Mohammad Alshammari, Saleh Alshammari · Boundary Value Problems · 2025
In this paper, the time-fractional order Belousov-Zhabotinsky (BZ) reaction system is studied mathematically within the framework of conformable fractional derivative to characterize the memory and hereditary features in oscillatory chemical kinetics. Two efficient semi-analytical methods, the Conformable Elzaki Adomian Decomposition Method (CEADM) and Consfomable Fractional Reduced Differential Transform Method (CFRDTM) which avoid the analytical complexities due to strong nonlinearity in the system are proposed and investigated. The selection of the Elzaki transform permits fast computation of time-fractional terms due to its better convergence and handling with fractional operators when compared to classical Laplace-type transforms. A convergence theorem and error estimates are established in the Banach space showing that the solutions obtained are reliable and stable. Numerical results and graphical simulations show that both methods are accurate compared with the exact solutions for different fractional orders α with small absolute errors. Oscillatory dynamics are investigated for different fractional order, showing crossover between memory-dependent and classical behaviors. Comparative analyses show the computational efficiency and rapid convergence rate of CEADM compared with CFRDTM. In general, the presented conformable-based method provides a reliable, efficient as well as accurate approach for simulating fractional systems arising in chemical and physical sciences.
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Qin Shu-ren, Zhong You-ming · 2003
At present, there exist many transformation methods in signal analysis and there is an increasing number of methods being developed. It is of great importance to study how to grasp transformation methods of signal analysis and how to implement them by using software on a computer. In this paper an attempt is made to build a unified mathematical model for signal transformations. Concepts such as domain variable, domain variable function, transform kernel function etc. are given and the unified mathematical model of the Fourier transform, the short time Fourier transform and the wavelet transform are studied and established. Furthermore, the flowchart of the model is given and the physical meaning of the model is described. Finally the values of the parameters and parameter functions of Fourier transform, short time Fourier transform and wavelet transform in the model are given in this paper.
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Oscar Leonardo Mosquera-Dussán, Daniel Alfonso Botero‐Rosas, Maurício Cagy et al. · 2015
Digital signal processing of the electroencephalogram (EEG) became important in monitoring depth of anesthesia (DoA) being used to provide a better anesthetic technique. The objective of this work was to conduct a review about nonlinear mathematical methods applied recently to the analyses of nonlinear non-stationary EEG signal. A review was conducted showing time- and frequency-domain nonlinear mathematical methods recently applied to EEG analysis: Approximate Entropy, Sample Entropy, Spectral Entropy, Permutation Entropy, Wavelet Transform, Wavelet Entropy, Bispectrum, Bicoherence and Hilbert Huang Transform. Some algorithms were implemented and tested in one EEG signal record from a patient at The Sabana University Clinic. Recently published results from different methods are discussed. Nonlinear techniques such as entropy analysis in time domain and combination with wavelet transform, and Hilbert Huang transform in frequency domain have shown promising results in classifications of depth of anesthesia stages.
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Bo Xiao, Han Xue-hui · 2010
Three kinds of methods for automatic zonation,including mathematical statistics,non-mathematical statistics methods and artificial intelligence methods are presented in this paper.Most of the approaches,such as intraformation discrepance method,orderly cluster analysis,extreme value variance clustering method,self-organizing neural network,fuzzy pattern recognition method,the activity function,wavelet transform and Walsh transform methods are analyzed.Comparing the advantages and disadvantages of zoning approaches and combining with the logging responses' geological and physical foundation,we conclude that some defects exist in the existing approaches and denoising,improvement of the vertical resolution and zoning approaches should be improved separately and jointed especially in the future,and that will allow to provide more favorable support for the lithology identification,logging facies analysis,reservoir delineation and reservoir parameters research.
Cited by 1
Rui Zhang, Yongyang Zhou, Jun Huang · International Journal of u- and e- Service Science and Technology · 2017
The analysis of the voltage fluctuation and flicker is important to inhibit flicker. Mathematical morphology filter testing methods are proposed in this paper on the basis of Hilbert transform. Using Hilbert transform to extract flicker envelope, and the mathematical morphological filtering method is used to filter out high frequency noise of the grid. Simulation results show that this method can realize flicker signal detection, determine spectrum of flicker signal through mathematical morphology filtering method, and the measurement precision compared with spectrum amplitude of the signal with noise have larger increase.
