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The main aim of this article is to focus on the fundamental properties of the gyrator transform on the Schwartz spaces. A more generalization Hörmander symbol class is introduced and studied the boundedness properties of pseudo‐differential operators associated with the gyrator transform. Integral representation and kernel of the pseudo‐differential operators are derived. It is shown that pseudo‐differential operators satisfies certain norm inequalities on Sobolev space. As an application, we have successfully applied the gyrator transform to solve heat equation and Fredholm integral equation. [ABSTRACT FROM AUTHOR]

Sandwich structures with ceramic honeycomb cores are extensively employed in thermal protection systems owing to their exceptional ability to resist high temperatures. This work aims at exploring the effect of cracking on the transient thermal process of the sandwich panel subject to impulsive and cyclic thermal loadings. Both the conventional and re-entrant hexagonal alumina honeycombs are considered for the core material. By the integral transform method, combined with singular integral equations, the transient temperatures of the whole sandwich panel are determined from the semi-analytical solution. The straightforward temperature difference of the crack face's midpoints is exploited to characterize the heat intensification near the crack. Parametric investigations are carried out for the internal cell angle, the relative density, crack length, crack position, and thickness of face sheets, which provides a better understanding of the honeycomb materials working in thermal protection systems. [ABSTRACT FROM AUTHOR]

We prove exact formulas for weighted 2kth moments of the Riemann zeta function for all integer k ⩾ 1 in terms of the analytic continuation of an auto-correlation function. This latter enjoys three functional equations. One of them, following from a fundamental lemma of Bettin and Conrey (Algebra Number Theory 7(1):215–242, 2013), yields to a new formula for the sixth moment, which can be seen as a generalization of formulas by Titchmarsh (Proc Lond Math Soc 27(2):137–150, 1927) for the second and fourth moments. A basic and powerful tool is a special Fourier transform unveiled by Ramanujan (Quart J Math 46:253–260, 1915). [ABSTRACT FROM AUTHOR]

Expressing distributions in Euclidean space in terms of spherical coordinates gives rise to an alternative class of continuous linear functionals, termed signumdistributions, acting on test functions showing a pointwise singularity at the origin. In this paper the theory of signumdistributions is further explored from the viewpoint of integral transforms, viz. the Fourier and Hilbert transforms, and the interplay between them. [ABSTRACT FROM AUTHOR]

In this work, we prove the joint convergence in distribution of q variables modulo one obtained as partial sums of a sequence of i.i.d. square-integrable random variables multiplied by a common factor given by some function of an empirical mean of the same sequence. The limit is uniformly distributed over [ 0 , 1 ] q . To deal with the coupling introduced by the common factor, we assume that the absolutely continuous (with respect to the Lebesgue measure) part of the joint distribution of the random variables is nonzero, so that the convergence in the central limit theorem for this sequence holds in total variation distance. While our result provides a generalization of Benford's law to a data-adapted mantissa, our main motivation is the derivation of a central limit theorem for the stratified resampling mechanism, which is performed in the companion paper (Flenghi and Jourdain, Central limit theorem for the stratified selection mechanism, 2023, http://arxiv.org/abs/2308.02186). [ABSTRACT FROM AUTHOR]

In the field of recommendation algorithms, Knowledge Graphs are often utilized as supplementary information to enhance recommendation accuracy. However, while applying Knowledge Graphs enriches recommendation information, it also introduces potentially misleading effects due to Knowledge Graph noise. To address these challenges, we propose a method to achieve Knowledge Graph Noise Reduction and Knowledge Perception Enhancement through positive contrast learning. The method employs Fourier Transform, Inverse Transform, and Convolution Optimization Computation techniques to transform and analyze Knowledge Graph triplet information in the frequency domain. The process filters and reduces noise through Convolution Optimization Computation by integrating frequency domain feature information, eliminating misleading relational information that cannot effectively infer user preferences. Subsequently, Positive Contrastive Learning enhances the acquired ternary information and improves the applicability of the information to recognize user preference information accurately. The proposed method reduces noise and enhances knowledge perception, strengthens the application of strong relationships, reduces the impact of weak relationships, and improves recommendation accuracy by utilizing frequency-domain features. The KG-CFCL_RippleNet and KG-CFCL_MKR models validate the effectiveness of this optimization method, and significant improvements are achieved in the area of book, music, and movie recommendations compared to existing models. Experiments demonstrate the advantages of KG-CFCL in terms of noise reduction, Knowledge Perception Enhancement, and data optimization, improving the interpretability of the models. [ABSTRACT FROM AUTHOR]

Image super-resolution is a critical aspect of image enhancement, facilitating the reconstruction of high-quality images from low-resolution inputs. Traditional quality assessment metrics like SSIM, MSE, and PSNR have limitations in effectively evaluating super-resolution models due to their focus on pixel values and statistical properties, overlooking overall visual quality. This article introduces a technique for comparing super-resolution models using a pattern-based approach. The proposed method evaluates image quality by analyzing the harmonics, providing a performance comparison index that surpasses traditional metrics. By focusing on the frequency domain and magnitudes of Fourier components, this technique effectively captures image features and patterns, enabling a more comprehensive assessment of super-resolution model performance. [ABSTRACT FROM AUTHOR]

