This is a compilation of definite integrals of the product of the hyperbolic cosecant function and polynomial raised to a general power. In this work, we used our contour integral method to derive a Fourier sine transform in terms of the Lerch functi...
There is no denying fact that nanoparticles of carbon nanotubes are employed to improve the performance of thermal stability in comparison with traditional nanoparticles, this is because nanoparticles of carbon nanotubes possess outstanding material...
This paper studies the analytical solutions of the fractional fluid models described by the Caputo derivative. We combine the Fourier sine and the Laplace transforms. We analyze the influence of the order of the Caputo derivative the Prandtl number,...
In this paper, a frequency estimation method based on a revised three-level discrete Fourier transform (DFT) with an estimation delay reduction technique is proposed. First, the input signal passes through a sine filter twice to improve the ability t...
The objective of this paper is to examine the augmentation of the heat transfer rate utilizing graphene (Gr) and multi-walled carbon nanotubes (MWCNTs) as nanoparticles, and water as a host fluid in magnetohydrodynamics (MHD) flow through an upright...
Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into...
We generalize the classic Fourier transform operator F p by using the Henstock–Kurzweil integral theory. It is shown that the operator equals the H K -Fourier transform on a dense subspace of L p , 1 < p ≤ 2 ....
For embedded impedance spectroscopy, a suitable method for analyzing AC signals needs to be carefully chosen to overcome limited processing capability and memory availability. This paper compares various methods, including the fast Fourier transform...
Two-dimensional advection–diffusion processes with memory and a source concentrated in the symmetry center of the domain have been investigated. The differential equation of the studied model is a fractional differential equation with short-tai...
The central-symmetric time-fractional heat conduction equation with heat absorption is investigated in a solid with a spherical hole under time-harmonic heat flux at the boundary. The problem is solved using the auxiliary function, for which the Robi...
This article presents the results of studies on the impact of acoustic waves on geophones and microphones used to measure airblasts carried out in a reverberation chamber. During the tests, a number of test signals were generated, of which two are pr...
Explicit links of the multivariate discrete (anti)symmetric cosine and sine transforms with the generalized dual-root lattice Fourier–Weyl transforms are constructed. Exact identities between the (anti)symmetric trigonometric functions and Weyl...
Multi-buoy sonar systems achieve target localization by receiving broadband Linear Frequency Modulation signals emitted from the transmitter. Accurate estimations of the parameters of Linear Frequency Modulation signals significantly enhance the loca...
This paper presents an innovative numerical technique for specific classes of stochastic heat equations. Our approach uniquely combines a sixth-order compact finite difference algorithm with fast discrete Fourier transforms. While traditional discret...
This paper proposes a three-level discrete Fourier transform (DFT) method to provide an accurate estimate of power system frequency in real time. The first level decomposes a power system signal into two orthogonal cosine- and sine-filtered signals....
In this work, the advection-dispersion model (ADM) is time-fractionalized by the exploitation of Atangana-Baleanu (AB) differential operator to describe contaminant transport in a geological environment. Dispersion, adsorption, and decay, which are k...
The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm...
The paper proposes an adaptive selection method for the shape parameter in the multi-quadratic radial basis function (MQ-RBF) interpolation of two-dimensional (2D) scattered data and achieves good performance in solving integral equations (O-MQRBF)....
Synthetic Aperture Radar (SAR) is a remote sensing technology that can realize all-weather and all-day monitoring, and it is widely used in ocean ship monitoring tasks. Recently, many oriented detectors were used for ship detection in SAR images. How...
This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimension...
In this paper, a new physical layer authenticated encryption (PLAE) scheme based on the multi-parameter fractional Fourier transform–Orthogonal frequency division multiplexing (MP-FrFT-OFDM) is suggested for secure image transmission over the I...
I address the problem of breather turbulence in ocean waves from the point of view of the exact spectral solutions of the nonlinear Schrödinger (NLS) equation using two tools of mathematical physics: (1) the inverse scattering transform (IST) fo...
In Fourier transform spectroscopy (FTS), the conventional Mertz method is commonly used to correct phase errors of recovered spectra, but it performs poorly in correcting nonlinear phase errors. This paper proposes a phase correlation method–al...