Cited by 0Open access
Antonio Glaría, Rodrigo Salas, Stéren Chabert et al. · Frontiers in Applied Mathematics and Statistics · 2022
Linear functional analysis historically founded by Fourier and Legendre played a significant role to provide a unified vision of mathematical transformations between vector spaces. The possibility of extending this approach is explored when basis of vector spaces is built Tailored to the Problem Specificity (TPS) and not from the convenience or effectiveness of mathematical calculations. Standardized mathematical transformations, such as Fourier or polynomial transforms, could be extended toward TPS methods, on a basis, which properly encodes specific knowledge about a problem. Transition between methods is illustrated by comparing what happens in conventional Fourier transform with what happened during the development of Jewett Transform, reported in previous articles. The proper use of computational intelligence tools to perform Jewett Transform allowed complexity algorithm optimization, which encourages the search for a general TPS methodology.
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Nomaz Mirzaev, Johongir Urinboev, Nuraddin Gafforov et al. · 2025
This work provides an overview of modern methods for processing speech signals used in speech recognition systems. Processing methods in the time, frequency, and frequency-time domains have been analyzed. Key approaches such as Fourier transform, wavelet transform, cepstral analysis, linear prediction methods, correlation analysis, using neural network, hidden Markov models, and dynamic time warping are examined. The conducted research allows for an assessment of the capabilities of existing methods, their effectiveness, as well as promising directions for the implementation of new mathematical apparatuses.
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David Gottlieb, Steven A. Orszag · Society for Industrial and Applied Mathematics eBooks · 1977
This monograph gives a mathematical analysis of spectral methods for mixed initial-boundary value problems. Spectral methods have become increasingly popular in recent years, especially since the development of fast transform methods, with applications in numerical weather prediction, numerical simulations of turbulent flows, and other problems where high accuracy is desired for complicated solutions. The development of a mathematical theory is given that explains why spectral methods work and how well they work.
Cited by 766Open access
V. Kh. Yasoveev, Marat Akhmetshin · MATEC Web of Conferences · 2016
Basic methods of analysis of vibration transducers signals were reviewed. Continuous wavelet transform, being a time-frequency transform, was found to be an advanced mathematical tool for analysis of vibration signals. Experimental studies revealed obvious changes in the continuous wavelet transform spectrum depending on the existing defects. A method for detection and identification of technological violations based on the analysis of CWT spectrum components and normalized correlation coefficient was suggested. In accordance with the suggested method software for vibration diagnostics was developed.
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Hassan Eltayeb, Adem Kılıçman, Mohamed Jleli · Greater South Information System · 2015
It is well known that the methods connected to the employment of integral transforms are very useful in mathematical analysis.Those methods are successfully applied (i) to solve differential and integral equations, (ii) to study special functions, (iii) to compute integrals.In this special issue we publish many articles of the highest quality.The aim of these papers is to highlight the importance of fractional operators of integral transform and their applications and let the readers of this journal know about the possibilities of this new tool.In particular, various potential topics are discussed: (i) mathematical analysis of fractional integral transform theoretical methods, (ii) new methods for solving Cauchy problem for the space-time fractional partial differential equation, (iii) applications of integral transform fractional, including fractional methods, (iv) applying fractional integral transform to solution of systems of differential equations and applications in physics, mechanics, and fractional Schrödinger equation in quantum theory, (v) applications of integral transform for special functions, for example, prefunction, and (vi) applications of integral transform to fractional convolution products.As editors of this special issue, the most difficult problem that we came across was to choose the best papers from the submitted high-quality works.
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Hassan Eltayeb, Adem Kılıçman, Mohamed Jleli · Greater South Information System · 2015
It is well known that the methods connected to the employment of integral transforms are very useful in mathematical analysis.Those methods are successfully applied (i) to solve differential and integral equations, (ii) to study special functions, (iii) to compute integrals.In this special issue we publish many articles of the highest quality.The aim of these papers is to highlight the importance of fractional operators of integral transform and their applications and let the readers of this journal know about the possibilities of this new tool.In particular, various potential topics are discussed: (i) mathematical analysis of fractional integral transform theoretical methods, (ii) new methods for solving Cauchy problem for the space-time fractional partial differential equation, (iii) applications of integral transform fractional, including fractional methods, (iv) applying fractional integral transform to solution of systems of differential equations and applications in physics, mechanics, and fractional Schrödinger equation in quantum theory, (v) applications of integral transform for special functions, for example, prefunction, and (vi) applications of integral transform to fractional convolution products.As editors of this special issue, the most difficult problem that we came across was to choose the best papers from the submitted high-quality works.