The free metaplectic transform (FMT), a generalized form of the linear canonical transform (LCT), has proven to be a useful analytical tool in signal processing applications. This paper aims to generalize the FMT to a quaternionic framework involving the two‐dimensional signals. We further study some properties that correspond to those of the standard ones, including linearity, uniform continuity, inversion, and Parseval's identity for this new integral transform, which we coin as the quaternionic free metaplectic transform (QFMT). Furthermore, utilizing the relationship between the general quaternionic Fourier transform and the QFMT, several uncertainty principles (UPs) for the QFMT are established, including the Heisenberg–Weyl UP, Hardy UP, logarithmic UP, Donoho–Stark UP, and entropic UP. We expect that this paper will open up avenues of promising research and applications involving this new transformation. [ABSTRACT FROM AUTHOR]

Amperometry is a commonly used electrochemical method for studying the process of exocytosis in real-time. Given the high precision of recording that amperometry procedures offer, the volume of data generated can span over several hundreds of megabytes to a few gigabytes and therefore necessitates systematic and reproducible methods for analysis. Though the spike characteristics of amperometry traces in the time domain hold information about the dynamics of exocytosis, these biochemical signals are, more often than not, characterized by time-varying signal properties. Such signals with time-variant properties may occur at different frequencies and therefore analyzing them in the frequency domain may provide statistical validation for observations already established in the time domain. This necessitates the use of time-variant, frequency-selective signal processing methods as well, which can adeptly quantify the dominant or mean frequencies in the signal. The Fast Fourier Transform (FFT) is a well-established computational tool that is commonly used to find the frequency components of a signal buried in noise. In this work, we outline a method for spike-based frequency analysis of amperometry traces using FFT that also provides statistical validation of observations on spike characteristics in the time domain. We demonstrate the method by utilizing simulated signals and by subsequently testing it on diverse amperometry datasets generated from different experiments with various chemical stimulations. To our knowledge, this is the first fully automated open-source tool available dedicated to the analysis of spikes extracted from amperometry signals in the frequency domain. [ABSTRACT FROM AUTHOR]

In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPFT). Further, we derive the Parseval formula and the Riemann–Lebesgue lemma using this transform. Furthermore, we formulate two important inequalities (sharp Pitt's and sharp Hausdorff–Young's inequalities) and three main uncertainty principles (logarithmic, Donoho–Stark's, and Heisenberg's uncertainty principles) for the OQPFT. To complete our investigation, we construct three elementary examples of signal theory with graphical interpretations to illustrate the use of OQPFT and discuss their particular cases. [ABSTRACT FROM AUTHOR]

Stock price prediction has long been a topic of interest in academia and the financial industry. Numerous factors influence stock prices, such as a company's performance, industry development, national policies, and other macroeconomic factors. These factors are challenging to quantify, making predicting stock price movements difficult. This paper presents a novel deep neural network framework that leverages the dynamic fusion of multi-dimensional and multi-level features for stock price prediction, which means we utilize fundamental trading data and technical indicators as multi-dimensional data and local and global multi-level information. Firstly, the model dynamically assigns weights to multi-dimensional features of stocks to capture the impact of each feature on stock prices. Next, it applies the Fourier transform to the global features to capture the long-term trends of the global environment and dynamically fuses these with local and global features of the stocks to capture the overall market environment's impact on individual stocks. Finally, temporal features are captured using an attention layer and an RNN-based model, which incorporates historical price data to forecast future prices. Experiments on stocks from various industries within the Chinese CSI 300 index reveal that the proposed model outperforms traditional methods and other deep learning approaches in terms of stock price prediction. This paper proposes a method that facilitates the dynamic integration of multi-dimensional and multi-level features in an efficient manner and experimental results show that it improves the accuracy of stock price predictions. [ABSTRACT FROM AUTHOR]

A wide variety of methods have been proposed for clustering of stochastic processes. However, for clustering of periodically correlated processes (PC) it is demanding to introduce some similarity measures that take into account the inherent periodicity of these processes. The frequency-domain based methods seem more desirable to determine groups of PC processes with similar frequency characterizations. In this article, we present new similarity measures based on Hilbert-Schmidt inner product of finite Fourier transforms of PC processes. Based on simulated stochastic processes and a real gene expression dataset we illustrate the accuracy of the methods. [ABSTRACT FROM AUTHOR]

