Search

The dynamic responses of an unsaturated ground with or without an embankment are analysed using 2.5D finite element method (FEM) to investigate the effects of the soil saturation and the embankment. The Galerkin method is utilised to establish the weak form governing equations for an unsaturated poroviscoelastic medium in the framework of 2.5D FEM. To reduce the reflected waves from the truncated boundaries of the 2.5D FE model, the formulations of the perfectly match layer (PML) technique are coupled with the governing equations of the unsaturated medium. The unsaturated ground vibrations with an embankment under moving loads are analysed by the proposed 2.5D FE approach, to investigate the influences of an embankment on unsaturated ground vibrations. The results of this research found that the PML technique can effectively reduce the reflected waves in the 2.5D FE model of unsaturated grounds. The increased soil saturation would increase the ground vibration amplitude, as well as the pore water pressure. Constructing embankment on the unsaturated ground could reduce the vibrations amplitude under the moving load, however increase the ground vibrations at the foot of the embankment. [ABSTRACT FROM AUTHOR]

In this paper, we develop a continual analog of decomposition over orthogonal bases in spaces generated by equidistant shifts of a single function. By doing so, we obtain an explicit expression for the best approximation by spaces of shifts in L 2 (R) . The result is formulated in terms of classical Fourier transform and tends to have various applications in approximation by spaces of shifts and, in particular, in spline approximation. [ABSTRACT FROM AUTHOR]

We present a very detailed proof of the growth of the Lebesgue constants of hyperbolic Bochner-Riesz means for double Fourier series. [ABSTRACT FROM AUTHOR]

We address here a viscoelastic Timoshenko model on the (one-dimensional) real line with memory damping coupled on a shear force. Our main results concern a complete decay structure of the system under the so-called equal wave speeds assumption, as well as without this condition. This is the first result of this type for partially dissipative beam systems with memory-type damping on the shear force. Our method is based on expanded structural conditions such as the so-called SK condition. In addition, we give a characterization of the dissipative structure of the system by using a spectral analysis method, which confirms that our decay structure is optimal. [ABSTRACT FROM AUTHOR]

This article is the second within a three-part series on Fourier ptychography, which is a computational microscopy technique for high-resolution, large field-of-view imaging. While the first article laid out the basics of Fourier ptychography, this second part sheds light on its algorithmic ingredients. We present a non-technical discussion of phase retrieval, which allows for the synthesis of high-resolution images from a sequence of low-resolution raw data. Fourier ptychographic phase retrieval can be carried out on standard, widefield microscopy platforms with the simple addition of a low-cost LED array, thus offering a convenient alternative to other phase-sensitive techniques that require more elaborate hardware such as differential interference contrast and digital holography. [ABSTRACT FROM AUTHOR]

Northern China is vigorously promoting cogeneration and clean heating technologies. The accurate prediction of building energy consumption is the basis for heating regulation. In this paper, the daily, weekly, and annual periods of building energy consumption are determined by Fourier transformation. Accordingly, a period-based neural network (PBNN) is proposed to predict building energy consumption. The main innovation of PBNN is the introduction of a new data structure, which is a time-discontinuous sliding window. The sliding window consists of the past 24 h, 24 h for the same period last week, and 24 h for the same period the previous year. When predicting the building energy consumption for the next 1 h, 12 h, and 24 h, the prediction errors of the PBNN are 2.30%, 3.47%, and 3.66% lower than those of the traditional sliding window PBNN (TSW-PBNN), respectively. The training time of PBNN is approximately half that of TSW-PBNN. The time-discontinuous sliding window reduces the energy consumption prediction error and neural network model training time. [ABSTRACT FROM AUTHOR]

The article studies the spectra of daytime, nighttime and cyrtopic human visions in the frequency domain. To understand the structure of the human vision organ, mathematical analysis has been used, where the human eye visibility spectra are taken as a dynamic link. To obtain the impulse response of the link, the inverse Fourier transform is used. It has been found that the wideband index of these spectra in the frequency domain exhibits the properties of ultra-wideband signals. It has been revealed that in the time domain, the gain of the link is greater than unity, and the amplitude-frequency characteristic has two sections, in one of which the gain of the link is greater than unity. In accordance with the Bouguer–Lambert law, these coefficients can be greater than unity when the absorption coefficient takes a negative value. It has been found that the cyrtopic vision has the maximum wavelength bandwidth and the maximum gain, the daytime vision has the minimum values of these parameters, and the night vision has the intermediate values of these parameters. [ABSTRACT FROM AUTHOR]

Today, the development of technology enables the rapid development of artificial intelligence studies. One of the most popular topics among the developing artificial intelligence studies is the creation and use of realistic false faces in virtual environments. In the study, a series of studies were conducted to distinguish between false and real faces based on images containing false and real faces. In the study, two different classification models (VGG, Xception) and three different methods (normal image, Fourier transform image, discrete cosine transform image) were applied to images and separate classification processes were performed. The obtained results were compared and provided to the researchers as a resource. [ABSTRACT FROM AUTHOR]

The high-power hydraulic rock drill is the key to the development of modern hydraulic drill rig. With the increase of power and frequency of new type rock drill, the rebound of drill tool will be obvious during drilling, which will seriously affect the structural safety and operation efficiency. For this phenomenon, it is necessary to research the characteristics of double damping system to absorb the rebound energy of drill tool. A new model of incident stress wave is revised on the basis of rectangular wave. By combining the reflected stress wave with the model of damping system, the pressure fluctuation of damping system is analysed. Based on the theory of stress wave transmission, the rebound model of drill tool is established, and the transmission law of incident wave and reflection wave in drilling process is analysed. The stress wave experiment was designed and the incident wave shape was obtained by testing. Based on the experimental results, the incident wave in the rebound model is corrected by Fourier transform principle. The accumulator model and the double damping internal structure model are established. The two parameters that can independently change the energy absorption effect of the double damping system are summarised. [ABSTRACT FROM AUTHOR]

