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In this paper, we introduce a new type of integral transforms, called the ARA integral transform that is defined as: G n [ g ( t ) ] ( s ) = G ( n , s ) = s ∫ 0 ∞ t n − 1 e − s t g ( t ) d t ,   s > 0 . We prove some properties of ARA transform and give some examples. Also, some applications of the ARA transform are given.

In this paper, we introduce a new integral transform called the Formable integral transform, which is a new efficient technique for solving ordinary and partial differential equations. We introduce the definition of the new transform and give the sufficient conditions for its existence. Some essential properties and examples are introduced to show the efficiency and applicability of the new transform, and we prove the duality between the new transform and other transforms such as the Laplace transform, Sumudu transform, Elzaki transform, ARA transform, Natural transform and Shehu transform. Finally, we use the Formable transform to solve some ordinary and partial differential equations by presenting five applications, and we evaluate the Formable transform for some functions and present them in a table. A comparison between the new transform and some well-known transforms is made and illustrated in a table.

Electric power utilities must ensure a consistent and undisturbed supply of power, with the voltage levels adhering to specified ranges. Any deviation from these supply specifications can lead to malfunctions in equipment. Monitoring the quality of supplied power is crucial to minimize the impact of fluctuations in voltage. Variations in voltage or current from their ideal values are referred to as \"power quality (PQ) disturbances,\" highlighting the need for vigilant monitoring and management. Signal processing methods are widely used for power system applications which include understanding of voltage disturbance signals and used for retrieval of signal information from the signals Different signal processing methods are used for extracting information about a signal. The method of Fourier analysis involves application of Fourier transform giving frequency information. The method of Short-Time Fourier analysis involves application of Short-Time Fourier transform (STFT) giving time–frequency information. The method of continuous wavelet analysis involves application of Continuous Wavelet transform (CWT) giving signal information in terms of scale and time where frequency is inversely related to scale. The method of discrete wavelet analysis involves application of Discrete Wavelet transform (DWT) giving signal information in terms of approximations and details where approximations and details are low and high frequency representation of original signal. In this paper, an attempt is made to perceive power quality disturbances in MATLAB using Fourier, Short-Time Fourier, Continuous Wavelet and Discrete Wavelet Transforms. Proper understanding of the signals can be possible by transforming the signals into different domains. An emphasis on application of signal processing techniques can be laid for power quality studies. The paper compares the results of each transform using MATLAB-based visualizations. The discussion covers the advantages and disadvantages of each technique, providing valuable insights into the interpretation of power quality disturbances. As the paper delves into the complexities of each method, it takes the reader on a journey of signal processing complexities, culminating in a nuanced understanding of power quality disturbances and their representations across various domains. The outcomes of this research, elucidated through energy values, 3D plots, and comparative analyses, contribute to a comprehensive understanding of power quality disturbances. The findings not only traverse theoretical domains but also find practical utility in real-world scenarios.

The continuous wavelet transform (CWT) has played a key role in the analysis of time-frequency information in many different fields of science and engineering. It builds on the classical short-time Fourier transform but allows for variable time-frequency resolution. Yet, interpretation of the resulting spectral decomposition is often hindered by smearing and leakage of individual frequency components. Computation of instantaneous frequencies, combined by frequency reassignment, may then be applied by highly localized techniques, such as the synchrosqueezing transform and ConceFT, in order to reduce these effects. In this paper, we present the synchrosqueezing transform together with the CWT and illustrate their relative performances using four signals from different fields, namely the LIGO signal showing gravitational waves, a 'FanQuake' signal displaying observed vibrations during an American football game, a seismic recording of the Mw 8.2 Chiapas earthquake, Mexico, of 8 September 2017, followed by the Irma hurricane, and a volcano-seismic signal recorded at the Popocatépetl volcano showing a tremor followed by harmonic resonances. These examples illustrate how high-localization techniques improve analysis of the time-frequency information of time-varying signals. This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

In order to enhance the security of exchanged medical images in telemedicine, we propose in this paper a blind and robust approach for medical image protection. This approach consists in embedding patient information and image acquisition data in the image. This imperceptible integration must generate the least possible distortion. The watermarked image must present the same clinical reading as the original image. The proposed approach is applied in the frequency domain. For this purpose, four transforms were used: discrete wavelets transform, non-subsampled contourlet transform, non-subsampled shearlet transform and discreet cosine transform. All these transforms was combined with Schur decomposition and the watermark bits were integrated in the upper triangular matrix. To obtain a satisfactory compromise between robustness and imperceptibility, the integration was performed in the medium frequencies of the image. Imperceptibility and robustness experimental results shows that the proposed methods maintain a high quality of watermarked images and are remarkably robust against several conventional attacks.