In response to economic and environmental challenges like sea-level rise, salinity intrusion, groundwater extraction, sand mining, and sinking delta phenomena, the demand for solutions to adapt to changing conditions in riverine environments has increased significantly. High-quality analyses of land use and land cover (LULC) dynamics play a critical role in addressing these challenges. This study introduces a novel high-spatial resolution satellite-based approach to identify sub-seasonal LULC dynamics in the Mekong River Delta (MRD), employing a three-year (2021–2023) Sentinel-1 and Sentinel-2 satellite data time series. The primary obstacle is discerning detailed vegetation dynamics, particularly the seasonality of rice crops, answered through quantile mapping, harmonic regression with Fourier transform, and phenological metrics as inputs to a random forest machine learning classifier. Due to the substantial data volume, Google's cloud computing platform Earth Engine was utilized for the analysis. Furthermore, the study evaluated the relative significance of various input features. The overall accuracy of the classification is 82.6% with a kappa statistic of 0.81, determined using comprehensive reference data collected in Vietnam. While the purely pixel-based approach has limitations, it proves to be a viable method for high-spatial resolution satellite image time series classification of the MRD. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of phase retrieval with short-time linear canonical transform (STLCT). The relation between signal, window and their STLCT is provided through Fourier transform. Based on this theorem, a uniqueness result is established for all square integrable functions. For nonseparable real continuous signal, we prove the uniqueness theorems under some weaker conditions. In complex bandlimited and cardinal B -spline spaces, uniqueness results are provided with magnitude-only STLCT. [ABSTRACT FROM AUTHOR]

Ceramic insulators on High Voltage Overhead Lines (SUTT) in Indonesia, particularly on the Payakumbuh-Koto Panjang transmission line, are often exposed to natural contamination. This research evaluated the impact of natural contamination on the Total Harmonic Distortion (THD) of leakage current in 150 kV insulators, representing a new approach to understanding insulator performance in contaminated environments. Tests were conducted at the High Voltage Laboratory at Universitas Gadjah Mada using various types of contamination: moss, dust, flashover marks, and clean insulator conditions. The results showed that insulators contaminated with moss exhibited a maximum leakage current of 0.306 mA, with the highest THD reaching 36%, while insulators in clean condition had an average THD of 32.5%. Insulators contaminated with moss, dust, and flashover marks showed THD values of 25.37%, 19.03%, and 28.71%, respectively. Moss and flashover can significantly increase THD, especially when the number of disc-type insulators increases. These findings underscored the importance of a more intensive and targeted maintenance strategy for insulators to minimize the negative impacts of natural contamination, particularly in mountainous areas. This approach contributes to the enhancement of the reliability of high-voltage transmission lines in Indonesia. [ABSTRACT FROM AUTHOR]

In this study, stall flutter onset prediction in a transonic compressor is carried out using the (uncoupled) energy method with Fourier transform. As the study is conducted computationally using computational fluid dynamics (CFD)-based simulations, the energy method was employed due to its higher computational efficiency by implementing the one-way FSI (Fluid Structure Interaction) model. The energy method is relatively uncommon for determining the aerodynamic damping and flutter prediction, specifically in blade stall conditions for the 3D blade passages. The NASA Rotor 67 was chosen for the validation of the study due to the availability of a wide range of experimental data. A flutter prediction analysis was performed computationally using CFD for the two-blade passages of the rotor in the peak efficiency and stall regions. Prior to this, the modal analysis on the prestressed blade was conducted, considering the centrifugal effects. The modal analysis provided accurate blade frequency and amplitude, which were the inputs of the flutter analysis. The first three modes of blade resonance were studied with a range of nodal diameters within near-peak efficiency and stall regions. The energy method implemented in this study for the flutter analysis was successfully able to predict the aerodynamic damping coefficients of the first three modes for a range of nodal diameters from the periodic-unsteady solution of the defined blade oscillation within the regions of interest (peak efficiency and stall point). The results of the study confirm the rotor blade's stability within the near-peak region and, most importantly, the prediction of the flutter onset in the stall region. The study concluded that the computationally inexpensive and time-efficient energy method is capable of predicting the stall flutter onset. In the future, further validations of the energy method and investigations related to flow mechanism of stall flutter onset are planned. [ABSTRACT FROM AUTHOR]

Benefitting from a large bandwidth and compact configuration, a time-domain pulse-shaping (TPS) system provides possibilities for generating broadband radio frequency (RF) arbitrary waveforms based on the Fourier transform relationship between the input–output waveform pair. However, limited by the relatively low sampling rate and bit resolution of an electronic arbitrary-waveform generator (EAWG), the diversity and fidelity of the output waveform as well as its reconfiguration rate are constrained. To remove the EAWG's limitation and realize dynamic real-time reconfiguration of RF waveforms, we propose and demonstrate a novel approach of RF arbitrary-waveform generation based on an improved TPS system with an integrated dual parallel Mach–Zehnder modulator (DPMZM) and multi-tone inputs. By appropriately adjusting the DC bias voltages of DPMZM and the power values, as well as the center frequencies of the multi-tone inputs, any desired RF arbitrary waveform can be generated and reconfigured in real time. Proof-of-concept experiments on the generation of different user-defined waveforms with a sampling rate up to 27 GSa/s have been successfully carried out. Furthermore, the impact of modulation modes and higher-order dispersion on waveform fidelity is also discussed in detail. [ABSTRACT FROM AUTHOR]

