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.

Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

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.

Recently Candida auris has emerged as a multi-resistant fungal pathogen, with a significant clinical impact, and has become a critical issue in WHO fungal priority list, due to its unique ability to persist for long time on human skin and hospital environments. It is therefore fundamental to reinforce hospital surveillance protocols to limit nosocomial outbreaks. The study purpose was the Fourier-Transform Infrared Spectroscopy (FT-IR) application to investigate the phylogenetic relationships between isolated strains within the C. auris outbreak at the university Intensive Care Unit of a Tertiary University hospital in Turin (Italy). In order to calculate a clustering cut-off, intra- and inter-isolates distance values were analysed. Data showed the presence of a major cluster Alfa and a minor cluster Beta with a defined C. auris clustering cut-off. The results were validated by an external C. auris strain and Principal Component and Linear Discriminant Analysis. The application of FT-IR technology had allowed to obtain important information about the phylogenetic relationships between the analysed strains, defining for the first time a “not WGS-based” clustering cut-off with a statistical-mathematical approach. FT-IR could represent a valid alternative to molecular methods for rapid and cost saving typing of C. auris strains with important clinical implications.

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.

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.

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.

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.

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 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 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.

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).

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.

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 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.

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.

The reliable online analysis of volatile compounds in exhaled breath remains a challenge as a plethora of molecules occur in different concentration ranges (i.e. ppt to %), and need to be detected against an extremely complex background matrix. While this complexity is commonly addressed by hyphenating a specific analytical technique with appropriate preconcentration and/or preseparation strategies prior to detection, we herein propose the combination of three analytical tools based on truly orthogonal measurement principles as an alternative solution: field-asymmetric ion mobility spectrometry (FAIMS), Fourier-transform infrared (FTIR) spectroscopy-based sensors utilizing substrate-integrated hollow waveguides (iHWG), and luminescence sensing (LS). These three tools have been integrated into a single compact analytical platform suitable for online exhaled breath analysis. The analytical performance of this prototype system was tested via artificial breath samples containing nitrogen (N2), oxygen (O2), carbon dioxide (CO2) and acetone as a model volatile organic compound (VOC) commonly present and detected in breath. Functionality of the combined system was demonstrated by detecting these analytes in their respectively breath-relevant concentration range and mutually independent of each other generating orthogonal yet correlated analytical signals. Finally, adaptation of the system towards the analysis of real breath samples during future studies is discussed.

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.

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.

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.

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.

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.

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 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 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.

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.

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.

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 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 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.

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.

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.

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.

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 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).

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.

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.

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.

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.

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).

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.

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 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.

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.

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.

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.

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.

Breast cancer is the most commonly diagnosed cancer in women in both developed and developing countries. Due to the increasing alarms in the detection of cases every year, it is considered a priority to evaluate new molecules as potential antitumoral agents. Among these molecules, cationic peptides have emerged as promising therapeutic agents with a membrane-based mechanism of action very hard to counteract by the cancer cells. This biophysical study seeks to offer preliminary insights into how NA-CATH:ATRA-1-ATRA-1, a synthetic cationic peptide derived of the peptide NA-CATH, isolated from the species Natra aja or Chinese cobra, is a potential antitumoral compound at the membrane level on breast cancer cell lines. The interaction of the NA-CATH-ATRA-1-ATRA-1 with two lipid systems representative of tumoral and non-tumoral membranes was followed by differential scanning calorimetry and Fourier-transform infrared spectroscopy. The results showed a strong interaction of NA-CATH-ATRA-1-ATRA-1 with the lipids present in the eukaryotic membranes, especially phosphatidylserine, suggesting a mechanism based on the electrostatic interaction of the peptide with the anionic lipids of the tumoral cancer membranes. The biophysical studies are essential to understand the mechanism of action of a potential pharmaceutics.

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.

