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1

Finitely additive functions in measure theory and applications

Alpay Daniel, Jorgensen Palle

Opuscula Mathematica

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2024

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Vol. 44, no. 3

323--339

EN

In this paper, we consider, and make precise, a certain extension of the Radon–Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of μ-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures μ, and to adjoints of composition operators.

2

Secured healthcare monitoring system in wireless body area network using polynomial based technique

Shanthapriya R., Vaithianathan V.

Polish Journal of Medical Physics and Engineering

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2019

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Vol. 25, Iss. 3

171--177

EN

Nowadays healthcare is a standout amongst the most rapidly developing application zone in body area networks (BANs). BANs are anticipated to play a significant role in the stream of patient-health monitoring. To provide, secure BAN access to the entire system without disturbing the confidentiality of patients’ therapeutic data is a major challenge. Security of the BAN can be improved by using a polynomial curve-based steganography technique. The performance of the proposed BAN is evaluated by using a Fourier transform and Wavelet transform. The results of the proposed BAN are presented and compared for both the transforms.

3

The directions of current applications of transforms to seismic data processing and analysis

Kasina Z.

Geoinformatica Polonica

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2009

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T. 9

57--77

EN

In the presented paper the directions of current applications of the mathernatical transforms to seismic data processing and analysis have been described. In the analysis the following transforms were taken into consideration: Gabor transform, Karhunen-Loeve transform (K-L Transform ). wavelet transform (WT transform ), curvelet transform. The theoretical background of the analyzed transforms were presented and their main applications relating to coherent and random noise attenuation in the seismic data processing. Additionally, the applications were described relating to seismic sections analysis based on the instantaneous spectral analysis ISA) as well as the applications used in the image analysis. The comparison of the results of different kinds of spectral decompositions were presented using selected model and field data.

PL

W pracy przedstawiono kierunki najnowszych zastosowań transformat matematycznych w przetwarzaniu i analizie danych sejsmicznych. W analizie uwzględniono transformację Gabora. transformację Karhunena-Loevego (K-L Transform), transformację falkową (Wavelet Transform ) oraz transformację krzywkową (Curvelet Transform ). Przedstawiono podstawy teoretyczne tych transformacji oraz ich główne zastosowania, związane z usuwaniem zakłóceń koherentnych i przypadkowych w procesie przetwarzania danych sejsmicznych. Opisano także zastosowania związane z analizą sekcji sejsmicznych opartą na chwilowej analizie spektralnej (ISA) oraz zastosowania związane z analizą obrazów. Przedstawiono porównanie wyników różnych typów dekompozycji spektralnej na wybranych danych modelowych i polowych.