Urban mobility optimization is crucial in managing transportation systems efficiently. This study addresses a broad research area of urban mobility by focusing on taxi demand prediction, a key component of the transportation ecosystem. The specific problem addressed in this research is the need for accurate and efficient taxi demand prediction, especially in large, dynamic urban environments. Existing solutions, including basic time series approaches like simple moving averages and exponential weighted moving averages, while valuable, have limitations in handling the intricacies of urban taxi demand patterns. In this study, we employed a combination of data preprocessing techniques, advanced regression models, and Fourier features to predict taxi demand in dynamic urban environments. The data preprocessing techniques included data cleaning, normalization, and feature engineering. The advanced regression models used in this study were Random Forest and XGBoost, which were trained and tested using NYC taxi datasets. The Fourier features were used to capture the periodicity of the taxi demand patterns. These models are demonstrated to outperform standard solutions, effectively achieving the targeted mean absolute percentage error (MAPE) of less than 12%. Evaluation of the solution revealed its effectiveness in reducing the prediction error by more than 1%, thus highlighting the positive results of this research. [ABSTRACT FROM AUTHOR]

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study Sobolev H s (R n) , s ∈ R , stability of the Fourier phase problem to recover f from the knowledge of | f ^ | with an additional Bessel potential H t , p (R n) a priori estimate when t ∈ R and p ∈ [ 1 , 2 ] . These estimates are related to the ones studied recently by Steinerberger in ”On the stability of Fourier phase retrieval” J. Fourier Anal. Appl., 28(2):29, 2022. While our estimates in general are different, they share some comparable special cases and the main improvement given here is that we can remove an additional imaginary term and obtain sharper constants. We also consider these estimates for the quotient distances related to the non-uniqueness of the Fourier phase problem. Our arguments closely follow the Fourier analysis proof of the Sobolev embeddings for Bessel potential spaces with minor modifications. [ABSTRACT FROM AUTHOR]

We propose an extension of the model introduced by Barndorff-Nielsen and Shephard, based on stochastic processes of Ornstein–Uhlenbeck type taking values in Hilbert spaces and including the leverage effect. We compute explicitly the characteristic function of the log-return and the volatility processes. By introducing a measure change of Esscher type, we provide a relation between the dynamics described with respect to the historical and the risk-neutral measures. We discuss in detail the application of the proposed model to describe the commodity forward curve dynamics in a Heath–Jarrow–Morton framework, including the modelling of forwards with delivery period occurring in energy markets and the pricing of options. For the latter, we show that a Fourier approach can be applied in this infinite-dimensional setting, relying on the attractive property of conditional Gaussianity of our stochastic volatility model. In our analysis, we study both arithmetic and geometric models of forward prices and provide appropriate martingale conditions in order to ensure arbitrage-free dynamics. [ABSTRACT FROM AUTHOR]

We show how the octonion Fourier transform can be embedded and studied in Clifford geometric algebra of three‐dimensional Euclidean space Cl(3,0)$$ Cl\left(3,0\right) $$. We apply a new form of dimensionally minimal embedding of octonions in geometric algebra that expresses octonion multiplication nonassociativity with a sum of up to four (individually associative) geometric algebra product terms. This approach leads to new polar representations of octonion analytic signals and signal reconstruction formulas. [ABSTRACT FROM AUTHOR]

Texture is the surface qualities and visual attributes of an object, determined by the arrangement, size, shape, density, and proportion of its fundamental components. In the manufacturing industry, products typically have uniform textures, allowing for automated visual inspections of the product surface to recognize defects. During this process, texture defect recognition techniques can be employed. In this paper, we propose a method that combines a convolutional autoencoder architecture with Fourier transform analysis. We employ a normal reconstructed template as defined in this study. Despite its simple structure and rapid training and inference capabilities, it offers recognition performance comparable to state-of-the-art methods. Fourier transform is a powerful tool for analyzing the frequency domain of images and signals, which is essential for effective defect recognition as texture defects often exhibit characteristic changes in specific frequency ranges. The experiment evaluates the recognition performance using the AUC metric, with the proposed method showing a score of 93.7%. To compare with existing approaches, we present experimental results from previous research, an ablation study of the proposed method, and results based on the high-pass filter used in the Fourier mask. [ABSTRACT FROM AUTHOR]

We obtain the exact order estimates for approximation of the functions of many variables from the generalized Nikol'skii–Besov classes B p , θ Ω R d by de la Vallée Poussin sums in the metrics of the spaces L ∞ R d and L 1 R d . These classes of functions for some given Ω coincide with the well-known classical isotropic Nikol'skii–Besov classes. [ABSTRACT FROM AUTHOR]