Primate vision is an active process that constructs a stable internal representation of the 3D world based on 2D sensory inputs that are inherently unstable due to incessant eye movements. We present here a mathematical framework for processing visual information for a biologically-mediated active vision stereo system with asymmetric conformal cameras. This model utilizes the geometric analysis on the Riemann sphere developed in the group-theoretic framework of the conformal camera, thus far only applicable in modeling monocular vision. The asymmetric conformal camera model constructed here includes the fovea’s asymmetric displacement on the retina and the eye’s natural crystalline lens tilt and decentration, as observed in ophthalmological diagnostics. We extend the group-theoretic framework underlying the conformal camera to the stereo system with asymmetric conformal cameras. Our numerical simulation shows that the 1 theoretical horopter curves in this stereo system are conics that well approximate the empirical longitudinal horopters of the primate vision system.

This contribution is an attempt to reconstruct the favorable atmosphere that prevailed in Lau-sanne in 1986-87 and provided the backdrop of our invention of two-dimensional ion cyclotron resonance mass spectroscopy (2D ICR-MS). To avoid a self-centered histoire d’ancien combattant, we shall try to emphasize the context, the contributions of key players within our nascent research group at UNIL and the established group of Tino Gäumann at EPFL, the role of external speakers, and the open atmosphere that was not yet polluted by bibliometrics, obsessive concern with im-pact factors, and top-down management of research. We shall also explain why the idea of 2D ICR-MS has been ignored for many years and still has a limited impact: different scientific cul-tures in the ICR and NMR communities, different concerns with fundamental vs. applied research, different status of theory and numerical simulations, different levels of commitment of instrument manufacturers, not to mention many theoretical problems that appear to be at least as challenging in ICR as in NMR.

The aim of this paper is to introduce a new methodology for the fault diagnosis of induction machines working in transient regime, when time-frequency analysis tools are used. The proposed method relies on the use of the optimized Slepian window for performing the short time Fourier transform (STFT) of the stator current signal. It is shown that for a given sequence length of finite duration the Slepian window has the maximum concentration of energy, greater than can be reached with a gated Gaussian window, which is usually used as analysis window. In this paper the use and optimization of the Slepian window for fault diagnosis of induction machines is theoretically introduced and experimentally validated through the test of a 3.15 MW induction motor with broken bars during the start-up transient. The theoretical analysis and the experimental results show that the use of the Slepian window can highlight the fault components in the current's spectrogram with a significant reduction of the required computational resources.

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.

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

Retired Electric vehicles (EVs) batteries are reused in second life energy storage applications. However, the overall performance of repurposed energy storage system (ESS) is limited by the unevenness of individual batteries use in it. Therefore, battery grading is required for optimal performance of ESS. Electrochemical impedance spectroscopy (EIS) based evaluation of battery aging is a promising way to grade lithium-ion batteries. However, it is not practical to measure impedance of mass retired batteries due to high complexity and slowness. In this paper, a broadband multi-sine binary signal (MSBS) perturbation integrated with multichannel EIS system is presented to measure impedance spectra for high-speed aging evaluation of lithium-ion batteries or modules. The measurement speed is multi-times higher than conventional EIS with single-channel configuration. The broadband MSBS is validated with reference sinusoidal sweep perturbation and corresponding root-mean-square error (RMSE) analysis is performed. Moreover, the accuracy of the presented multichannel EIS system is validated by impedance spectra measurement of Samsung INR18650-29E batteries and comparing it with those measured with commercial EIS instrument. A chi-squared error under 0.641% is obtained for all 8-channels. Since the non-linearity of battery has significant impact on quality of impedance spectra. Therefore, Kronig-Kramer (KK) transform validation is also performed.