Cited by 0Open access
V. Musoko · 2015
Abstract: The paper presents the fundamental mathematical methods used in the analysis and processing of three-dimensional (3D) image objects. The methods to be discussed include 3D discrete Fourier transform (DFT) and Wavelet transform (WT). Firstly there is a need to generate an object for testing followed by its 3D visualization and the generation of the random noise. Computer visualization and processing is applied to the 3D biomedical image data.
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Konstantin Yu. Mashunin, Yu. K. Mashunin · Journal of Computer and Systems Sciences International · 2013
A new technology (technique) that helps construct a mathematical model of a complex engineering system by optimal decision making based on it is given. To construct the model of an engineering system, methods of regressive analysis are used to transform the initial (experimental) data into a vector (multiobjective) mathematical programming problem. To solve it, methods are presented that rely on criteria normalization and principle of guaranteed result. The technique of constructing models of engineering systems, methods of solving the vector mathematical programming problem and optimal decision making are demonstrated by the test examples in Matlab.
Cited by 17
Jun Zhang, Ruzong Fan, Fangyang Shen et al. · Journal of Applied Analysis & Computation · 2023
Mathematics serves as a fundamental intelligent theoretic basis for computation, and mathematical analysis is very useful to develop computational methods to solve various problems in science and engineering. Integral transforms such as Laplace Transform have been playing an important role in computational methods. In this paper, we will introduce Sumudu Transform in a new computational approach, in which effective computational methods will be developed and implemented. Such computational methods are straightforward to understand, but powerful to incorporate into computational science to solve different problems automatically. We will provide computational analysis and essentiality by surveying and summarizing some related recent works, with additional automatic proof details by applying system built-in functions. Applications include the computation of coefficients of Taylor's expansions, calculation of generating functions, mathematical identity proofs, solving differential equations and integral equations. For demonstration purposes, some of the methods were implemented in Maple with demonstrational results matching the expected values.
Cited by 1Open access
YASUDA, SILVIO KOZO · Zenodo (CERN European Organization for Nuclear Research) · 2025
Title: The YK Transform: A Novel Spectral Analysis Method with Applications Description:This work introduces the YK (Yasuda-Keidai) Transform, a groundbreaking spectral analysis technique that revolutionizes the detection of ultra-subtle patterns in astronomical data. The method demonstrates unprecedented capabilities in identifying quantum-level spectral features that would be virtually undetectable using conventional Fourier analysis. Key Features:- Novel mathematical framework based on 24-discretization processing- Selective frequency filtering analogous to magnetic needle detection- Detection of features requiring SNR > 1000 in traditional methods- Integration with Dark Light Theory Major Discoveries:1. Quantum-Level Structures: - Cascade patterns with exact energy ratios - Regular separations of 0.001Å - Quantum coherence at galactic scales 2. Ultra-Rare Emission Lines: - [FeXXI] 1354.08Å (T > 10⁷ K) - [ArXIV] 4412.20Å - [NiXIII] 5115.80Å 3. Ultra-Fine Oscillations: - Sub-0.1% amplitude patterns - Extreme wavelength regularity - Potential dark matter signatures Technical Implementation:- Complete Python implementation- Mathematical formalization- Performance benchmarks- Validation methodology This repository contains:- Full LaTeX manuscript- Python source code- Test data and examples- Documentation and usage guidelines Impact:The YK Transform enables detection of spectral features that would require millions of observation hours using traditional methods, potentially revolutionizing our ability to study dark matter and other ultra-weak astrophysical phenomena. Keywords: spectral analysis, dark matter detection, quantum astrophysics, JWST, data analysis, astronomical spectroscopy, mathematical transforms, signal processing
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Qasem M. Tawhari · AIMS Mathematics · 2025
This paper investigated the Schrödinger and Korteweg-de Vries equations within the framework of fractional-order differential equations, utilizing the variational iteration transform method and the q-homotopy analysis transform method. These equations, crucial for modeling wave propagation and nonlinear dispersive systems, were analyzed using the Caputo fractional derivative to explore the influence of non-integer orders on their dynamics. The findings contributed to a deeper understanding of how fractional-order parameters affected the behavior of nonlinear wave models and oscillations, underscoring the growing importance of fractional calculus in mathematical physics and engineering. Both methods presented in this study effectively converted fractional-order problems into iterative schemes that were straightforward to solve, leading to quicker convergence of the analytical solutions. A comparative analysis evaluated the accuracy, computational efficiency, and convergence properties of the variational iteration transform method (VITM) and the q-homotopy analysis transform method q-HATM. The results, supported by numerical simulations and various graphical representations, validated the practicality and effectiveness of these methods for solving complex fractional differential equations. This study not only enhanced our comprehension of fractional wave dynamics but also strengthened the body of knowledge in both analytical and computational methods in mathematical physics and engineering.
