AFB1. Raman spectroscopy (RS) was used to investigate whether the excess HCHO found earlier in the AFB1 spot (comparing with background) originated partly from the demethylation of the toxin, or only from the enhanced demethylation of the normal cell ingredients because of the stress situation. Fourier transform (FT) Raman and surface‐enhanced FT‐Raman spectra were obtained in situ about the AFB1 chromatographic and background spots in bacteria‐free and inoculated thin layer chromatography (TLC) layers, and ex situ about their dried methanolic extract. The reduction of the δ CH₃ band of AFB1 (1386 cm⁻¹) in the presence of Psm can indicate the demethylation of aflatoxin at its methoxy‐group in BioArena. It seems from the Raman spectra that, apart from demethylation, aflatoxin does not suffer other structural changes. However, Psm can reduce the Raman activity of νCO bond of the pyran ring of AFB1, causing lower intensity and a broader band (1747 and 1754 cm⁻¹). Psm can also disrupt the strong interactions between the AFB1 and the adsorbent layer through the νCO bond of the cyclopentene ring causing a blue‐shift (1667 → 1686 cm⁻¹). The very reactive HCHO that originated from exogenous sources, e.g. from the demethylation of AFB1, has no determined biochemical pathway, so it means higher risk. Copyright © 2008 John Wiley & Sons, Ltd.     

On the Riemann Summability of Fourier Integrals and Real Hardy Spaces

We consider the Riemann means of single and multiple Fourier integrals of functions belonging to L¹ or the real Hardy spaces defined on ℝⁿ, where n ≥ 1 is an integer. We prove that the maximal Riemann operator is bounded both from H¹(ℝ) into L¹(ℝ) and from L¹(ℝ) into weak –L¹(ℝ). We also prove that the double maximal Riemann operator is bounded from the hybrid Hardy spaces H^(1,0)(ℝIsup2), H^(0,1)(ℝ²⁾ into weak –L¹(ℝ²). Hence pointwise Riemann summability of Fourier integrals of functions in H^(1,0) ∪ H^(0,1)(ℝ²) follows almost everywhere.The maximal conjugate Riemann operators as well as the pointwise convergence of the conjugate Riemann means are also dealt with.     

Approximation by Nörlund means of double Fourier series for Lipschitz functions

We study the rate of uniform approximation by Nörlund means of the rectangular partial sums of the double Fourier series of a function |(x, y) belonging to the class Lip α, 0 < α 1, on the two-dimensional torus −π < x, y π. As a special case we obtain the rate of uniform approximation by double Cesàro means.     

Approximation by Nörlund means of Walsh-Fourier series

We study the rate of approximation by Nörlund means for Walsh-Fourier series of a function in L^p and, in particular, in Lip(α, p) over the unit interval [0, 1), where α > 0 and 1 p ∞. In case p = ∞, by L^p we mean C_W, the collection of the uniformly W-continuous functions over [0, 1). As special cases, we obtain the earlier results by Yano, Jastrebova, and Skvorcov on the rate of approximation by Cesàro means. Our basic observation is that the Nörlund kernel is quasi-positive, under fairly general assumptions. This is a consequence of a Sidon type inequality. At the end, we raise two problems.