The present study investigates the relationship between the local structure, photocatalytic ability, and cathode performances in sodium-ion batteries (SIBs) and lithium-ion batteries (LIBs) using Ni-substituted goethite nanoparticles (Ni_xFe_1-xOOH NPs) with a range of 'x' values from 0 to 0.5. The structural characterization was performed applying various techniques, including X-ray diffractometry (XRD), Thermogravimetry differential thermal analysis (TG-DTA), Fourier Transform Infrared Spectroscopy (FT-IR), X-ray absorption spectroscopy (XANES/EXAFS), both measured at room temperature (RT), and ⁵⁷Fe Mössbauer spectroscopy recorded at RT and at low temperatures (LT) from 20 K to 300 K, Brunauer-Emmett-Teller surface area measurement (BET), and diffuse reflectance spectroscopy (DRS). In addition, the electrical properties of Ni_xFe_1-xOOH NPs were evaluated by impedance spectroscopy. XRD showed the presence of goethite as the only crystalline phase in prepared samples with x ≤ 0.20, and goethite and α-Ni(OH)₂ in the samples with x > 0.20. Sample with x = 0.10 (Ni10) showed the highest photo-Fenton ability with a first-order rate constant value (k) of 15.8×10^-3 min^-1. The ⁵⁷Fe Mössbauer spectrum of Ni0, measured at RT, displayed a sextet corresponding to goethite, with an isomer shift (δ) of 0.36 mm s^-1 and a hyperfine magnetic distribution (B_hf) of 32.95 T. Moreover, the DC conductivity decreased from 5.52×10^-10 to 5.30×10^-12 (Ω.cm)^–1 with 'x' increasing from 0.10 to 0.50. Ni20 showed the highest initial discharge capacity of 223 mAh g^-1, attributed to its largest specific surface area of 174.0 m² g^-1. In conclusion, Ni_xFe_1-xOOH NPs can be effectively utilized as visible-light-activated catalysts and active cathode materials in secondary batteries.

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

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.

Abstract: The two-dimensional Fuzzy Transform was applied in image compression. The quality of the image compressed with this methodis better than that obtained using methods based on fuzzy relation equations and comparable with that of the JPEG method, with better compression execution times. In this paper we propose a variation of the method based on the two-dimensional Fuzzy Transform of image compression, in which the image is first partitioned into blocks and then each block is compressed with the higher compression rate. The advantage of this method consistsinto a greater compression of the image, guaranteeing a high quality of the reconstructed image.The results show that our method is better than the Fuzzy Transform method improving also the quality of the reconstructed image.

This paper reviews the unilateral and bilateral, one- and two-dimensional Laplace transforms. The unilateral and bilateral Laplace transforms are compared in the one-dimensional case, leading to the formulation of the initial-condition theorem. This problem is solved with all generality in the one- and two-dimensional cases with the bilateral Laplace transform. General two-dimensional linear systems are introduced and the corresponding transfer function defined.

High Efficiency Video Coding (HEVC) uses an 8-point filter and a 7-point filter, which are based on the discrete cosine transform (DCT), for the 1/2-pixel and 1/4-pixel interpolations, respectively. In this paper, discrete sine transform (DST)-based interpolation filters (IF) are proposed. The first proposed DST-based IFs (DST-IFs) use 8-point and 7-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. The final proposed DST-IFs use 12-point and 11-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. These DST-IF methods are proposed to improve the motion-compensated prediction in HEVC. The 8-point and 7-point DST-IF methods showed average BD-rate reductions of 0.7% and 0.3% in the random access (RA) and low delay B (LDB) configurations, respectively. The 12-point and 11-point DST-IF methods showed average BD-rate reductions of 1.4% and 1.2% in the RA and LDB configurations for the Luma component, respectively.