Long time series forecasting (LTSF), which involves modeling relationships within long time series to predict future values, has extensive applications in domains such as weather forecasting, financial analysis, and traffic prediction. Recently, numerous transformer-based models have been developed to address the challenges in LTSF. These models employ methods such as sparse attention to alleviate the inefficiencies associated with the attention mechanism and utilize decomposition architecture to enhance the predictability of the series. However, these complexity reduction methods necessitate additional calculations, and the series decomposition architecture overlooks the random components. To overcome these limitations, this paper proposes the Frequency Enhanced Decomposed Attention Free Transformer (FEDAF). FEDAF introduces two variants of the Frequency Enhanced Attention Free Mechanism (FEAFM), namely FEAFM-s and FEAFM-c, which seamlessly replace self-attention and cross-attention. Both variants perform calculations in the frequency domain without incurring additional costs, with the time and space complexity of FEAFM-s being O (L log L) . Additionally, FEDAF incorporates a time series decomposition architecture that considers random components. Unlike other models that solely decompose the series into trend and seasonal components, FEDAF also eliminates random terms by applying Fourier denoising. Our study quantifies data drift and validates that the proposed decomposition structure can mitigate the adverse effects caused by data shift. Overall, FEDAF demonstrates superior forecasting performance compared to state-of-the-art models across various domains, achieving a remarkable improvement of 19.49% for Traffic in particular. Furthermore, an efficiency analysis reveals that FEAFM enhances space efficiency by 12.8% compared to the vanilla attention mechanism and improves time efficiency by 43.63% compared to other attention mechanism variants. [ABSTRACT FROM AUTHOR]

The Fourier transform is shown to play an important role in solving many applied problems of system analysis. Its properties, which affect the efficiency of using the optimal decision theory in the problems, are analyzed. The necessary condition for the convergence of the Fourier transform is established, which provides a powerful tool for its use in implementing practical problems. [ABSTRACT FROM AUTHOR]

In this experimental study, we are presenting the ability of laser-induced plasmas with successive pulsation to identify combustion instabilities (CI) of a premixed lab-scale combustor. An acoustic disturbance equivalent to a shockwave perturbation is generated in the main air supply line of a swirled injector prior to the fuel addition by focusing nanosecond laser pulses of 1.6 W average power at 10 Hz. The shockwaves are attenuated to be strong pressure waves when reaching the combustor and impact the pressure field for short periods. After plasma breakdowns, the system returns back to its original state after 4 ms once the added acoustic energy has been fully dissipated. Given a set geometry, it is observed that the laser-induced breakdown amplifies the characteristic frequency peaks of the combustor system when actuated in cold flow. Furthermore, when applied to reacting flows, the pulsating acoustic perturbations impact the pressure fluctuation in the combustor, e.g., reducing the amplitude of the primary characteristic frequency peak at certain conditions. The identification of the main instability modes thanks to the plasma shockwave provides proof of the potential use of this novel diagnosis strategy in various and complex combustion systems. [ABSTRACT FROM AUTHOR]

A thermoelastic model for a solid cylinder consisting of two different isotropic thermoelastic homogeneous materials is created. Boundary conditions for the heat flow and stress tensors were discussed. A dual-phase lag model was applied to investigate its thermophysical properties. For their numerical evaluation, a two-layered structure with an interfacial thermal contact resistance and an integral elastic wave resistance, as well as some special cases, were considered. This study will be useful for theoretical modeling the thermoelasticity at the nanoscale and for designing nano and multilayered devices, plates, and surface coatings. [ABSTRACT FROM AUTHOR]

Gaussian processes are popular in spatial statistics, data mining and machine learning because of their versatility in quantifying spatial variability and in propagating uncertainty. Although there has been a prolific research activity about Gaussian processes over Euclidean domains, only recently this research has extended to non-Euclidean manifolds. This paper digs into vector-valued Gaussian processes defined over the product of a hypersphere and a Euclidean space of arbitrary dimension, which are of interest in various disciplines of the natural sciences and engineering. Under mild regularity conditions, we establish a surprising one-to-one correspondence between matrix-valued kernels associated with vector Gaussian processes over the product space, and what we term partial ultraspherical and Fourier transforms that are taken over either the sphere or the Euclidean subspace. The properties of our approach are illustrated in terms of new parametric classes of matrix-valued kernels for product spaces of a hypersphere crossed with a Euclidean space. We also provide two algorithms that allow for fast simulation of approximately Gaussian (in the sense of the central limit theorem) processes in such product spaces. [ABSTRACT FROM AUTHOR]

Using an asymptotic method, this article deals with flexural-gravity wave scattering with undulating bottom topography, including the effect of uniform currents. The interest in this problem lies in developing second-order solutions using the Fourier transform, which minimises the error gap between first and second-order solutions. The present method allows the physical processes involved in the sea-bed topography, uniform current, plate-covered surface, and wave interaction to be studied. Specifically, we observe Bragg resonance between the flexural-gravity waves and the bottom ripples, which are associated with the reflection of incident wave energy. We examine the effects of wave current and emphasise how crucial the asymptotic expansion method is to the emergence of the current response. We demonstrate that bottom topography dominates the effects of Bragg resonance for depth Froude numbers valued at 0.8 or less. Further, most reflected wave components have their frequencies shifted by the current, and wave action conservation causes reflected wave energy to be enhanced for following currents. Using the Joint North Sea Wave Observation Project spectrum and the discrete Fourier transform, the theory derived in the frequency domain is shown in the time domain to analyse wave propagation through the whole system. • A mathematical model to study flexural-gravity wave scattering with undulating bottom in the presence of uniform current. • The problem is studied using an asymptotic approach under linear water wave theory. • Develop the second-order solutions using the Fourier transform technique. • Identify the existence of Bragg resonance between the flexural-gravity waves and the bottom ripples. • The frequency domain analysis is illustrated in the time domain using JONSWAP. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Railway Science & Engineering is the property of Journal of Railway Science & Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The authors show that the Fourier transform plays an important role in many applied problems of system analysis. Its properties are analyzed, which directly affect the efficiency of using the optimal decision theory in the problems. The necessary condition for the convergence of the Fourier transform is established, which provides a powerful tool for its use in the implementation of practical problems. [ABSTRACT FROM AUTHOR]

