The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In this paper, we propose and evaluate the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. This discrete theory is shown to arise from discretization schemes that have been previously employed with the 1D DFT and the discrete Hankel Transform (DHT). The proposed transform possesses orthogonality properties, which leads to invertibility of the transform. In the first part of this two-part paper, the theory of the actual manipulated quantities is shown, including the standard set of shift, modulation, multiplication, and convolution rules. Parseval and modified Parseval relationships are shown, depending on which choice of kernel is used. Similar to its continuous counterpart, the 2D DFT in polar coordinates is shown to consist of a 1D DFT, DHT and 1D inverse DFT.

Computation of Discrete Fourier Transform (DFT) is a challenging task. Especially, on computational machines/embedded systems where resources are limited. The importance of Fourier Transform (FT) cannot be denied in the field of signal processing. This paper proposes a technique that can compute Discrete Fourier Transforms for a matrice or vector with the help of matrix multiplication. Moreover, this paper discusses the trivial methods used for computation of DFT along with methods based on matrix multiplication used to compute discrete Fourier Transform in addition to the shortcomings. The proposed method can help in the calculation of a Discrete Fourier Transformation matrix by truncation of values from the proposed generic method which can help in computing DFT of varying lengths of vectors. On legacy computing machines and programming environments, having support for matrix multiplication, the proposed methodology can be implemented.

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

The Fourier Continuous Derivative ($D_C$) offers a unique perspective on fractional differentiation grounded in the theory of Fourier series. This approach has the potential to address problems across various disciplines, including physics, engineering, and mathematics. The primary insight underpinning this approach is that a convex function defined on $\mathbb{Z}$ retains its convexity on $\mathbb{R}$. This paper delves into the Fourier Continuous Derivative, compares it with traditional fractional derivatives, and outlines its possible real-world applications, such as modeling viscoelastic materials, solving wave equations, and financial data analysis.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

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 for time-frequency analysis because is a method that can compute on the fly the Fourier transform (FT) of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients, (4) the fitting of the historical Bitcoin market data from 2014-12-01 to 2018-01-08 and (5) the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT), which is a well-known method for time-frequency analysis.

Real time camouflaged object detection so far using CAMO or COD10K datset has been able to achieve mAP50 less than 64%. We present a fourier transfom and Milkyway filament extraction based method extracting shape and edges of camouflaged object, achieving 88%+ mAP50 while continuing to deliver real time detection using YOLOv8s based models. This allows for search and rescue of wilelife and humans in smoke, fog, natural disasters possible by combining low compute Yolov8s model on headup display for rescue workers such as firefighters, first reponders etc.

Fourier expansions by the polyharmonic-Neumann eigenfunctions showed improved convergence compared to the Fourier expansions by the classical trigonometric system due to the rapid decay of the corresponding Fourier coefficients. Based on this evidence, we investigate interpolations on a finite interval that are exact for the polyharmonic-Neumann eigenfunctions and show the same benefits. Further, we improve the convergence of the interpolations by applying the idea of quasi-periodicity, where the basis functions are periodic on a slightly extended interval. We show that those interpolations have much better convergence rates away from the endpoints of the approximation interval. Moreover, the interpolations are more accurate on the entire interval. We prove those properties for a specific case of the polyharmonic-Neumann eigenfunctions known as the modified Fourier system. For other basis functions, we provide evidence based on the results of numerical experiments.

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum - not taken into account by Fourier theory and let alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: a) compact support with excellent energy output treatment, b) low computational cost, O(N) for signals and O(N2) for images, c) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform (DHT) and inverse DFT sequence can be exploited for efficient code. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.

The obtention of simple formulae for the Lebesgue constants arising in the the classical Fourier series approximation is presented. Both even and odd cases are treated enlarging Fejér result. Asymptotic formulae are also obtained.

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

Texture is essential information for image representation, capturing patterns, and structures. Consequently, texture plays a crucial role in the manufacturing industry and has been extensively studied in the fields of computer vision and pattern recognition. However, real-world textures are susceptible to defects, which can degrade the image quality and cause various issues. Therefore, there is a need for accurate and effective methods to detect texture defects. In this study, a simple autoencoder and Fourier transform were employed for texture defect detection. The proposed method combines Fourier transform analysis with the reconstructed template obtained from the simple autoencoder. Fourier transform is a powerful tool for analyzing the frequency domain of images and signals. Moreover, analyzing the frequency domain enables effective defect detection because texture defects often exhibit characteristic changes in specific frequency ranges. The proposed method demonstrates effectiveness and accuracy in detecting texture defects. Experimental results are presented to evaluate its performance and compare it with those of existing approaches.

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

This algorithm is designed to perform Discrete Fourier Transforms (DFT) to convert temporal data into spectral data. This algorithm obtains the Fourier Transforms by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this DFT algorithm is that it can produce spectral data at any user-defined resolution.

We use Fourier analysis to access risk in financial products. With it we analyze price changes of e.g. stocks. Via Fourier analysis we scrutinize quantitatively whether the frequency of change is higher than a change in (conserved) company value would allow. If it is the case, it would be a clear indicator of speculation and with it risk. The entire methods or better its application is fairly new. However, there were severe flaws in previous attempts; making the results (not the method) doubtful. We corrected all these mistakes by e.g. using Fourier transformation instead of discrete Fourier analysis. Our analysis is reliable in the entire frequency band, even for frequency of 1/1d or higher if the prices are noted accordingly. For the stocks scrutinized we found that the price of stocks changes disproportionally within one week which clearly indicates speculation. It would be an interesting extension to apply the method to crypto currencies as these currencies have no conserved value which makes normal considerations of volatility difficult.

Form deviation generated during the milling profile process poses challenges to the precision and functionality of industrial fixtures and product manufacturing across various sectors. The inspection of contour profile quality often relies on commonly employed contact methods for measuring form deviation, but these methods frequently face limitations that can impact the reliability and overall accuracy of the inspection process. This paper introduces a novel approach, the novel intelligent inspection method (NIIM), developed to accurately inspect and categorize contour profiles in machined parts manufactured through the milling process by computer numerical control (CNC) machines. The NIIM integrates a calibration piece, a vision system (RAM−StarliteTM), and machine learning techniques to analyze the line profile and classify the quality of contour profile deformation generated during CNC milling. The calibration piece is specifically designed to identify form deviations in the contour profile during the milling process. The RAM−StarliteTM vision system captures contour profile images corresponding to curves, lines, and slopes. An algorithm generates a profile signature, extracting Fourier descriptor features from the contour profile to analyze form deviations when compared to an image reference. A feed-forward neural network is employed to classify contour profiles based on quality properties. Experimental evaluations involving 60 machined calibration pieces, resulting in 356 images for training and testing, demonstrate the accuracy and computational efficiency of the proposed NIIM for profile line tolerance inspection. Results demonstrate that the NIIM offers 96.99% accuracy, low computational requirements, 100% inspection capability, quality classification.

Covid-19 is a lung disease caused by a Coronavirus family virus. Due to its extraordinary prevalence and death rates, it has spread quickly to every country in the world. Thus, achieving peaks and outlines and curing different types of relapses is extremely important. Given the worldwide prevalence of Coronavirus and the participation of physicians in all countries, Information has been gathered regarding the properties of the virus, its diverse types, and the means of analyzing it. Numerous approaches have been used to identify this evolving virus. It is generally considered the most accurate and acceptable method of examining the patient's lungs and chest through a CT scan. As part of the feature extraction process, a method known as fractional Fourier transform (FrFT) has been applied as one of the time-frequency domain transformations. The proposed method was applied to a database consisting of 2481 CT images. Following the transformation of all images into equal sizes and the removal of non-lung areas, multiple combination windows are used to reduce the number of features extracted from the images. In this paper, the results obtained for KNN and SVM classification have been obtained with accuracy values of 99.84% and 99.90%, respectively.

A new set of basis functions is presented. The foundation in mathematics is established. To reconstruct a signal, it is compared to the Fourier basis functions. The M-basis functions' potential applications are also presented.

This paper presents a simple and streamlined compensation technique for improving the quality of Synthetic Aperture Radar (SAR) images based on the Range Doppler Algorithm (RDA). Incorrect Doppler estimation in space orbit, caused by unexpected radar motion errors, orbit mismatches, and other factors, can significantly degrade SAR image quality. These inaccuracies result in mismatches between the azimuth-matched filter and the received Doppler chirp signal. To address this issue, we propose a Doppler estimation method that leverages the Fractional Fourier Transform (FrFT) and cross-correlation techniques. The received signals are compared with the azimuth-matched filter based on the rotation angle in the FrFT domain, and the Doppler centroid is adjusted to achieve optimal alignment. This process ensures high correlation values and enhanced resolution in the final SAR image. The efficacy of the proposed technique is validated through experiments using real spaceborne SAR data from the practical satellite. The results demonstrate significant improvements in image quality and resolution compared to conventional algorithms, highlighting the advantages of our approach for various remote sensing applications.