Analysis of non-stationary and nonlinear sound signals obtained from dynamical processes is one of the greatest challenges in signal processing. Turning machine operation is a highly dynamic process persuaded by many events such as dynamical responses, chip formations and operational conditions of machining. Traditional and widely used fast Fourier transformation and spectrogram is not suitable for processing sound signals acquired from dynamical systems as its result have significant deficiencies because of stationary assumptions and having priori basis. The relatively new technique, Discrete Wavelet Transform, which uses Wavelet decomposition and the recently developed technique, Hilbert Huang Transform (HHT) which uses Empirical Mode Decomposition have notably better properties in the analysis of nonlinear and non-stationary sound signals. This paper presents a comparative study on the decomposition of multicomponent sound signals using Empirical Mode Decomposition and Wavelet Decomposition to highlight the suitability found in HHT to analyze tool-emitted sound signals received from turning processes. Apart from the short mathematical and theoretical foundations of the transformations, this paper demonstrates their decomposition strength using an experimental case study of tool flank wear monitoring in turning. It also concludes HHT is more suitable than DWT to analyze tool-emitted sound signals received from turning processes.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

As an implementation of inverse Radon transform, the Second-order Divided-difference Back Projection (SDBP) technique has been proposed in this paper, by which the accurate CT reconstruction can be theoretically realized. A computational model for CT reconstruction filter expressions has been derived on the basis of SDBP technique. The method reveals the correlation between the convolution kernel for data restoration and the filter expression. By substituting kernel functions into the computational model, the amplitude sequences of a variety of filters can be calculated. On the proposed filter construction method, the decomposition form of filters has been discovered, where a series of basic filters have been acquired. The properties of any filter depend on the decomposed basic filters. Basic filters can be used to compose filters in actual needs.

Background. Escalating global plastic production, expected to reach 34,000 million tons by 2050, poses a significant threat to human and environmental well-being, particularly in aquatic ecosystems. Microplastics (MP) and nanoplastics (NP), which originate from the degradation of plastics, are of concern due to their potential bioaccumulation and uptake of pollutants. This study addresses identification methods and focuses on insect meal, a raw material for aquaculture feed. Methods. By using different techniques, the study was able to detect MP and NP in insect meal samples. Chemical digestion with KOH at 60°C efficiently removed organic matter without affecting the synthetic polymer polyethylene (PE). Filtration, confocal Raman microscopy, SEM and TEM were used for comprehensive analysis and integrity tests on PE films were performed using Raman and FTIR spectroscopy. The results showed the presence of PE microplastic particles in the insect meal, which was confirmed by correlative Raman and SEM mapping on a positively charged surface. In addition, the increased resolution of the Raman microscope identified submicrometric PE NP (800 nm). Transmission electron microscopy (TEM) with energy dispersive X-ray spectroscopy (EDX) confirmed plastic-like structures in the insect meal, highlighting the presence of PE plastics characterized by irregular shapes and some agglomeration. The higher carbon concentration in the EDX analysis supported the plastic nature, which was also confirmed by Raman spectroscopy. Conclusions. The study provides a robust method for the detection of MP and NP in insect meal and provides valuable insight into the possible presence of plastics in insect-based aquafeeds. The combination of different analytical methods increases the reliability of the results and sets the stage for future investigations that could focus on the quantification of NP and the assessment of their potential environmental impact.

Addressing global environmental problem, water splitting to produce hydrogen fuel by solar energy is getting so much attention. In the water splitting, the essential problem to solve is the development of efficient　catalysts for oxygen production. In this paper, having the prospect for a practical application of photocatalysts to artificial photosynthesis, molecular mechanisms in the current literature are briefly reviewed. At first, recent progress in the function of Mn cluster at the natural photosystem II is briefly described. The kinds of devices in which oxygen evolution reaction (OER) catalysts are used were designated; water electrolyzers, photoelectrodes, and photocatalysts. Some methods for analyzing molecular mechanism in OER catalysis, emphasized by FTIR method, are shown briefly. After describing common OER mechanisms, the molecular mechanisms are discussed for TiO2 and BiVO4 photoelectrodes with our novel data, followed by presenting of co-catalysts IrO2, RuO2, NiO2, and other metal oxides for OER catalysts. Recent reports describing OER catalysts of perovskites, layered double hydroxides (LDH), metal-organic frameworks (MOF), single atom catalysts, as well as metal complexes are reviewed. Finally, by comparing with natural photosystem, the requiring factors to improve the activity of the catalysts for artificial photosynthesis will be discussed.