Bent functions have a number of practical applications in cryptography, coding theory, and other fields. Fourier transform is a key tool to study bent functions on finite abelian groups. Using Fourier transforms, in this paper, we first present two necessary and sufficient conditions on the existence of bent functions via faithful actions of finite abelian groups and then show two constructions of sequences with ideal auto-correlation (SIACs). In addition, we construct a periodic complementary sequence set (PCSS) by rearranging a periodic multiple shift sequence (PMSS) corresponding to a bent function on a finite abelian group. Some concrete constructions of SIACs and PCSSs are provided to illustrate the efficiency of our methods. [ABSTRACT FROM AUTHOR]

Let n , m ≥ 1 and α > 0 . We denote by F α , m the m-analytic Bargmann–Segal–Fock space, i.e., the Hilbert space of all m-analytic functions defined on C n and square integrables with respect to the Gaussian weight exp (- α | z | 2) . We study the von Neumann algebra A of bounded linear operators acting in F α , m and commuting with all "horizontal" Weyl translations, i.e., Weyl unitary operators associated to the elements of R n . The reproducing kernel of F 1 , m was computed by Youssfi [Polyanalytic reproducing kernels in C n , Complex Anal. Synerg., 2021, 7, 28]. Multiplying the elements of F α , m by an appropriate weight, we transform this space into another reproducing kernel Hilbert space whose kernel K is invariant under horizontal translations. Using the well-known Fourier connection between Laguerre and Hermite functions, we compute the Fourier transform of K in the "horizontal direction" and decompose it into the sum of d products of Hermite functions, with d = n + m - 1 n . Finally, applying the scheme proposed by Herrera-Yañez, Maximenko, Ramos-Vazquez [Translation-invariant operators in reproducing kernel Hilbert spaces, Integr. Equ. Oper. Theory, 2022, 94, 31], we show that F α , m is isometrically isomorphic to the space of vector-functions L 2 (R n) d , and A is isometrically isomorphic to the algebra of matrix-functions L ∞ (R n) d × d . [ABSTRACT FROM AUTHOR]

Abstract Amperometry is a commonly used electrochemical method for studying the process of exocytosis in real-time. Given the high precision of recording that amperometry procedures offer, the volume of data generated can span over several hundreds of megabytes to a few gigabytes and therefore necessitates systematic and reproducible methods for analysis. Though the spike characteristics of amperometry traces in the time domain hold information about the dynamics of exocytosis, these biochemical signals are, more often than not, characterized by time-varying signal properties. Such signals with time-variant properties may occur at different frequencies and therefore analyzing them in the frequency domain may provide statistical validation for observations already established in the time domain. This necessitates the use of time-variant, frequency-selective signal processing methods as well, which can adeptly quantify the dominant or mean frequencies in the signal. The Fast Fourier Transform (FFT) is a well-established computational tool that is commonly used to find the frequency components of a signal buried in noise. In this work, we outline a method for spike-based frequency analysis of amperometry traces using FFT that also provides statistical validation of observations on spike characteristics in the time domain. We demonstrate the method by utilizing simulated signals and by subsequently testing it on diverse amperometry datasets generated from different experiments with various chemical stimulations. To our knowledge, this is the first fully automated open-source tool available dedicated to the analysis of spikes extracted from amperometry signals in the frequency domain.

Abstract In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPFT). Further, we derive the Parseval formula and the Riemann–Lebesgue lemma using this transform. Furthermore, we formulate two important inequalities (sharp Pitt’s and sharp Hausdorff–Young’s inequalities) and three main uncertainty principles (logarithmic, Donoho–Stark’s, and Heisenberg’s uncertainty principles) for the OQPFT. To complete our investigation, we construct three elementary examples of signal theory with graphical interpretations to illustrate the use of OQPFT and discuss their particular cases.