The problems of formation and propagation of surface seismic waves in vertically layered and horizontally inhomogeneous media are studied. A mathematical model has been developed for the propagation of surface seismic waves in an inhomogeneous medium based on the use of the fundamental principles of wave dynamics and Fourier transforms. The existence of various types of groups of these waves is proved, and their main properties are studied. It has been established that the reflection coefficients of different groups of a dispersive wave on models of half-spaces (a layered, inhomogeneous medium) with a sharp velocity differentiation are characterized by the same dependence on the angle of incidence as in the absence of dispersion. In the region of the critical angle, which depends on the period of the incident wave, a local decrease in the intensity of wave reflection is observed, which is associated with the origin of the head dispersive wave. It has been found that the reflection coefficients of Rayleigh waves from low-velocity layers, thin (d / λ2 = 0.205) and thick (d / λ2 = 0.82) are approximately 0.2 ± 0.04 and practically do not change with increasing angle of incidence. On the basis of theoretical studies, it was revealed that reflected surface waves carry information both about the elastic properties of the reflecting medium and about the dimensions of the reflecting horizontal inhomogeneity. An experimental dispersion curve of the group velocity of Rayleigh waves on the Central Asia-Caucasus path has been obtained. The seismic stress state of the "subgrade-base" system was studied. Based on the analysis of the results of numerical experiments, it has been established that in order to obtain a complete picture of the seismically stressed state of the subgrade, it is necessary to take into account the contribution to it of each component of the accelerogram of a real earthquake.

Long-term, high-accuracy mapping of built-up land dynamics is essential for understanding urbanization and its consequences for the environment. Despite advances in remote sensing and classification algorithms, built-up land mapping using early satellite imagery (e.g., from the 2000s and earlier) remains prone to uncertainty. We mapped the extent of built-up land in the North China Plain, one of China’s most important agricultural regions, from 1990 to 2019 at three-year intervals. Using dense time-stack Landsat data, we applied discrete Fourier transformation to create temporal predictors and reduce mapping uncertainties for early years. We improved overall accuracy by 8% compared to using spectral and indices predictors alone. We implemented a temporal correction algorithm to remove inconsistent pixel classifications, further improving accuracy to a consistently high level (>94%) across years. A cross-product comparison showed that our study achieved the highest levels of accuracy across years. Total built-up land in the North China Plain increased from 37,941 km² in 1990–1992 to 131,578 km² in 2017–2019. Consistent, high-accuracy built-up land mapping provides a reliable basis for policy planning in one of the most rapidly urbanizing regions of the planet.

The speed with which text can be read is determined in part by the spatial regularity and similarity of vertical letter strokes as assessed by the height of the first peak in the horizontal autocorrelation of the text. The height of this peak was determined for two passages in 20 fonts. The peak was unaffected by the size of the text or its content but was influenced by the font design. Sans serif fonts usually had a lower peak than serif fonts because the presence of serifs resulted in a more even spacing of letter strokes. There were small effects of justification and font- dependent effects of font expansion and compression. The visual comfort of images can be estimated from the extent to which the Fourier amplitude spectrum conforms to 1/f. Students were asked to adjust iBooks to obtain their preferred settings of font and layout. The preference was predicted by the extent to which the Fourier amplitude spectrum approximated 1/f, which in turn was jointly affected by the design of the font, its weight and the ratio of x-height to line separation. The above algorithms can be usefully applied to any orthography to estimate likely speed and comfort of reading.

The natural frequency of buildings decreases during a strong-motion earthquake, and the structure loses its stiffness. As a result, understanding the damaging process in the structure owing to changes in structural properties is critical during a seismic excitation. The time-frequency technique can detect the damaged building’s time-varying frequency contents. Wigner distributions (WD), Wigner-Ville distributions (WVD), pseudo-Wigner-Ville distributions (PWVD), smoothed pseudo-Wigner-Ville distributions (SPWVD), and synchrosqueezing transforms (SST) have all become popular in recent years for a variety of earthquake engineering applications, including building damage detection. This study proposes the local maximum synchrosqueezing transform (LMSST) for detecting frequency shifts in buildings during strong earthquakes. The data presented in the research show that the suggested method outperforms as compared to the conventional time-frequency methods for detecting frequency shifting in earthquake-damaged structures.

In this study we investigate the formation of dynamical energy cascades in higher order KdV-type equations. In the beginning we recall what is known about the dynamic cascades for the classical KdV (quadratic) and mKdV (cubic) equations. Then, we investigate further the mKdV case by considering a richer set of initial perturbations in order to check the validity and persistence of various facts previously established for the narrow-banded perturbations. Afterwards we focus on higher order nonlinearities (quartic and quintic) which are found to be quite different in many respects from the mKdV equation. Throughout this study we consider both the direct and double energy cascades. It was found that the dynamic cascade is always formed, but its formation is not necessarily accompanied by the nonlinear stage of the modulational instability. Direct cascade structure remains invariant regardless the size of the spectral domain. In contrast, the double cascade shape can depend on the size of the spectral domain, even if the total number of cascading modes remains invariant. Results obtained in this study can be potentially applied to plasmas, free surface and internal wave hydrodynamics.

In this study, we investigate the formation of dynamical energy cascades in higher-order KdV-type equations. In the beginning, we recall what is known about the dynamic cascades for the classical KdV (quadratic) and mKdV (cubic) equations. Then, we investigate further the mKdV case by considering a richer set of initial perturbations in order to check the validity and persistence of various facts previously established for the narrow-banded perturbations. Afterwards, we focus on higher-order nonlinearities (quartic and quintic) which are found to be quite different in many respects from the mKdV equation. Throughout this study, we consider both the direct and double energy cascades. It was found that the dynamic cascade is always formed, but its formation is not necessarily accompanied by the nonlinear stage of the modulational instability. Direct cascade structure remains invariant regardless of the size of the spectral domain. In contrast, the double cascade shape can depend on the size of the spectral domain, even if the total number of cascading modes remains invariant. Results obtained in this study can be potentially applied to plasmas, free surface and internal wave hydrodynamics.

In this paper, the Fourier-based synchrosqueezing transform (FSST) method is introduced into the power system to realize low frequency oscillation identification. Firstly, the modal components of low frequency oscillation signal are separated by FSST, and calculating the instantaneous parameters including magnitude, frequency and phase of every mode component with Hilbert transform. Then , calculating the damping ration of every modal component based on above parameters and derived the formulas. Thus, it realized effective identification of of modal parameters of low frequency oscillation signal. The experimental results of simulated data and 16-generator system demonstrate the validity and correctness of the FSST method. Comparing with the classical Prony method shows that the FSST method is better in the identification accuracy when the low frequency oscillation signal is polluted by noise. Finally, the effectiveness of the FSST in Actual power grid is verified based on the real data from Sichuan power grid.

In this paper Brinkman type fluid over an infinite plate between side walls is being investigated. The flow is generated by oscillating shear stress of the bottom plate and the solutions are obtained by using Fourier integral transformation. The obtained results are presented in steady and transient states for both sin and cos shear stresses. The general solutions are reduced to some special cases corresponding, namely to the Brinkman type fluid over an infinite plate and flow of a Newtonian viscous fluid. Graphical illustrations are carried out to have in depth analysis of the involved physical parameters

This paper introduces a new destriping algorithm for remote sensing data. The method is based on combined Haar Stationary Wavelet transform and Fourier filtering. State-of-the-Art methods based on the discrete wavelet transform (DWT) may not always be effective and may cause different artifacts. Our contribution is three-fold: i) we propose to use the Undecimated Wavelet transform (UWT) to avoid as much as possible shortcomings of the classical DWT; ii) we combine a spectral filtering and UWT using the simplest possible wavelet, the Haar basis, for a computational efficiency; iii) we handle 2D fields with missing data, as commonly observed in ocean remote sensing data due to atmospheric conditions (e.g., cloud contamination). The performances of the proposed filter are tested and validated on the suppression of horizontal strip artifacts in cloudy L2 Sea Surface Temperature (SST) and ocean color snapshots.

This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset.

The special affine Fourier transform (SAFT) is a useful and powerful analyzing tool in signal processing, optics and communications. In this paper, we mainly discuss the randomized nonuniform sampling and reconstruction for random signals bandlimited in the SAFT domain. First, we show that the nonuniform sampling is identical to the uniform sampling after a pre-filter in the sense of second order statistic characters. Then, we propose an approximate reconstruction based on sinc interpolation for the nonuniform sampling of random signals bandlimited in the SAFT domain. Finally, we give the mean square error estimate for the proposed approximate recovery approach.

Microplastics have been detected as widespread in an aquatic environment at the microscale, also known as plastic debris. They have continuously increased due to the increase in population, production of synthetic plastics and poor waste management. They are ubiquitous and slowly degrade in soil and water. They are emerging contaminants that have received attention from research communities and public audiences over the last few years. They have high stability and can absorb several other pollutants like heavy metals, pesticides, etc. After entering the environment, they can accumulate and persist for a long time. They can create a serious threat to freshwater ecosystems and human health. These particles can cause physical damage to freshwater organisms. Raman spectroscopy, Fourier-transform infrared spectroscopy, visual identification, density separation, microscopic method, chemical method, thermos-analytical method and hyperspectral imaging method are the commonly known approaches for identification and quantification of microplastics. The noticed concentration of microplastics depends on the analysis method, sampling location and technique. The authors reviewed the sources, health impact, transport and treatment of microplastics in freshwater environments in detail. This study will provide the baseline data for the researchers to do more research on microplastic pollution in the future.

Two-dimensional heat diffusion problem with heat source which is quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are used as a boundary conditions. Since the problem is not linear, Picard’s successive approximation theorem is used. Under certain conditions of natural regularity and consistency imposed on the input data, establish the existence, uniqueness and constant dependence of the solution on the data using the generalized Fourier method. As a numerical solution, implicit finite difference scheme is used. The results ob-tained from analytical and the numerical solutions are so close to each other.