Lined anti-corrosion pipes are widely used in oil and gas, petrochemical, pharmaceutical industries. However, defects, especially delamination, may occur in the production and service of pipes which result in safety accidents. Based on nonlinear ultr...
This paper presents a modified Orthogonal Frequency Division Multiplexing (OFDM) system that combines Discrete Wavelet Transform (DWT) with Discrete Sine Transform (DST) to enhance data rate capacity over traditional Discrete Fourier Transform (DFT)-...
This manuscript optimizes the conjugate heat transfer and thermal-stress analysis for hydromagnetic Brinkman fluid with chemical reaction in permeable media. The governing equations of non-Newtonian Brinkman fluid have been traced out and then fracti...
This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of...
To enable the realization of ultra-low magnetic fields for scientific and technological research, magnetic shielding is required to create a space with low residual magnetic field and high shielding factors. The shielding factors of magnetic shields...
An efficient eigenvalue algorithm is developed for the axial vibration analysis of embedded short-fiber-reinforced micro-/nano-composite rods under arbitrary boundary conditions. In the formulation, nonlocal elasticity theory is used to capture the s...
The modulation transfer function (MTF) is an important parameter for performance evaluation of optical imaging systems in photogrammetry and remote sensing; the slanted-edge method is one of the main methods for measuring MTF. To solve the problem of...
Since the introduction of a series of methods for solving the time-dependent Schrödinger equation (TDSE) in the 80s of the last centry, such as the Fourier transform, the split operator (SO), the Chebyshev polynomial propagator, and complex absorbing...
To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performi...
This paper presents a modelling of nanofluid flow using Caputo fractional derivatives through conservative equations of mass and momentum, and provides an exact solution on un-steady convective flow over a vertical plate with the mass diffusion effec...
For decades, how to improve the resolution limit of seismic data has been a concern for seismologists. For this reason, several geoscientists have proposed various methods of improving the bandwidth of the data. Discovering an easy and scientifically...
The existing ultrasonic thickness measurement systems require high sampling frequencies for echo signal acquisition, leading to complex circuit designs and high costs. Moreover, extracting the characteristics of ultrasonic echo signals for accurate t...
Marine controlled source electromagnetic (CSEM) is an efficient method to explore ocean resources. The amplitudes of marine CSEM signals decay rapidly with the measuring offsets. The signal is easily contaminated by various kinds of noise when the of...
The diffraction contrast modalities accessible by X-ray grating interferometers are not imaged directly but have to be inferred from sine-like signal variations occurring in a series of images acquired at varying relative positions of the interferome...
This paper presents the theoretical background, the numerical implementation, and the applications of a new software that has been developed in recent years for the analysis of wave-structure interactions. The software is developed in the frequency d...
A data-driven fault diagnosis method is proposed in this study to address the challenge of handling a large volume of pressure data in the air brake pipe of high-speed trains. The suggested method utilizes a BP (back propagation) neural network to tr...
The potential for throttle control of hybrid rocket systems has long been known as a potential advantage for a variety of applications. Because only a single flow path is controlled, theoretically, hybrids should be significantly easier to throttle t...
This paper presents a novel non-destructive testing and health monitoring system using a network of tactile transducers and accelerometers for the condition assessment and damage classification of foundation piles and utility poles. While in traditio...
Hydrocyclones are extensively known as important separation devices which are used in many industrial fields. However, the general method to estimate device performance is time-consuming and has a high cost. The aim of this paper was to investigate t...
Precisely recognizing diseases in tomato leaves plays a crucial role in enhancing the health, productivity, and quality of tomato crops. However, disease identification methods that rely on single-mode information often face the problems of insuffici...
Short-term power load forecasting refers to the use of load and weather information to forecast the Day-ahead load, which is very important for power dispatch and the establishment of the power spot market. In this manuscript, a comprehensive study o...
This paper studies the stability of a real-world wind farm, Bison Wind Generation System (BWGS) in the state of North Dakota in the United States. BWGS uses an AC collector grid rated at 34.5 kV and a symmetrical bipolar high-voltage DC (HVDC) transm...