Abstract Reconstructing signals which are embedding spatial patterns such as Electrical resistivity tomography, is a process that should require to reconstruct first the spatial correlation of the damaged signals. This paper proposes an approach that implements an Unstationary Kriging (UNK) to reconstruct the experimental variogram of a damaged synthetic pseudo section within a set of pseudo sections coming from the same survey. We used and compared 02 other simple methods which are Linear Regression (LR) and Ordinary Kriging (OK), to test the hypothesis we formulate to link the experimental variograms coming from the same ERT survey. We implemented the UNK using Discrete Fourier Transforms (DFT) for trend modeling. After an implementation of the hybrid process (UNK) on 02 sets of data which are synthetics, we observed that the LR and the UNK methods present an interest. They both reconstruct signals with a +90% rate of accuracy, but when there is no structure or spatial correlation within the data, the LR is unstable. DFT was also tested alone for reconstruction but was mainly used in this study to help in computing the trends for each set of variographic signals. In the end, we conclude on an evidence that is: the proposed hybrid process is a promising way to reconstruct variographic signals, since we can improve it after more time invested to dig deep into the modeling of each of his components.

Let { R n } n = 1 ∞ ⊂ M 2 (Z) be a sequence of expanding matrices and let { B n } n = 1 ∞ ⊂ Z 2 be a sequence of p-element digit sets with R n = r n s n 0 r n a n d Z (δ ^ B n) = ⋃ j = 1 p - 1 j p ω n ρ n + Z 2 , where { ρ n , ω n } ⊂ { 1 , ⋯ , p - 1 } , gcd (ρ n , ω n) = 1 and p ≥ 3 is a prime number. The associated Moran measure is generated by the infinite convolution μ { R n , B n } : = δ R 1 - 1 B 1 ∗ δ R 1 - 1 R 2 - 1 B 2 ∗ ⋯. In the paper, we prove that μ { R n , B n } is a spectral measure if and only if r n , s n ∈ p Z under certain conditions on R n and B n . [ABSTRACT FROM AUTHOR]

Fourier transform is one of the oldest and well-known technique in the field of mathematics and engineering mathematical works. As the concept of uncertainty has been introduced in the mathematics, most of the works gravitate towards the use Neutrosophic set. So, it is also important to study the Fourier transform in the sense of Neutrosophic set. In this paper we have applied the Neutrosophic Fourier transform in solving heat equation, and integral equation. Where detailed examples are given to clarify each case. [ABSTRACT FROM AUTHOR]

Photothermal radiometry has recently been investigated for use in the multidimensional thermal characterization of anisotropic samples. In application, there are two principal thermal models available for such characterization: a Cartesian model for the heat equation, which requires the application of three Fourier transforms to arrive at a solution (dubbed the Fourier technique), and a cylindrical model for the heat equation, which requires the application of a Hankel transform and a single Fourier transform (dubbed the Hankel technique). The Fourier technique allows for three‐dimensional characterization, while the Hankel technique is expected to greatly reduce the computational time required. As these models can be very computationally expensive, the potential to reduce this cost is of great interest. In this work, these multidimensional models are presented after which they are compared for accuracy, computational time, and assumption limitations. It was found that both the Fourier and Hankel techniques could accurately arrive at desired thermal properties, but that the Hankel Technique reduced the computational time by between 100× and 250× depending upon mesh spacings. Accuracy limitations were found as the eccentricity of the heating laser was increased with a less than 13% error being induced from a beam with a 3–1 axis ratio. The Hankel technique shows ideal application in computationally expensive models which employ a relatively circular beam shape. [ABSTRACT FROM AUTHOR]

Extension of some Integral Transform by the Method of Multiple Integrals by Lebesgue measurable and Lebesgue integrable.

Diamond is considered a promising detector in radiobiological studies. However, the difference in densities between diamond and tissue imply that their energy deposition spectra are not identical, even for diamond and tissues of the same size. The energy deposition spectrum in diamond was converted to match a tissue sample of the same size. A method based on a mathematical model of energy deposition distribution and the Fourier transform was proposed. The results indicate that the spectra converted from diamond to tissue align closely with those of the tissue. Nevertheless, the applicability of this method is constrained by the mathematical model of energy deposition distribution. Thus, developing a mathematical model that describes the energy deposition spectrum under various conditions can enhance the applicability of this conversion method.

Modern electricity networks are facing significant challenges in terms of power quality due to the increasing integration of power electronics. Even though low order harmonic control has largely been achieved, the emergence of supraharmonics is becoming a new cause for concern. This topic has gained interest in the past decade since power quality issues have become important due to the proliferation of highly sensitive electrical and electronic equipment. This special case of harmonics is mainly due to the power electronic converters utilized in industrial as well as residential applications, including electromobility, motor drive systems, and photovoltaic installations. While the adverse effects of supraharmonics have been pointed out in numerous studies and intensive research is underway on the crucial subject of supraharmonic measurements, the parameters affecting their levels have not received adequate attention. We attempted to shed more light on this important issue in the specific case of a small grid-connected PV system. In particular, the supraharmonic emission levels of the system were investigated through experimental measurements, and useful conclusions on the impact of specific environmental factors were derived.