Eight lesions were analyzed using some algorithms of Intelligence Artificial: basal cell carcinoma (BCC), squamous cell carcinoma (SCC), melanoma (MEL), actinic keratosis (AK), benign keratosis (BKL), dermatofibromas (DF), melanocytic nevi (NV), and vascular lesions (VASC). This manuscript presents the possibility of using concatenated signatures (instead of images) obtained from different integral transforms, such as Fourier, Mellin, and Hilbert, to classify skin lesions. Eleven other Artificial Intelligence models were applied so that eight skin lesions could be classified by analyzing the particular signatures of each lesion. The database was randomly divided into 80%–20% for the training and test datasets images, respectively. The metrics that are being reported are accuracy, sensitivity, specificity, and precision. Each case was repeated 30 times to avoid bias, according to the central limit theorem in this work, and the average and ±standard deviation were reported. Although all the results were very satisfactory, the best average mark for the eight lesions analyzed was obtained using the Subspace KNN model, where the metrics for the test were 99.98% accuracy, 99.96% sensitivity, 99.99% specificity, and 99.95% precision.

This work presents the first evidence that dissolved globular proteins change the arrangement of hydrogen bonds in water, with different proteins showing quantitatively different effects. Using ATR-FTIR (Attenuated Total Reflection – Fourier Transform Infrared) spectroscopic analysis of OH-stretch bands, we obtain quantitative estimates of the relative amounts of the previously reported four subpopulations of water structures coexisting in a variety of aqueous solutions. Where solvatochromic dyes can measure the properties of solutions of non-ionic polymers, the results correlate well with ATR-FTIR measurements. In protein solutions to which solvatochromic dye probes cannot be applied, NMR (Nuclear Magnetic Resonance) spectroscopy was used for the first time to estimate the hydrogen bond donor acidity of water. We found strong correlations between the solvent acidity and arrangement of hydrogen bonds in aqueous solutions for several globular proteins. Even quite similar proteins are found to change water properties in dramatically different ways.

The Brahmaputra is one of the largest rivers in the world, ranking fifth in average discharge. As a result, it is heavily braided with various intricate paths in order to dissipate its huge energy. Although this river is normally classed as a braided river, it has recently been classified as an anastomosing river due to its multi-channel features over alluvial plains. Additionally, the Brahmaputra river’s morphology is random in nature as a result of its high flow variability and bank erodibility. Its anastomosing planform changes in response to seasonal water and sediment waves, resulting in a morphology that is extremely complex. The purpose of this study is to examine the Brahmaputra river’s anastomosing planform entropy as a measure of complexity, power spectral density as a measure of fluctuation and their relationship to the energy expenditure as an imprint of flflow rate of river systems on alluvial landscapes.

Harmonic resonances are part of the Power Quality (PQ) problems of electrified railways and have serious consequences for the continuity of service and integrity of components in terms of overvoltage stress. The interaction between Traction Power Stations (TPSs) and trains that causes line resonances is briefly reviewed showing the dependence on infrastructure conditions. The objective is real-time monitoring of resonance conditions seen first of all from the onboard panto-graph interface, but it is equally applicable at TPS terminals. Voltage and current spectra, and de-rived impedance and power spectra, are analyzed proposing compact and efficient methods based on Short-Time Fourier Transform, suitable for real-time implementation with the hardware avail-able for energy metering and harmonic interference monitoring. The methods are tested by sweeping long recordings taken at some European railways, covering cases of longer and shorter supply sections, with a range of resonance frequencies of about one decade. They give insight into the spectral behavior of resonances, their dependency on position and change over time, and criteria to recognize genuine infrastructure resonances from rolling stock emissions.

Since the advent of Fourier Domain Mode-Locked (FDML) lasers, they have demonstrated outstanding performance in several fields. They achieve high-speed, narrow-linewidth laser output with the new mode-locking mechanism, which has been intensively researched in the past decades. Compared with conventional wavelength-scanning light sources, FDML lasers have successfully increased the scanning rate of frequency-sweeping lasers from kHz to MHz. They are widely used in optical coherence tomography, spectral analysis, microscopy, measurement, and microwave signal generation. With the deepening research on FDML lasers, several performance metrics have been optimized and improved, offering superior performance for FDML laser-based applications. This paper reviews the principles and key performance indicators of FDML lasers, as well as the recent progress made in some important applications, and highlights further research directions for FDML lasers in the future.

This paper presents an approach to the analysis of beams with rectangular cross-sections subjected to Saint-Venant torsion using the Fourier analysis, body forces being not considered. The Saint-Venant torsion of beams, also called free torsion or unrestrained torsion, is characterized by the absence of axial stresses due to torsion; only shear stresses are developed. The solution to this torsion problem consists of finding the Prandtl stress function that satisfies the governing equation and the boundary conditions, the governing equation being such that the Laplacian of the stress function has a constant value within the cross-section. In this paper, Fourier sine series was utilized to describe the constant value of the above mentioned Laplacian, while double sine series or simple sine series was utilized to describe the Prandtl stress function. Closed-form solutions in form of infinite series were derived for shear stresses, torsional constant and warping function. Those solutions were identical to the exact solutions.

This paper provides the numerical investigation of two-dimensional stochastic Navier-Stokes equation driven by additive white noises. The vorticity-stream function method is presented to calculate the incompressible fluid flow. In order to solve the formulation of steam function equation, we propose a Crank-Nicolson Fourier pseudo-spectral method. Numerical results obviously show that the presence of stochastic forcing can have an impact upon the shapes of vortex in fluid flow. To a certain extent, the phenomenon of eddy shedding and the formation of some new vortex in a random medium can be observed, which make it possible for us to conduct optimal control experiments in the development of vortex structures.

We examine a linear q-difference differential equation which is singular in complex time t at the origin. Its coefficients are polynomial in time and bounded holomorphic on horizontal strips in one complex space variable. The equation under study represents a q-analog of a singular partial differential equation, recently investigated by the author, which comprises Fuchsian operators and entails a forcing term that combines polynomial and logarithmic type functions in time. A sectorial holomorphic solution to the equation is constructed as a double complete Laplace transform in both time t and its complex logarithm log t and Fourier inverse integral in space. For a particular choice of the forcing term, this solution turns out to solve some specific nonlinear q-difference differential equation with polynomial coefficients in some positive rational power of t. Asymptotic expansions of the solution relatively to time t are investigated. A Gevrey type expansion is exhibited in a logarithmic scale. Furthermore, a formal asymptotic expansion in power scale is displayed, revealing a new fine structure involving remainders with both Gevrey and q-Gevrey type growth.

Antarctica and its surrounding environment are considered untouched and thought that it is free from microplastics (MPs) pollution. However, recent studies and science projects have reported MPs in both water and sediment in the South Polar Regions. The reports state that the MP’s pollution occurs in this region due to fishing, tourism, and research activities by the nearby countries and nature's circulation is also part of it. The Antarctic Treaty System (ATS) has received attention on MP’s pollution and initiated research on it. MPs are tiny plastic particles with a size of less than 5 mm. It has two types, 1. Primary MPs have been manufactured directly for various applications like cosmetics and scrubbing etc 2. The secondary MPs are generated by photochemical degradation of large plastics.Although several studies have been done there is a quite gap in our understanding of the concentration, characteristics, and impact of plastics on the ecosystem of the Antarctic Region. The impact of MP’s pollution in this region may be very high. The presence of MP is a serious issue that is affecting not only the aquatic environment but also humans. It is an alarming situation that causes environmental damage. The main objective of this paper is to review MP's introduction, occurrence, sources, harmful effects, and detection methods. This review highlighted the various methodologies and analyses like density separation, microscope observation of MP’s properties Fourier-transform infrared spectroscopy (FTIR), and Raman spectrometer respectively, and urged for more research in the future and gave several recommendations to maintain the pristine region near Antarctica.

Hydrogels, soft materials with 3D polymer networks in aqueous solution, have been developed for engineering and bio-related fields. However, these conventional hydrogels are weak and brittle due to lack of energy dissipation mechanisms. Recently, dual-network hydrogels have been proposed, combining rigid and flexible networks and exhibiting high strength, stretchability, and toughness. This paper explores the rheological properties of dual-network hydrogels based on acrylamide and sodium alginate under large deformations. This dual network is a combination of a covalently crosslinked polyacrylamide network and a supramolecular crosslinked sodium alginate network at the presence of divalent calcium cations. Small and large amplitude oscillatory shear methods with Fourier transform rheology, stress decomposition method, and Chebyshev polynomial analysis of large amplitude oscillatory shear (LAOS) data were employed to evaluate non-linearity limit, toughness, and network rigidity. The concentration of calcium ions affects (concentrations 0-80 mg/ml) the nonlinear transition and limit points, and all gel samples exhibit strain hardening, shear thickening, and shear densification.

Two algorithms of data processing are proposed to shorten the unmeasurable dead-zone close to the zero-position of measurement, i.e., the minimum working distance of a dispersive interferometer using optical frequency comb, which is a critical issue in millimeter-order short-range absolute distance measurement. After demonstrating the limitation of the conventional data processing algorithm, the principles of the proposed algorithms, namely the spectral fringe algorithm, and the combined algorithm that combines the spectral fringe algorithm with the excess fraction method, are presented, together with simulation results for demonstrating the possibility of the proposed algorithms for shortening the dead-zone with a high accuracy. An experimental setup of dispersive interferometer is also constructed for implementing the proposed data processing algorithms over spectral interference signals. Experimental results demonstrate that the dead-zone by the proposed algorithms can be as small as half of that by the conventional algorithm while the measurement accuracy can be further improved with the combined algorithm.