This article is concerned with the question of uniqueness of self-similar profiles for Smoluchowski’s coagulation equation which exhibit algebraic decay (fat tails) at infinity. More precisely, we consider a rate kernel Establishing uniqueness of self-similar profiles for Smoluchowski’s coagulation equation is generally considered to be a difficult problem which is still essentially open. Concerning fat-tailed self-similar profiles this article actually gives the first uniqueness statement for a non-solvable kernel.

We define the wavelet and the continuous wavelet transform in the framework of the Lebedev–Skalskaya transform (LSCWT) and discuss some operational results. Using these results, we obtain the Parseval’s type relation and a reconstruction formula for LSCWT. Moreover, we investigate the composition of LSCWTs and derive its Parseval’s type relation and reconstruction formula.

A hybrid deep learning approach was designed that combines deep learning with enhanced short-time Fourier transform (STFT) spectrograms and continuous wavelet transform (CWT) scalograms for pipeline leak detection. Such detection plays a crucial role in ensuring the safety and integrity of fluid transportation systems. The proposed model leverages the power of STFT and CWT to enhance detection capabilities. The pipeline’s acoustic emission signals during normal and leak operating conditions undergo transformation using STFT and CWT, creating scalograms representing energy variations across time–frequency scales. To improve the signal quality and eliminate noise, Sobel and wavelet denoising filters are applied to the scalograms. These filtered scalograms are then fed into convolutional neural networks, extracting informative features that harness the distinct characteristics captured by both STFT and CWT. For enhanced computational efficiency and discriminatory power, principal component analysis is employed to reduce the feature space dimensionality. Subsequently, pipeline leaks are accurately detected and classified by categorizing the reduced dimensional features using t-distributed stochastic neighbor embedding and artificial neural networks. The hybrid approach achieves high accuracy and reliability in leak detection, demonstrating its effectiveness in capturing both spectral and temporal details. This research significantly contributes to pipeline monitoring and maintenance and offers a promising solution for real-time leak detection in diverse industrial applications.

The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to several other topics as quadrature domains, inverse potential problems and the Laplacian growth. In this present paper we consider the normal matrix model with cubic plus linear potential. In order to regularize the model, we follow Elbau & Felder and introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain We also study in detail the mother body problem associated to To construct the mother body measure, we define a quadratic differential Following previous works of Bleher & Kuijlaars and Kuijlaars & López, we consider multiple orthogonal polynomials associated with the normal matrix model. Applying the Deift-Zhou nonlinear steepest descent method to the associated Riemann-Hilbert problem, we obtain strong asymptotic formulas for these polynomials. Due to the presence of the linear term in the potential, there are no rotational symmetries in the model. This makes the construction of the associated

Video steganography approach enables hiding chunks of secret information inside video sequences. The features of video sequences including high capacity as well as complex structure make them more preferable for choosing as cover media over other media such as image, text, or audio. Video steganography is a prominent as well as the evolving field in the information security domain and significant number of video steganography methods are proposed in recent years. This article provides a comprehensive review of video steganography methods proposed in the literature. This article initially reviews various raw domain-based video steganography methods. In particular, the raw domain-based methods include spatial domain approaches such as least significant bits (LSB), transform domain-based methods such as discrete wavelet transform, discrete cosine transform, etc. Furthermore, the article looks into various compressed domain steganography methods. A critical comparative analysis is included in the article to analyze and contrast the steganography methods proposed in the literature. A brief description of various evaluation matrices for video steganography methods is provided in this article. Moreover, a brief introduction to steganalysis and video steganalysis is provided. The article concludes with a discussion focused on the limitations and challenges of the video steganography methods. Further, a brief insight into future directions in video steganography systems is provided.