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  • Author or Editor: P. Vass x
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Treating the Fourier transform as an over-determined inverse problem is a new conception for determining the frequency spectrum of a signal. The concept enables us to implement several algorithms depending on the applied inversion tool. One of these algorithms is the Hermit polynomial based Least Squares Fourier Transform (H-LSQ-FT). The H-LSQ-FT is suitable for reducing the influence of random noise. The aim of the investigation presented in the paper was to study the noise reduction capability of the H-LSQ-FT in some circumstances. Four wavelet-like signals with different properties were selected for testing the method. Examinations were completed on noiseless and noisy signals. The H-LSQ-FT provided the best noise reduction for the noisy signal having low peak frequency and wide band width. Finally, the results obtained by the H-LSQ-FT were compared to those of other traditional methods. It is showed that the H-LSQ-FT yields better noise filtering than these methods do.

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Aiming at developing cyanobacterial-based biosensors for heavy metal detection, expression of heavy metal inducible genes of the cyanobacterium Synechocystis PCC 6803 was investigated by quantitative RT-PCR upon 15 minutes exposure to biologically relevant concentrations of Co 2+ , Zn 2+ , Ni 2+ , Cd 2+ , Cr 6+ , As 3+ and As 5+ . The ziaA gene, which encodes a Zn 2+ -transporting P-type ATPase showed a markedly increased mRNA level after incubation with Cd 2+ and arsenic ions, besides the expected induction by Zn 2+ ions. The Co 2+ efflux system-encoding gene coaT was strongly induced by Co 2+ and Zn 2+ ions, moderately induced by As 3+ ions, and induced at a relatively low level by Cd 2+ and As 5+ ions. Expression of nrsB , which encodes a part of a putative Ni 2+ efflux system was highly induced by Ni 2+ salts and at a low extent by Co 2+ and Zn 2+ salts. The arsB gene, which encodes a putative arsenite-specific efflux pump was highly induced by As 3+ and As 5+ ions, while other metal salts provoked insignificant transcript level increase. The transcript of chrA , in spite of the high sequence similarity of its protein product with several bacterial chromate transporters, shows no induction upon Cr 6+ salt exposure. We conclude that due to the largely unspecific heavy metal response of the studied genes only nrsB and arsB are potential candidates for biosensing applications for detection of Ni 2+ and arsenic pollutants, respectively.

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In the paper a 2D joint inversion method is presented, which is applicable for the simultaneous determination of layer thickness variation and petrophysical parameters by processing well-logging data acquired in several boreholes along the profile. The so-called interval inversion method is tested on noisy synthetic data sets generated on hydrocarbon-bearing reservoir models. Numerical experiments are performed to study the convergence and stability of the inversion procedure. Data and model misfit, function distance related to layer thickness fitting are measured as well as estimation errors and correlation coefficients are computed to check the accuracy and reliability of inversion results. It is shown that the actual inversion procedure is stable and highly accurate, which arises from the great over-determination feature of the inverse problem. Even a case study is attached to the paper in which interval inversion procedure is applied for processing of multi-borehole logging data acquired in Hungarian hydrocarbon exploratory wells in order to determine petrophysical parameters and lateral changes of layer thicknesses.

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This paper presents a new algorithm for the inversion-based 1D Fourier transformation. The continuous Fourier spectra are assumed as a series expansion with the scaled Hermite functions as square-integrable set of basis functions. The expansion coefficients are determined by solving an over-determined inverse problem. In order to define a quick and easy-to-use formula in calculating the Jacobi matrix of the problem a special feature of the Hermite functions are used. It is well-known, that the basic Hermite functions are eigenfunctions of the Fourier transformation. This feature is generalized by extending its validity for the scaled Hermite functions. Using the eigenvalues, given by this generalization, a very simple formula can be derived for the Jacobi matrix of the problem resulting in a quick and more accurate inversion-based Fourier transform algorithm. The new procedure is numerically tested by using synthetic data.

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