Infrared spectroscopy is an effective method for the determination of compositions and concentrations of liquids, with advantages of fast response, no-sampling, flexible in use and is able for on-line monitoring. However, for trace substances in drinking water, such as nitrates and heavy metals, infrared spectroscopy is not sensitive enough for the quantitative and qualitative measurement. In this study, we improved the sensitivity of infrared spectroscopy for nitrite determination by developing an ion-exchange-enhanced diffuse reflectance spectroscopy, which consist of an accessory based on ion-exchange resin for enrichment and a FTIR spectrometer for measurement. Using this method, the limit of detection for nitrate is 1.7 mg/L, which is enough for drinking water sensing. We also verified the quantitative measurement ability of the method. Furthermore, the limit of detection and quantitative measuring range could be adjusted by changing the mass of resin and adsorption time. This study demonstrated the method can be used to detect trace nitrites in drinking water, can be applied in the field, and is sensitive, rapid, and inexpensive with a wide dynamic range.

Incorporating linear-scanning MEMS micromirrors into Fourier transform spectral acquisition systems can greatly reduce the size of the spectrometer equipment, making portable Fourier transform spectrometers (FTS) possible. How to minimize the tilting of the MEMS mirror plate during its large linear scan is a major problem in this application. In this work, an FTS system has been constructed based on a biaxial MEMS micromirror with a large piston displacement of 180 μm, and a biaxial H∞ robust controller is designed. Compared with open-loop control and PID closed-loop control, H∞ robust control has good stability and robustness. The experimental results show that the stable scanning displacement reaches 110.9 μm under the H∞ robust control, and the tilting angle of the MEMS mirror plate in that full scanning range falls within ±0.0014°. Without control, the FTS system cannot generate meaningful spectra. In contrast, the FTS yields a clean spectrum with an FWHM spectral linewidth of 96 cm-1 under the H∞ robust control. Moreover, the FTS system can maintain good stability and robustness under various driving conditions.

This paper presents a new scientific contribution on the two-dimensional (2-D) subdomain technique in polar coordinates taking into account the finite relative permeability of the ferromagnetic material. The constant relative permeability corresponds to linear part of the nonlinear B(H) curve. As in conventional technique, the method of separation of variables and the Fourier’s series are used for the resolution of magnetostatic Maxwell’s equations in each region. Although, the general solutions of magnetic field in the subdomains and boundary conditions (BCs) between regions are different in the conventional and proposed method. In this later, the magnetic field solution in each subdomain is a superposition of two magnetic quantities in the two directions (i.e., r- and Q-axis) and the BCs between two regions are also in both directions. For example, the scientific contribution has been applied to an air- or iron-cored coil supplied by a constant current. The distribution of local quantities (i.e., the magnetic vector potential and flux density) has been validated by a corresponding 2-D finite-element analysis (FEA). The obtained semi-analytical results are in very good agreement with those of numerical method.

Owing to the nondiffracting, self-accelerating, and self-healing properties, Airy beams of different nature have become a subject of immense interest in the past decade. Their interesting properties have opened doors to many diverse applications. Consequently, the questions of how to properly design spatial manipulation of Airy beams or how to implement them in different setups have become important and timely in the development of various optical devices. Here, based on our previous work, we present a short review on the spatial control of Airy beams, including the interactions of Airy beams in nonlinear media, beam propagation in harmonic potential, and the dynamics of abruptly autofocusing Airy beams in the presence of a dynamic linear potential. We demonstrate that under the guidance of nonlinearity and external potential, the trajectory, acceleration, structure, and even the basic properties of Airy beams can be adjusted to suit specific needs. We describe other fascinating phenomena observed with Airy beams, such as self-Fourier transformation, periodic inversion of Airy beams, and the appearance of spatial solitons in the presence of nonlinearity. These results have promoted the development of Airy beams, and have been utilized in various applications, including particle manipulation, self-trapping, and electronic matter waves.

This paper presents a study of the 2D roughness profiles on a flat surface generated on a steel work piece, by ball nose end milling, with linear equidistant tool paths (pick-intervals). The milled surface exploration with a surface roughness tester (on pick and feed directions) produces usually 2D roughness profiles having periodical evolutions. These evolutions can be seen as time-dependent signals, describable as a sum of sinusoidal components (the wavelength of each component being regarded as a period). In order to detect a well approximated description of these components, two appropriate signal processing techniques are used in this work: first technique provides a direct mathematical (analytical) description and is based on computer aided curve (signal) fitting (more accurate), the second technique (providing an indirect and incomplete description) is based on the spectrum generated by fast Fourier transform (less accurate). This study can be seen as a way for a better understanding the interaction between the tool and the work piece or to achieve a mathematical description of the machined surface microgeometry in terms of roughness (e. g. its description being a collection of closely spaced 2D roughness profiles).

The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.

The duality is one of the most interesting properties of the Laplace and Fourier transforms associated to the integer order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier transforms. The scale and nabla derivatives are used.

The administration of regional neuraxial analgesia for pain relief during labor is widely recognized as a safe and effective method involving medication delivery into the epidural or subarachnoid space in the lower back. This study proposes an innovative semantic image segmentation methodology emphasizing enhanced interpretability using convolutional Random Fourier Features and layer-wise weighted class-activation maps tailored explicitly for foot segmentation in regional analgesia monitoring. Namely, our contribution is twofold: i) a novel Random Fourier Features layer is introduced to deal with image data to enhance three well-known architectures (FCN, UNet, and ResUNet); ii) three novel quantitive measures are presented to evaluate the interpretability of a given deep learning model devoted to segmentation tasks. Our approach is rigorously evaluated on a demanding dataset of foot thermal images from pregnant women who received epidural anesthesia. Its small size and considerable variability characterize the dataset. Our validation results demonstrate that the proposed methodology not only achieves competitive foot segmentation performance but also significantly enhances the explainability of the process, rendering it well-suited for applications such as epidural insertion during labor.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

Uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys.\ Lett.\ A\textbf{382}, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

Detection of early stage corrosion on slender steel members is crucial for preventing buckling failures of steel structures. An active photoacoustic fiber optic sensors (FOS) system has been reported for early stage steel corrosion detection of steel plates and rebars using surface ultrasonic waves. The objective of this paper is to investigate the surface corrosion/rust detection problem on steel rods using numerically simulated surface ultrasonic waves. The finite element method (FEM) is applied in simulating the propagation of ultrasonic waves on steel rod models. Transmission mode of damage detection is adopted, in which one source (transmitter) and one sensor (receiver) are considered. In this research, radial displacements at the receiver were simulated and analyzed by short-time Fourier transform (STFT) for detecting, locating, and quantifying a surface rust located between the transmitter and the receiver. From our time domain and frequency domain analyses, it is found that the presence, location, and dimensions (length, width, and depth) of surface rust can be estimated by ultrasonic waves propagating through the surface rust.

This study explored the antimicrobial potential of Piper betle L. (PBL) and Piper nigrum L. (PNL) extracts against MRSA. Plant parts including stem, leaf, and fruit were extracted using aquadest, methanol, and hexane, resulting in 18 distinct extracts. FT-IR combined with cluster analysis (CA) categorized the extracts, and anti-MRSA activity was assessed through the paper disk dif-fusion method. The most potent extracts were further analyzed using GC-MS to identify bioac-tive compounds. Additionally, molecular docking studies were conducted for MRSA protein targets (4DKI, 6H5O, and 4CJN). The hexane extract of PNL and the aqueous extract of PBL fruit showed the strongest inhibitory effects. GC-MS identified Piperine (14.22%) and Diisooctyl phthalate (14.67%) as major compounds, with Piperolein B, Piperanine, Beta-caryophyllene ox-ide, and Alpha-caryophylladienol as minor compounds in the hexane extract of PNL, while hy-droxychavicol (81.89%) and Chavibetol (12.01%) were predominant in the aquadest extract of PBL. Molecular docking revealed that Piperolein B and Piperine had strong binding affinities to MRSA proteins 4DKI, 6H5O, and 4CJN, comparable to ciprofloxacin. In conclusion, this study confirms the potential of PBL and PNL as sources of novel anti-MRSA agents, supporting fur-ther research to develop new therapies.

Dielectrophoresis (DEP) cell-separation technology is an effective means of separating rare cells. To develop highly efficient cell-separation devices, detailed analysis of the nonuniform electric field’s intensity distribution within the device is needed, as it affects separation performance. Here we analytically expressed the distributions of the electric field and DEP force in a parallel-plate cell-separation DEP device by employing electrostatic analysis through the Fourier series method. The solution was approximated by extrapolating a novel approximate equation as a boundary condition for the potential between adjacent fingers of interdigitated electrodes and changed the underlying differential equation into a solvable form. The distributions of the potential and electric fields obtained by the analytical solution were compared with those from numerical simulations using finite element method software to verify their accuracy. The results showed excellent agreement. Three-dimensional fluorescence imaging analysis used live non-tumorigenic human mammary (MCF10A) cells. The distribution of cell clusters adsorbed on the interdigitated electrodes was compared with the analytically obtained distribution of the DEP force, and the mechanism underlying cell adsorption on the electrode surface was discussed. Furthermore, parametric analysis using the width and spacing of these electrodes as variables revealed that spacing is crucial for determining DEP force. The results showed that, by optimizing cell-separation devices using interdigitated electrodes, adjusting electrode spacing significantly enhances device performance.