Cited by 2Open access
Einar Mæland · Geophysics · 2000
Abstract Linear integral transforms play an important role in many fields in physics. A transform of this kind is given by the general formula (1)where K(x, ξ) is the kernel of transform and the function g(x) is the transform of the function f(x). Of great importance is the Fourier transform, for which the kernel takes the form of a complex exponential function . Besides its applications in signal analysis (Papoulis, 1977), the Fourier transform is the foundation for a wide array of mathematical concepts and methods in optics.
Cited by 4
Neha Soorma, Jaikaran Singh, Mukesh Tiwari · arXiv (Cornell University) · 2014
This paper describe the features extraction algorithm for electrocardiogram (ECG) signal using Huang Hilbert Transform and Wavelet Transform. ECG signal for an individual human being is different due to unique heart structure. The purpose of feature extraction of ECG signal would allow successful abnormality detection and efficient prognosis due to heart disorder. Some major important features will be extracted from ECG signals such as amplitude, duration, pre-gradient, post-gradient and so on. Therefore, we need a strong mathematical model to extract such useful parameter. Here an adaptive mathematical analysis model is Hilbert-Huang transform (HHT). This new approach, the Hilbert-Huang transform, is implemented to analyze the non-linear and nonstationary data. It is unique and different from the existing methods of data analysis and does not require an a priori functional basis. The effectiveness of the proposed scheme is verified through the simulation.
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Carl J. Nelson · Durham e-Theses (Durham University) · 2017
Mathematical morphology is an established field of image processing first introduced as an application of set and lattice theories. Originally used to characterise particle distributions, mathematical morphology has gone on to be a core tool required for such important analysis methods as skeletonisation and the watershed transform. In this thesis, I introduce a selection of new image analysis techniques based on mathematical morphology. Utilising assumptions of shape, I propose a new approach for the enhancement of vessel-like objects in images: the bowler-hat transform. Built upon morphological operations, this approach is successful at challenges such as junctions and robust against noise. The bowler-hat transform is shown to give better results than competitor methods on challenging data such as retinal/fundus imagery. Building further on morphological operations, I introduce two novel methods for particle and blob detection. The first of which is developed in the context of colocalisation, a standard biological assay, and the second, which is based on Hilbert-Edge Detection And Ranging (HEDAR), with regard to nuclei detection and counting in fluorescent microscopy. These methods are shown to produce accurate and informative results for sub-pixel and supra-pixel object counting in complex and noisy biological scenarios. I propose a new approach for the automated extraction and measurement of object thickness for intricate and complicated vessels, such as brain vascular in medical images. This pipeline depends on two key technologies: semi-automated segmentation by advanced level-set methods and automatic thickness calculation based on morphological operations. This approach is validated and results demonstrating the broad range of challenges posed by these images and the possible limitations of this pipeline are shown. This thesis represents a significant contribution to the field of image processing using mathematical morphology and the methods within are transferable to a range of complex challenges present across biomedical image analysis.
Cited by 0
Adeliya Yu. Burova, Timur O. Usatenko · Journal of Physics Conference Series · 2021
Abstract The issues related to the digitalization of the spectral analysis of the polyharmonic signal are considered. There are various digital methods of discrete Fourier transform (DFT) of such a signal. The purpose of the study is a comparative analysis of the known methods for transforming a complex signal, which make it possible to minimize the required number of multiplication operations in its transformation algorithms. The research used methods of mathematical and software modeling of digital signal processing algorithms. The methods of discrete Fourier transform based on multiband digital filtering (MDF) with one low-frequency digital filter and with an extended window based on the so-called bank of non-recursive digital filters (BDF) are described. There are the results of a comparative analysis of these methods.
Cited by 12Open access