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.

In this paper, we establish the existence and uniqueness results of the fractional Navier-Stokes evolution equation using the Banach fixed point theorem, where the fractional order β is in the form of the Atangana-Baleanu Caputo fractional order. The iterative method combined with the Laplace transform and Sumudu transform are employed to find the exact and approximate solutions of the fractional Navier-Stokes equation of a one-dimensional problem of unsteady flow of a viscous fluid in a tube. Mathematica software is used to present the solutions graphically.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

The key objective of the present paper is to propose a numerical scheme based on the homotopy analysis transform technique to analyze the time-fractional nonlinear predator-prey population model. The population model is coupled fractional order nonlinear partial differential equations often employed to narrate the dynamics of biological systems in which two species interact, first is a predator and the second is a prey. The proposed scheme provides the series solution with great freedom and flexibility by choosing appropriate parameters. The convergence of results is free from small or large parameters. Three examples are discussed to demonstrate the correctness and efficiency of the used computational approach.

Sentiment analysis to characterize properties of Bitcoin prices and their forecasting is here developed thanks to the capability of the Fuzzy transform to capture stylized facts and mutual connections between time series having different nature. Six years of daily Bitcoin Prices and Google Trends are analyzed in order to establish new perspectives in the management of their dynamics.

Objective:The Glioma brain tumor detection and segmentation methods are proposed in this paper using machine learning approaches. Methods:The boundary edge pixels are detected using Kirsch’s edge detectors and then contrast adaptive histogram equalization method is applied on the edge detected pixels. Then, Ridgelet transform is applied on this enhanced brain image in order to obtain the Ridgelet multi resolution coefficients. Further, features are derived from the Ridgelet transformed coefficients and the features are optimized using Principal Component Analysis (PCA) method and these optimized features are classified into Glioma or non-Glioma brain images using Co-Active Adaptive Neuro Fuzzy Expert System (CANFES) classifier.Results:The proposed method with PCA and CANFES classification approach obtains 97.6% of se, 98.56% of sp, 98.73% of Acc, 98.85% of Pr, 98.11% of FPR and 98.185 of FNR, then the proposed Glioma brain tumor detection method using CANFES classification approach only.

In this paper, a technique of image watermarking using multiple images as watermarks is presented. The technique is based on transform domain functions including discrete wavelet transform (DWT), discrete cosine transform (DCT) and singular value decomposition (SVD) with an image as the host signal i.e. the watermarks will be used as proofs of the authenticity of the host image. The technique is executed by performing multilevel DWT followed by applying DCT and SVD to both the host and watermark. Multiple watermarks are used for the insurance of better security level. The scheme is immune to common image processing operations & some attacks and exhibits PSNR of 108.3781dB, normalized cross correlation (NCC) over 0.99 and normalized correlation (NC) over 0.99.

In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the partition requirement, that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measuring terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy.

In recent years, artificial neural networks (ANNs) have won numerous contests in pattern recognition, machine learning, and artificial intelligence. The basic unit of an ANN is to mimic neurons in the brain. Neuron in ANNs is expressed as f (wx+b) or f (wx). This structure does not consider the information processing capabilities of dendrites. However, recently, studies shown that dendrites participate in pre-calculation in the brain. Concretely, biological dendrites play a role in the pre-processing to the interaction information of input data. Therefore, it is time to perfect the neuron of the neural network. This paper, add dendrite processing section, presents a novel artificial neuron, according to our previous studies (CR-PNN or Gang transform). The dendrite processing section can be expressed as . Because I perfected the basic unit of ANNs— neuron, there are so many networks to try. This article gives the basic architecture for reference in future research.

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.

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.

The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

Discrete Double Hilbert Exponential sums along polynomials. This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.