The effective macroscopic model describing interactions of a viscous compressible heat-conducting fluid and a two-level fine bristly thermoelastic structure is derived from microstructure by means of the Allaire–Briane multi-scale convergence method. This new model naturally generalizes the isothermal formulation earlier constructed by the authors in 2020, see in Siberian Electronic Mathematical Reports, vol. 17 (https://doi.org/10.33048/semi.2020.17.100). In applications, the established model can be used, for example, in description, with account of heat transfer phenomemon, of airflow near surface of plant’s leaf, in simulation of epithelium surfaces of blood vessels, and in design of biotechnological devices operating in liquids.

This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of dual-phase-lag heat conduction model with the Caputo fractional derivatives. It is shown that this model can be derived from a general linear constitutive relation for the heat transfer by conduction when the heat conduction relaxation kernel contains the Mittag-Leffler function. The model can be used to describe heat conduction phenomena in a material with power-law memory. The proposed algorithm of parameters estimation is based on the time integral characteristics method. The explicit representations of the thermal diffusivity and the fractional analogues of the thermal relaxation time and the thermal retardation are obtained via a Laplace transform of the temperature field and utilized in the algorithm. An implicit relation is derived for the order of fractional differentiation. In the algorithm, this relation is resolved numerically. An example illustrates the proposed technique.

Water pollution is the main problem in the current scenario which is being faced by mankind due to the industrial and commercial effects. Industrial effluents contain heavy metals and inorganic ions like nitrates and phosphate ions. These ions are being included in waterways through industrial runoff. When the concentration of these hazardous pollutants increases in aquatic flora and fauna causes severe health problems. So remediation of these toxicants from water reserves is of chief importance. Conventional processes along with modern processes are being used for the treatment of industrial wastes. Photo-degradation is a modern method used for the degradation of inorganic ions due to its environmentally friendly nature and cost-effectiveness. In a recent study Aluminum oxide (Al2O3) nanoparticles were synthesized via a green approach at different pH by using Cymbopogan citratus (lemongrass) plant extract and these nanoparticles were used for the removal of inorganic ions from wastewater. The nanoparticles of different pH showed different % degradation of the inorganic ions in acidic medium removal of inorganic waste was less, in basic media % degradation was more as compared to acidic media but maximum % degradation was observed in neutral media like that average % degradation 91% and 81% was observed for nitrate and phosphate ions. The maximum absorbance occurred at 212nm and Al2O3 nanoparticles showed absorbance from 210nm-217nm. The R2 values of pseudo1st, 2nd, and BMG models were 0.956, 0.837, 0.7007 0.95, 0.896, and 0.756 for the nitrate and phosphate ions. Characterizations of synthesized particles were investigated by using UV-visible spectroscopy and other analytical methods like X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR). The statistical analyses were done using Simple Linear regression (SLR).

This scientific paper presents a comprehensive investigation into transient Fourier analysis in some electrical engineering applications. The article deals with two effective approaches for solving transient analysis whose application is rather novel. The first contribution uses combined the Fourier series analytic Laplace-Carson (L­C) transform methods in the complex domain using complex time vectors, thereby significantly simplifying the calculation of the original function. As the inverse transform goes back into the time domain, it employs the Cauchy-Heaviside (C­H) method. The second contribution uses the Fourier transform (F­Τ)for transient analysis of a power converter electrical circuit with the passive and the active load. The method of complex conjugated amplitudes is used for steady-state analysis. Both contributions represent a new approach to this paper. The starting point is the Fourier series/expansions, computation of the Fourier coefficients, then continuing by solving the steady and transient states of the system and confirming the transient states using the Fourier transform. To validate our findings, the worked-out analytical results are verified by modelling in Matlab/Simulink environment.

The Stepped Frequency Waveform (SFW) is commonly employed in radar technology to synthesize wideband signals through the aggregation of narrow-band pulses, thereby achieving high-resolution range profiles without the need to increase the radar's instantaneous bandwidth. However, the inherent large time-bandwidth product of SFW introduces substantial ranging errors and energy dispersion, which significantly hinders its efficacy in detecting high-speed objects. This paper introduces a pioneering velocity estimation technique utilizing the fractional Fourier transform (FrFT) to address these limitations. Leveraging the characteristic of the Doppler signal from a moving target, which manifests as a chirp signal with a rate proportional to the target's velocity, the FrFT is utilized for precise velocity estimation. Subsequent to this, velocity compensation is applied using the deduced metrics, followed by the application of the inverse fast Fourier transform (iFFT) to pinpoint the target's exact location. To optimize the computational efficiency of determining the FrFT's optimal order, we propose an iterative algorithm founded on the golden section search method. The effectiveness of the proposed approach is verified by simulation data, and the results demonstrate that the proposed approach can accurately estimate the velocity and the range of the high-speed targets with a relatively low computational complexity.

Virgin coconut oil (VCO) is a functional food with important health benefits. Its economic interest encourages fraudsters to deliberately adulterate VCO with cheap and low-quality vegetable oils for financial gain, causing health and safety problems for consumers. In this context, there is an urgent need for rapid, accurate and precise analytical techniques to detect VCO adulteration. In this study, the use of Fourier Transform Infrared (FTIR) spectroscopy combined with Multivariate Curve Resolution - Alternating Least Squares (MCR-ALS) methodology was evaluated to verify purity or adulteration of VCO with reference to several low-cost commercial oils such as sun-flower, maize and peanut oils. Control charts were developed to assess the purity of oil samples using MCR-ALS scores values calculated from a data set of pure and adulterated oils. In addition, quantification models were developed using MCR-ALS with correlation constraint for adulterated coconut oil to assess the blend composition. Different data pre-treatment strategies were tested in order to best extract the information contained in the sample fingerprints, and the calibration models were optimised using a genetic algorithm (GA) to select the most important variables. The models gave satisfactory results in external validation procedure, with absolute errors of less than 4.6 % for samples adulterated with sunflower, maize and peanut oils.

We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with A. Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane w.r.t time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.

We examine a family of linear partial differential equations both singularly perturbed in a complex parameter and singular in complex time at the origin. These equations entail forcing terms which combine polynomial and logarithmic type functions in time and that are bounded holomorphic on horizontal strips in one complex space variable. A set of sectorial holomorphic solutions are built up by means of complete and truncated Laplace transforms w.r.t time and parameter and Fourier inverse integral in space. Asymptotic expansions of these solutions relatively to time and parameter are investigated and two distinguished Gevrey type expansions in monomial and logarithmic scales are exhibited.

Induction machines drive many industrial processes, and their unexpected failure can cause heavy production losses. The analysis of the current spectrum can identify online the characteristic fault signatures at an early stage, avoiding unexpected breakdowns. Nevertheless, frequency domain analysis requires stable working conditions, which is not the case for wind generators, motors driving varying loads, etc. In these cases an analysis in the time-frequency domain -such as a spectrogram- is required for detecting faults signatures. The spectrogram is built using the short frequency Fourier transform, but its resolution depends critically on the time window used to generate it: short windows provide good time resolution, but poor frequency resolution, just the opposite than long windows. Therefore, the window must be adapted at each time to the shape of the expected fault harmonics, by highly skilled maintenance personnel. In this paper, this problem is solved with the design of a new multi-band window, which generates simultaneously many different narrow-band current spectrograms, and combines them into a single, high resolution one, without the need of manual adjustments. The proposed method is validated with the diagnosis of bar breakages during the start-up of a commercial induction motor.

The most significant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell's equations applied in subdomain) is defined by: “The iron parts (i.e., the teeth and the back-iron) are considered to be infinitely permeable so that the saturation effect is neglected”. In this paper, the author presents a new scientific contribution on improving of this method in two-dimensional (2-D) and in Cartesian coordinates by focusing on the consideration of iron. The subdomains connection is carried out in the two directions (i.e., x- and y-edges). For example, the improvement was performed by solving magnetostatic Maxwell's equations for an air- or iron-cored coil supplied by a direct current. To evaluate the efficacy of the proposed technique, the magnetic flux density distributions have been compared with those obtained by the 2-D finite-element analysis (FEA). The semi-analytical results are in quite satisfying agreement with those obtained by the 2-D FEA, considering both amplitude and waveform.

This article focuses on obtaining the analytical solutions for parabolic Volterra integro- differential equations in d-dimensional with different types frictional memory kernel. Based on theories of Laplace transform, Fourier transform, the properties of Fox-H function and convolution theorem, analytical solutions of the equations in the infinite domain are derived under three frictional memory kernel functions respectively. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, Fox-H function and convolution form of Fourier transform. In addition, the graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equation with power-law memory kernel. It can be seen that the solution curves subject to Gaussian decay at any given moment.