The rapid detection of grid voltage faults is crucial to achieve grid voltage fault ride-through. However, conventional grid voltage detection methods, including Fourier transform, dq axis transform, wavelet transform, and voltage peak methods, generally yield varying degrees of distortions in the detection results of short-time disturbances in grid voltage. To address this, this paper proposes an approach for quickly detecting short-time disturbances in grid voltage. Leveraging the distinctive high harmonic content present in grids, the suggested strategy involves a transformation of grid voltage calculated using the Fourier transform method, known for its robust anti-interference performance, into high-frequency signals through coordinate conversion. The integration of the rolling sliding window method addresses the extended calculation time issue associated with the Fourier transform, enabling the detection of grid voltage disturbance signals within a single high-frequency signal cycle using this method. The simulation experiment results demonstrated the wide applicability of the proposed method compared with other methods. It is not only effective for short-time grid voltage disturbances, but also suitable for long-time grid voltage disturbances. Regardless of whether high-frequency harmonics are present or absent in the grid voltage, this method allows for the rapid detection of grid voltage disturbances (within about 2 ms). Moreover, its accuracy in detecting grid voltage amplitudes aligns with requirements in engineering applications.

Compass errors can be regarded as a deviation of the vessel from the expected heading. Gyrocompass errors are randomly oscillating in nature, and it is difficult to describe the behaviour of a gyrocompass sufficiently accurately using mathematical relationships. Fibre-optic gyroscopes have no mechanical components, so the variability in their indications has a different nature; the computational processes and inertial sensors used cause certain types of errors. Thus far, compass studies have focused on presenting absolute errors in the time domain. However, compasses exhibit specific characteristics in the frequency domain that affect the amplitude of their deviation. This leads to the issue of identifying the oscillatory spectrum of errors in the operation of such compasses, and how this spectrum is impacted by the dynamic movement of the vessel. We attempt to assess this phenomenon by means of measurements taken on board the training and research vessel M/S NAWIGATOR XXI. The application of a fast Fourier transform allows for calculation of the absolute compass errors in the frequency domain, meaning that the frequency of occurrence of errors can be observed as noise against the background of the useful signal. Our results confirm the value of applying a finite impulse response filter, which is used to filter out noise in the form of absolute compass errors from the useful signal background. The convolution function proposed here considerably extends the possibilities for analysing the signal spectrum in the frequency domain when testing for the accuracy of compass device indications, and enables the elimination of random errors with a low frequency of occurrence..

In the context of the coordinated development of new energy sources and distribution networks, a hybrid energy storage twolayer optimal configuration model was proposed for the optimal configuration of distributed energy storage connected to distribution networks. The upper layer optimization determined the energy storage access location and capacity, and divided the power by Fourier transform, using super capacitor and battery to bear the power of different frequency parts respectively. The lower layer optimization was designed with the objective function of maximizing the benefits from low storage and high discharge operations. It was optimized using a combination of the particle swarm algorithm and the Pareto file. The model's rationality and effectiveness were confirmed through simulation experiments conducted on the IEEE33 nodes network. The results show that the model can achieve multi-objective comprehensive optimization, including reducing network losses, optimizing power index and reducing investment costs of energy storage equipment, which provides an effective solution for the optimal configuration of distributed energy storage connected to distribution networks. [ABSTRACT FROM AUTHOR]

The teacher–student framework has been employed in unsupervised domain adaptation, which transfers knowledge learned from a labeled source domain to an unlabeled target domain. However, this framework suffers from two serious challenges: the domain gap, causing performance degradation, and noisy teacher pseudo-labels, which tend to mislead students. In this paper, we propose a Consistent and Contrastive Teacher with Fourier Transform (CCTF) method to address these challenges for high-performance cross-domain object detection. To mitigate the negative impact of domain shifts, we use the Fourier transform to exchange the low-frequency components of the source and target domain images, replacing the source domain inputs with the transformed image, thereby reducing domain gaps. In addition, we encourage the localization and classification branches of the teacher to make consistent predictions to minimize the noise in the generated pseudo-labels. Finally, contrastive learning is employed to resist the impact of residual noise in pseudo-labels. After extensive experiments, we show that our method achieves the best performance. For example, our model outperforms previous methods by 3.0% on FoggyCityscapes. [ABSTRACT FROM AUTHOR]

Ocean observation has advanced rapidly in recent decades due to its crucial role in resource exploration and scientific research, with the Doppler factor being widely utilized. However, the precision of Doppler estimation is frequently constrained by frequency resolution. Traditional frequency estimation methods using single-tone signals face considerable challenges with low accuracy and poor robustness. In response, this paper introduces a novel Doppler-sensitive Acoustic Frequency Comb (AFC) for estimating the Doppler factor, enabling multiple measurements with a single transmission and reception of the signal. The proposed Combined Uneven Uncertainty (CUU) method based on AFC achieves a bias of less than 1.1x10-5, significantly surpassing the optimal result of 3.2x10-5 attained by other frequency estimation methods in the absence of noise. Compared to traditional single-tonemethods, the AFC approach improves spectral leakage performance and enhances estimation accuracy without increasing computational complexity. Experimental results demonstrate that the CUU method realizes a difference performance of less than 3.4x10-6, notably lower than that of 3.2x10-5 induced by coherent spectral leakage in fast Fourier Transform (FFT). [ABSTRACT FROM AUTHOR]