Speech enhancement technology seeks to improve the quality and intelligibility of speech signals degraded by noise, particularly in telephone communications. Recent advancements have focused on leveraging deep neural networks (DNN), especially U-Net architectures, for effective denoising. In this study, we evaluate the performance of a 6-level skip-connected U-Net constructed using either conventional convolution activation blocks (CCAB) or innovative global local former blocks (GLFB) across different processing domains: temporal waveform, short-time Fourier transform (STFT), and short-time discrete cosine transform (STDCT). Our results indicate that the U-Nets can receive better signal-to-noise ratio (SNR) and perceptual evaluation of speech quality (PESQ) when applied in the STFT and STDCT domains, with comparable short-time objective intelligibility (STOI) scores across all domains. Notably, the GLFB-based U-Net outperforms its CCAB counterpart in metrics such as CSIG, CBAK, COVL, and PESQ, while maintaining fewer learnable parameters. Furthermore, we propose domain-specific composite loss functions, considering the acoustic and perceptual characteristics of the spectral domain, to enhance the perceptual quality of denoised speech. Our findings provide valuable insights that can guide the optimization of DNN designs for causal speech denoising.

The radio spectrum is a scarce and extremely valuable resource that demands careful real-time monitoring and dynamic resource allocation. Dynamic spectrum access (DSA) is a new paradigm for managing the radio spectrum, which requires AI/ML driven algorithms for optimum performance under rapidly changing channel conditions and possible cyber-attacks in the electromagnetic domain. Fast sensing across multiple directions using array processors, with subsequent AI/ML based algorithms for sensing and perception of the waveforms that are measured from the environment is critical for providing decision support in DSA. As part of directional and wideband spectrum perception, the ability to finely channelize wideband inputs using efficient Fourier analysis is much needed. However, a fine-grain fast Fourier transform (FFT) across a large number of directions is computationally intensive and leads to high chip area and power consumption. We address this issue by exploiting recently proposed approximate discrete Fourier transforms (ADFT) which has its own sparse factorization for real-time implementation at low complexity and power consumption. The ADFT is used to create a wideband multi-beam RF digital beamformer and temporal spectrum-based attention unit which monitors 32~discrete directions across 32~sub-bands in real-time using a multiplierless algorithm having low computational complexity. The output of this spectral attention unit is applied as a decision variable to an intelligent receiver that adapts its center frequency and frequency resolution via FFT channelizers that are custom-built for real-time monitoring at high resolution. This two-step process allows the fine-gain FFT to be applied only to directions and bands of interest as determined by the ADFT based low-complexity 2D spacetime attention unit. The fine-grain FFT provides a spectral signature that can find future use cases in neural network engines for achieving modulation recognition, IoT device identification, and RFI identification. Beamforming and spectral channelization algorithms, digital computer architecture, and early prototypes using a 32-element fully digital multichannel receiver and field programmable gate array (FPGA)-based high-speed software defined radio (SDR) is provided.

Chitosan (CS) nanoparticles are under investigation for a wide range of applications in nanomedicine. The structural, molecular and physicochemical properties of chitosan nanoparticles have a direct bearing on their efficacy in drug conjugation and delivery, gene delivery, and tissue engineering. Herein we report on the structural, morphological and molecular properties of chitosan nanoparticles synthesized using the ionic gelation method with the intended purpose of being used for drug delivery. The chitosan nanoparticles (CS-NPs) were prepared in the 0.25 to 1.0% w/v concentration range, whereas separate samples of the 1.0% w/v CS-NPs were also functionalized with polyethylene oxide (PEO) alone and with a diblock copolymer of PEO and polypropylene glycol (PPG). The average size of the CS-NPs was determined from TEM imaging to be in the range of 11.3 to 14.8 nm. The XRD and TEM analyses show that the CS-NPs have semi-crystalline structure with the degree of crystallinity depending upon the nature of synthesis. Our results show that functionalizing the 1.0% w/v CS-NPs with PEO increases the degree of crystallinity whereas functionalizing with the diblock copolymer PEO - PPG results in a significant increase in their degree crystallinity. The CS/TPP concentration (CS:TPP fixed at 1:1 ratio) had no apparent effect on the degree of crystallinity of the CS-NPs. The results from the FTIR analysis confirm incorporation of TPP with CS in the CS-NPs. Additionally, FTIR analysis shows an enhancement of hydrogen bonding that is consistent with the increase in the degree of crystallinity of the CS-NPs.

The object of this paper is the analysis of isotropic rectangular thin plates supported (simply supported or clamped) along two opposite edges whereby the other edges have arbitrary support conditions; the plates are subjected to external bending moments, concentrated or distributed, and perpendicular to the supported edges. The standard approach to this problem is to replace the bending moment with a couple of forces infinitely close and to use the known expressions of efforts and deformations for the plate subjected to concentrated forces; the results are then related to the first derivatives of those efforts and deformations with respect to the position of application of the load. In this study, the external bending moment was expanded into a Fourier series, leading to a distributed external bending moment, and the boundary conditions and continuity equations were applied. Various types of rectangular plates were analyzed, as well as plates of infinite length whose results were identical to those in the literature. In addition, results for cantilever plates of infinite length were presented.

This paper aims to analyze arbitrarily loaded isotropic rectangular thin plates with two opposite edges supported (simply supported or clamped), from which one or both are clamped, and the other edges have arbitrary support conditions. Rectangular thin plates with two opposite edges simply supported are routinely analyzed using for the deflection the simple trigonometric series of Lévy or the double trigonometric series of Navier, while the loads are expanded in Fourier series. In this paper the flexibility method (or force method) of the linear beam theory was applied whereby the unknowns were the bending moments along the opposite edges; in this regard, the primary system was the plate simply supported along the above-mentioned opposite edges and subjected to the external loads, system solved using the Lévy solution, and the redundant system was the plate simply supported along the opposite edges and subjected to bending moments along those edges. In the redundant system, a modified Lévy solution was introduced to account for the edge moments. The compatibility equations (vanishing of the slopes at selected positions of the opposite edges) were set to determine the unknowns and so the efforts in the plate. The results obtained were in good agreement with the exact results.

The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to non-uniform heating (NUH) using the Fourier transform method. The bottom and top surfaces of the plate are assumed to have different changes in temperature, whereas the change in temperature of the mid-surface is zero. According to classical plate theory, the governing equation of the plate contains second derivatives of the NUH; these derivatives are zero by constant value of the NUH, which leads to its absence in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the NUH, while the double trigonometric series of Navier and the simple trigonometric series of Lévy were utilized to describe the deflection curve. Thus, the NUH appeared in the governing equation, which simplified the analysis. Rectangular plates simply supported along all edges were analyzed, bending moments, twisting moments, and deflections being determined. In addition, rectangular plates simply supported along two opposite edges were analyzed; the other edges having various support conditions (free, simply supported, and fixed).

Single particle analysis with cryogenic electron microscopy (cryo-EM) can determine high resolution structures of macromolecular assemblies. To reconstruct final three-dimension(3D) density map, a reliable initial model is essential and ab-initio reconstruction usually can avoid model bias. The grand challenge for ab-initio reconstruction is to alignment two-dimension(2D) low signal-to-noise ratio(SNR) of particle images with random and unknown parameters. Here we formulate a fast ab initio reconstruction method(named AlignFM) based on Fourier Mellin transform and particle-swarm intelligence optimization(PSO) algorithm. It enables simultaneous 2D alignment and 3D refinement, which can fast generate a reliable 3D map. After experiments on several real datasets. AlignFM shows high performance on fast ab initio reconstruction with a small amount of data.

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter and singular in a complex time variable at the origin. These equations combine differential operators of Fuchsian type in time and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the complex parameter known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic type functions in time and are bounded holomorphic in space. A set of logarithmic type solutions are shaped by means of Laplace transforms relatively to time and parameter and Fourier integrals in space. Furthermore, a formal logarithmic type solution is modeled which represents the common asymptotic expansion of Gevrey type of the genuine solutions with respect to the complex parameter on bounded sectors at the origin.

This study applied multiple scientific approaches to establish the significance of an old work of art, Red Guitar, by examining its historical origin and the color materials used in its creation. Furthremore, the study provides thus far unknown pieces of Olga Picasso's family history to be added to her biography. Scientific approaches included digital X-ray radiography, X-ray fluorescence spectroscopy, infrared Fourier transform spectroscopy, Raman spectroscopy, and elemental thermal conductivity analysis. This combination of techniques provided broad confirmation about the time when the painting was created. The work includes colors (white, black, blue, yellow, green, red, and brown/red) and prevalent use of lead-and iron-based historic pigments Chrome Yellow, Yellow Ochre and Red Ochre. It also documents the use of unconventional materials, the colorant Pigment red 4 and nitrocellulose. This investigation led to the conclusion that the art, Red Guitar, is genuine and in accord with Picasso’s work during the first two decades of the 20th century.

In today’s world face detection is the most important task. Due to the chromosomes disorder sometimes a human face suffers from different abnormalities. For example, one eye is bigger than the other, cliff face, different chin-length, variation of nose length, length or width of lips are different, etc. For computer vision currently this is a challenging task to detect normal and abnormal face and facial parts from an input image. In this research paper a method is proposed that can detect normal or abnormal faces from a frontal input image. This method used Fast Fourier Transformation (FFT) and Discrete Cosine Transformation of frequency domain and spatial domain analysis to detect those faces.

The present study evaluates the bioremediation potential of indigenous bacterial species isolated from dye-contaminated soil samples from small dyeing outlet located in Ilorin. The water pollution index was estimated based on the physicochemical characteristics and heavy metal concentrations of the raw (Day 0) and treated textile wastewater such as pH, biochemical oxygen demand-5, chemical oxygen demand, total suspended solids and total dissolved solid with mean values of 8.85±0.45 mg/L, 1200±21.3 mg/L, 2440±31.3 mg/L, 1660±17.2 mg/L and 2650±28.1 mg/L respectively, similarly, Lead was the most abundant heavy metal detected in the sample while Cadmium concentration was the lowest with the mean values of 3.52±0.00 mg/L and 2.18±0.00 mg/L respectively. The bacterial strain with highest dye decolorization capacity was screened and identified as Bacillus licheniformis ZUL012.The isolate was consequently used for the bioremediation of the wastewater over a period of 10 days. The results showed an incredible reduction in the physiochemical characteristics and heavy metal concentrations of the textile wastewater in the following ranges (8.85-6.55), (1200-300) mg/L, (2440-518) mg/L, (1660-666) mg/L and (2650-920) mg/L with the highest removal efficiency of 75 %, 78 %, 60%, 65%, recorded for biochemical oxygen demand, chemical oxygen demand, total suspended solid, total dissolved solid, respectively while that of heavy metals such as lead, cadmium, chromium and nickel were 80 %, 60 %, 67 %, 72 % reduction, respectively. Laccase and Azoreductase activities tend to decrease as the pH gradually moved towards acidic condition during the bioremediation process. Toxicity of the treated effluent was assessed using Maize and Bean seed germination test. Conclusively, these research findings can serve as a framework for the outlet design of wastewater treatment plant for local textile outlets.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

Re-purposing wastewater is necessary to circumvent water shortage for vegetable farmers in urban areas and to reduce public health hazards associated with using contaminated water for irrigation. In this study, the efficiency of biochar filtration systems in removing contaminants from wastewater was investigated. The hydraulic retention time (HRT) and the cleaning mechanism of coconut biochar filtration systems were examined. The filtration systems were designed with biowastes, specifically coconut biochar, as an adsorbent to remove pollutants from wastewater. Two setups of bed, 40 cm and 30 cm thick, were examined under different HRTs. Fourier Transform Infrared Spectroscopy (FTIR) analysis and Scanning Electron Microscopy (SEM) imaging were used to ascertain the properties of the biochar that enhances the removal of pollutants in wastewater. For both setups, the removal of heavy metals (Lead, Pb and copper, Cu) as well as Total Coliform (TC) was judged satisfactory but appeared ineffective in removing E. coli.

The optimal functionality and dependability of mechanical systems are important for the sustained productivity and operational reliability of industrial machinery which has direct impact on it’s longevity and profitability. Therefore, failure of a mechanical system or any of it component would be detrimental to production continuity and availability. Consequently,this study proposes a robust diagnostic framework for analyzing the blade conditions of shot blast industrial machinery. The framework involves analyzing the spectral characteristics of the vibration signals generated by Industrial Shot Blast. Additionally, a peak detection algorithms is introduced to identify and extract the unique features present in the peak magnitudes of each signal spectrum. A feature importance algorithm is then deployed as the feature selection tool, and these selected features are fed into 10 machine learning classifier, with Extreme gradient boosting (XGB) as the core classifier. Results show that the XGB classifier achieved the best accuracy of 98.05%, with a cost-efficient computational cost of 0.83 seconds. Other global assessment metrics were also implemented in the study to further validate the model.

In this study, the biodegradation properties of leather treated with various finishing chemicals were evaluated in order to enhance the sustainability of leather processing. We applied advanced analytical techniques including FT-IR, thermogravimetric analysis (TGA), and solid-state NMR spectroscopy. Leather samples treated with different polymers, resins, bio-based materials, and traditional finishing agents were subjected to a composting process under controlled conditions to measure their biodegradability. The findings revealed that bio-based polyurethane finishes and acrylic wax exhibited biodegradability, while traditional chemical finishes like isocyanate and nitrocellulose lacquer showed moderate biodegradation levels. The results indicated significant differences in the biodegradation rates and the impact on plant germination and growth. Some materials, such as black pigment, nitrocellulose lacquer and wax, were beneficial for plant growth, while others, such as polyurethane materials, had adverse effects. These results support the use of eco-friendly finishes to reduce the environmental footprint of leather production. Overall, this study underscores the importance of selecting sustainable finishing chemicals to promote eco-friendly leather manufacturing practices.

Alzheimer's Disease (AD) is a neurodegenerative disease that is common in the elderly. This paper introduces the overview of Alzheimer's disease and the application of relevant signal processing methods in its detection. Signal processing is a technique that converts raw data into meaningful information and is widely used in the medical field. This paper lists common signal processing techniques, including Fourier transform, time-frequency analysis and statistical signal processing, and discusses their applications in the detection of Alzheimer's disease. Fourier transform can convert time domain signals into frequency domain representations, providing an effective tool for the study of EEG in Alzheimer's disease. Time-frequency analysis can perform a combined time and frequency analysis of the signal to help detect the signal characteristics of Alzheimer's disease. Statistical signal processing methods can be used to identify the features of Alzheimer's disease by building mathematical models. Finally, the challenges of Alzheimer's disease detection are discussed, including signal noise, diversity, and insufficient data volume. Through in-depth research and development of signal processing methods, it is expected to improve the accuracy and efficiency of early detection of Alzheimer's disease.

INT-FFT algorithm presented in this work uses an interpolation methodology to densify 3D-GPR datasets to sharpen images obtained in GPR surveys obtained in an archaeological context. It allows the reconstruction of missing data from the combined use of mathematical transforms (e.g., the Fourier and Curvelet transform) and predictive filters. This technique makes it possible to calculate the missing signal simply by meeting two requirements: the data in the frequency domain must be limited in a range of values and must be able to be represented by a distribution of Fourier coefficients (verified conditions). The INT-FFT algorithm uses an open-access routine (Suinterp, Seismic Unix) to interpolate the GPR profiles based on seismic trace interpolation. This process uses automatic event identification routines by calculating spatial derivatives to identify discontinuities in space by detecting very subtle changes in the signal, thus allowing for more efficient interpolation without artifacts or signal deterioration. We successfully tested the approach using GPR datasets from the Roman Villa of Horta da Torre (Fronteira, Portugal). The results show an increase in the geometric sharpness of the GPR reflectors and have not produced any numerical artifacts. The tests performed to apply the methodology to GPR-3D data allowed for assessing the interpolation efficiency, the level of recovery of missing data, and the level of information lost when one chooses to increase the distance between profiles in the acquisition stage of the data.

A family of linear singularly perturbed Cauchy problems is studied. The equations defining the problem combine both partial differential operators together with the action of linear fractional transforms. The exotic geometry of the problem in the Borel plane, involving both sectorial regions and strip-like sets, gives rise to asymptotic results relating the analytic solution and the formal one through Gevrey asymptotic expansions. The main results lean on the appearance of domains in the complex plane which remain intimately related to Lambert W function, which turns out to be crucial in the construction of the analytic solutions. On the way, an accurate description of the deformation of the integration paths defining the analytic solutions and the knowledge of Lambert W function are needed in order to provide the asymptotic behavior of the solution near the origin, regarding the perturbation parameter. Such deformation varies depending on the analytic solution considered, which lies in two families with different geometric features.

The simultaneous evaluation of heat/mass transference procures momentous significance in the polymer industry and engineering activities. Extensive utilization of such aspects includes propylene flares, heat exchangers, energy transfiguration in chilling towers, and amputation of post fortuitous heat in nuclear reactors. Owing to such prospective demands, we interpreted the Jeffrey liquid reactive flow under non-linear convection. We scrutinized the transference of heat/mass under generalized Fourier-Fick relations. Thermal conductivity depends on temperature while mass diffusivity is dependent on concentration. Besides, heat source along with first-order chemical reaction aspects are accounted for. Relevant transformations are exerted to achieve non-linear differential systems that are solved through the homotopy scheme. Influences of divers factors are exhibited via graphical benchmark.

The work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work by the first two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.

The extensive use of engineered nanoparticles (ENPs) such as zinc oxide nanoparticles (ZnO NPs) in various commercial fields has spurred significant concern about its possible toxicological effects of ZnO NPs on human health and eco-system. Therefore, it is substantial to understand the aggregation phenomena which could attenuate this effect. This data article provides information on aggregation of ZnO NPs under the influence of various parameters of water chemistry. Moreover, Taguchi orthogonal array L27(313) design matrix was used to evaluate the effect of multiple parameters in aqueous solution. The data were obtained from single beam UV-Vis spectrophotometer (Optizen 2120 UV, Mecasys, Korea) using Optizenview 4.2.5 PC interference software, Fourier transform infrared spectrometer (FT/IR-4700, spectroscopy, JASCO Analytical Instruments, Easton, USA) and particle electrophoresis (NanoZS, Zetasizer, Malvern Instruments Ltd, Worcestershire, UK). The dataset draws attention on dominant parameters influencing aggregation of ZnO NPs in water. The analysis of variance (ANOVA) data revealed that electrolyte concentration, type and natural organic matter (NOM) concentration were the most significant parameters. Furthermore, FT-IR data presents a possible mechanism of ZnO NPs stabilization in the presence of different NOM. This data will be helpful for the development of environmental risk assessment strategies and prediction of fate and mobility of other ENPs in the aquatic environment.

A common fault in turbomachinery is rotor--casing rub. Shaft vibration, measured with proximity probes, is the most powerful indicator of rotor-stator rub. However, in machines such as aeroderivative turbines, with increasing industrial relevance in power generation, constructive reasons prevent the use of those sensors, being only acceleration signals at selected casing locations available. This implies several shortcomings in the characterization of the machinery condition, associated with a lower information content about the machine dynamics. In this work we evaluate the performance of the Continuous Wavelet Transform to isolate the accelerometer signal features that characterize rotor-casing rub in an aeroderivative turbine. The evaluation is carried out on a novel rotor model of a rotor flexible casing system. Due to damped transients and other short-lived features that rub induces in the signals, the Continuous Wavelet Transform proves being more effective than both Fourier and Cepstrum Analysis. This creates the chance for enabling early fault diagnosis of rub before it may cause machine shutdown or damage.

We used numerical methods to define the normative structure of the different stages of sleep and wake (W) in a pilot study of 19 subjects without pathology (18–64 years old) using a double-banana bipolar montage. Artefact-free 120–240 s epoch lengths were visually identified and divided into 1 s windows with a 10% overlap. Differential channels were grouped into frontal, parieto-occipital, and temporal lobes. For every channel, the power spectrum (PS) was calculated via fast Fourier transform and used to compute the areas for the delta (0–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), and beta (13–30 Hz) bands, which were log-transformed. Furthermore, Pearson’s correlation coefficient and coherence by bands were computed. Differences in logPS and synchronization from the whole scalp were observed between the sexes for specific stages. However, these differences vanished when specific lobes were considered. Considering the location and stages, the logPS and synchronization vary highly and specifically in a complex manner. Furthermore, the average spectra for every channel and stage were very well defined, with phase-specific features (e.g., the sigma band during N2 and N3, or the occipital alpha component during wakefulness), although the slow alpha component (8.0–8.5 Hz) persisted during NREM and REM sleep. The average spectra were symmetric between hemispheres. The properties of K-complexes and the sigma band (mainly due to sleep spindles – SSs) were deeply analysed during the NREM N2 stage. The properties of the sigma band are directly related to the density of SSs. The average frequency of SSs in the frontal lobe was lower than that in the occipital lobe. In approximately 30% of patients, SSs showed bimodal components in anterior regions. qEEG can be easily and reliably used to study sleep in healthy subjects and patients.

The effect of sonication on the molecular characteristics of poliacrylic acid (Carbopol® Ultrez 10) and its rheological behavior in aqueous dispersions and microgels containing 0.25 wt. % of the polymer was analyzed in this work by rheometry, weight-average molecular weight (Mw) measurements via static light scattering (SLS), Fourier transform infrared (FTIR) spectroscopy and confocal microscopy. For this, the precursor dispersion and the microgels were sonicated in a commercial ultrasound bath at constant power and different times. We observed a softening of the microgel microstructure consisting of a systematic decrease in its shear modulus, yield stress and viscosity with increasing sonication time, while their overall Herschel-Bulkley (H-B) behavior was preserved. SLS measurements evidenced a reduction of Mw of polyacrylic acid with sonication time. Separately, FTIR measurements indicate that sonication produces scission in the C-C links of the Carbopol® backbone, which results in chains with the same chemistry but lower molecular weight. Finally, confocal microscopy measurements revealed a concomitant diminution of the size of the microsponge domains with sonication time, which is reflected in a softer microstructure resulting from reduction of the molecular weight of polyacrylic acid. The present results indicate that both the microstructure and the rheological behavior of Carbopol® microgels, in particular, and complex fluids in general, may be manipulated or tailored by high-power ultrasonication.

To make wind power more competitive, it is necessary to reduce turbine downtime and reduce costs associated with wind turbine Operation and Maintenance (O&M). Incorporating machine learning in developing condition-based predictive maintenance methodologies for wind turbines can enhance their efficiency and reliability. This paper presents a monitoring method that utilizes Base Density for the Support Vector Machine (BDSVM) and the evolutionary Fourier spectra of vibrations. This method allows smart monitoring of the function evolution of the turbine. A complex optimal function (FO) for 5-degree order has been developed that will be the boundary function of the BDSVM to timely determine the magnitude, frequency, and place of the failure occurring in wind turbine drive.

This paper is a slightly modified, abridged version of a previous work ``Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference ``Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

This paper is a slightly modified, abridged version of a previous work "Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference "Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

Laser-induced breakdown spectroscopy (LIBS) of pharmaceutical drugs that contain paracetamol is investigated in air and argon atmospheres. Characteristic neutral and ionic spectral lines of various elements and molecular signatures of CN violet and C₂ Swan band systems are observed. The relative hardness of all drug samples is measured as well. Principal component analysis, a multivariate method, is applied in data analysis for demarcation purposes of the drug samples. The CN violet and C₂ Swan spectral radiances are investigated for evaluation of possible correlation of the chemical and molecular structures of the pharmaceuticals. Complementary Raman and Fourier-transform-infra-red spectroscopies are used record molecular spectra of the drug samples. The applicationof the above techniques for the drug screening are important for identification and mitigation of drugs that reveal additives that may cause adverse side-effects.

Signal approximation, is the basic idea of signal processing and mathematical analysis where complex signals can be represented with simpler ones. This paper explores unifying two mathematical fundamentals, Dirichlet-type problems, and hyperbolic series identities, into signal approximation. In this paper, we address a well-known classic topic in mathematical analysis - the Dirichlet problem - to improve (the approximation of) signal using Fourier series. We also discuss using hyperbolic series representations to increase signal modeling flexibility. In this way, we hope to create new links that span some distance along this dimension and result in a somewhat theoretical view of signal behavior - present with the mathematical rigor needed for speculation but absent from an understanding capable of appropriately handling real-world complexity. This paper provides a theoretical investigation of the mechanics at play and reveals by analogy how these mathematical tools can potentially advance signal processing techniques and understanding. This paper illustrates Fourier series and fuzzy logic methods by two case studies on signal processing, satellite communication and financial risk measurement. The first case study performs signal approximation using the Fourier series and hyperbolic function identities to provide insight into how signals behave and are modeled. The second case study deals with applying fuzzy logic for risk evaluation of investment portfolios, emphasizing the utility in evasion systems solving uncertainty and imprecision problems related to financial decisions.

Fault detection at the early stage of development is of great importance in the maintenance of electric motors. In this regard, Motor Current Signature Analysis (MCSA) is cited in many articles to detect rotor bar fracture. The popularity of MCSA is due to its non-invasive and non-destructive nature, simplicity, and, compatibility with several signal processing tools. The vast variety of the signal processing tools which are commonly used for detecting the broken rotor bar fault is based on the Fast Fourier Transform (FFT) of the stator current signal and analysis of the produced Fourier spectrum; however, because of the small amplitude at the fault frequency relative to the main frequency amplitude, the former cannot be easily discriminated from the latter. Therefore, the peak at the fault frequency is hidden in the shadow of the main frequency component, hence the fault will not be detectable. As a solution to vanish the base frequency component, a method based on the Algebraic Identity of trinomial expansion is proposed in this paper which enables us to display the difference between the frequency of the fault signature and the base frequency. In this article, the fault of the broken rotor bars of the squirrel cage induction motor is revealed by the proposed method. In addition, a frequency weighting technique is presented to magnify the component at the fault related frequency compared to the lower frequencies. To validate the proposed methods, they are examined on the laboratory data obtained from three different operating conditions including the direct online start, the direct torque control, and the scalar control and the results show the ability of the proposed methods in fault detection of an induction motor.

In China, the production of crop straw has been estimated to be approximately 800 Million tons yearly of which about 40% was burned. Corn stover is one of the main agricultural wastes in China. It has shown that lignin in corn stover could be effectively removed byMyrothecium verrucaria. The effects of the pretreatment of corn strover by Myrothecium verrucaria on compost were studied. The results showed that corn stover pretreatment by Myrothecium verrucaria, the Cellulose, Hemicellulose, and lignin were degraded and the results were 33.43%, 11.53% and 18.70% respectively. Scanning electron microscope (SEM) analysis showed that the surface structure of corn stover was changed. Fourier transform infrared spectroscopy (FTIR) analysis showed that the degradation products of lignin were increased. The exposed area of cellulose and hemicellulose was increased. Compared with the control group, the pH value was stable and the temperature was higher. The content of nitrogen in the material decreased, while the contents of total phosphorus and total potassium increased.The C/N ratio of materials decreased after composting.The results showed that the pretreatment of Myrothecium verrucaria improve the degradation of lignocelluloses, a great contribution was made to reduce the causes loss of plant nutrient and to fight against environmental pollution.

The first part of the paper was aimed at analyzing the given nonlinear problem by different methods of computation of the Lyapunov exponents (Wolf method [1], Rosenstein method [2], Kantz method [3], method based on the modification of a neural network [4, 5], and the synchronization method [6, 7]) for the classical problems governed by difference and differential equations (Hénon map [8], hyper-chaotic Hénon map [9], logistic map [10], Rössler attractor [11], Lorenz attractor [12]) and with the use of both Fourier spectra and Gauss wavelets [13]. It was shown that a modification of the neural network method [4, 5] makes it possible to compute a spectrum of Lyapunov exponents, and then to detect a transition of the system regular dynamics into chaos, hyper-chaos, hyper hyper-chaos and deep chaos [14-16]. Different algorithms for computation of Lyapunov exponents were validated by comparison with the known dynamical systems spectra of the Lyapunov exponents. The carried out analysis helps comparatively estimate the employed methods in order to choose the most suitable/optimal one to study different kinds of dynamical systems and different classes of problems in both this and the next paper parts.