For any dilation matrix with integral entries A ∈ R d × d , d ≥ 1 , we construct two families of Parseval wavelet frames in L 2 (R d). Both families have compact support and any desired number of vanishing moments. The first family has | det ⁡ A | generators. The second family has any desired degree of regularity. For the members of this family, the number of generators depends on the dilation matrix A and the dimension d , but never exceeds | det ⁡ A | + d. Our construction involves trigonometric polynomials developed by Heller to obtain refinable functions, the Oblique Extension Principle, and a slight generalization of a theorem of Lai and Stöckler. [ABSTRACT FROM AUTHOR]

This article extends the pioneering Johansen cointegration test to allow for structural breaks in a cointegration system. Instead of using usual dummy variables, we utilize a Fourier function to control for an unknown number of multiple breaks in the cointegration system. The underlying presumption of the procedure is that structural breaks often can be captured by using a small number of low‐frequency components from a Fourier approximation. The number of parameters to estimate is reduced significantly, which can lead to a good performance of the tests. Monte Carlo simulations show that the new tests display good size and power properties, except for the cases of sharp breaks. Then, we consider a strategy using a union of rejections. The union test combines our suggested test with a test of the cointegration rank in VAR models in the presence of a possible break in trend at an unknown point. We further consider a procedure that selects a better model using a Schwarz‐type criterion among Johansen, trend break‐point, and Fourier models. The resulting test shows fairly correct sizes in all cases, including sharp breaks, smooth breaks, and no breaks. The power properties are also reasonable in almost all cases. [ABSTRACT FROM AUTHOR]

Background: Biological data suffers from noise that is inherent in the measurements. This is particularly true for time-series gene expression measurements. Nevertheless, in order to to explore cellular dynamics, scientists employ such noisy measurements in predictive and clustering tools. However, noisy data can not only obscure the genes temporal patterns, but applying predictive and clustering tools on noisy data may yield inconsistent, and potentially incorrect, results. Results: To reduce the noise of short-term (< 48 h) time-series expression data, we relied on the three basic temporal patterns of gene expression: waves, impulses and sustained responses. We constrained the estimation of the true signals to these patterns by estimating the parameters of first and second-order Fourier functions and using the nonlinear least-squares trust-region optimization technique. Our approach lowered the noise in at least 85% of synthetic time-series expression data, significantly more than the spline method ( p < 10 - 6 ). When the data contained a higher signal-to-noise ratio, our method allowed downstream network component analyses to calculate consistent and accurate predictions, particularly when the noise variance was high. Conversely, these tools led to erroneous results from untreated noisy data. Our results suggest that at least 5–7 time points are required to efficiently de-noise logarithmic scaled time-series expression data. Investing in sampling additional time points provides little benefit to clustering and prediction accuracy. Conclusions: Our constrained Fourier de-noising method helps to cluster noisy gene expression and interpret dynamic gene networks more accurately. The benefit of noise reduction is large and can constitute the difference between a successful application and a failing one. [ABSTRACT FROM AUTHOR]

Good marine practice and proper operation of navigation, radio navigation, and radio communication systems are nowadays of key importance for marine navigation safety. This applies to merchant vessels and navy ships and effectively monitoring unmanned vehicles along a set route. Technological progress has contributed to developing equipment for ships and unmanned vehicles, which are fitted out with devices of the automatic identification system (AIS). One of the issues in AIS operation is limited-service availability, which manifests itself in the presence of incomplete data for the navigation parameters sent by radio, compressed in dynamic data messages. This results in the unusability of the system information for ships equipped with an AIS transponder. This paper aims to develop an AIS service availability model based on the mean time of incomplete navigation parameter occurrence in AIS data messages and to present the test results in the time and frequency domain using a mathematical method—Fast Fourier Transform. The study results refer to five basic navigation parameters and are indicative of a high service availability index—over 0.99 for three out of the five navigation parameters tested. Data recorded by a ship's system receiver were the key source of practical knowledge concerning the limitations of AIS service availability. The experiment revealed interruptions in regular data inflow from navigation devices. In effect, a description was provided of a functional relationship based on a spectral analysis of the frequencies of the times occurring between service repair (time to repair—TTR), and the use of the model to analyze other variables was proposed. [ABSTRACT FROM AUTHOR]

In this paper, we establish the convolution and product theorems for the quadratic-phase Fourier transform (QPFT) and also deduce the convolution theorem associated with generalized translation. Moreover, the Shannon-type reconstruction formula for band-limited signals in the QPFT domain is formulated. [ABSTRACT FROM AUTHOR]

Renewable energy sources will be more vigorously deployed under the global trend of carbon emission reduction. The connection of numerous renewable energy sources poses an increasingly critical challenge to power quality (PQ) issues in power systems. Time-frequency analysis (TFA) is a foundational technique for real-time monitoring and disturbance detection for power signals. This paper develops an improved S-transform (IST) to accurately detect the disturbances such as oscillatory transient, time-varying harmonics and interharmonics, flicker, swell, sag, interrupt, phase jump, and frequency variation. The proposed IST features the exploration of a designed Gaussian window as the kernel function, whose shape and frequency spectrum can be controlled using a standard deviation based detection frequency parameter. This ensures that the detection requirements at different detection frequencies can be easily met. The IST can be realized by fast Fourier transform (FFT) and its inverse, which ensures that it can be implemented quickly. The IST can accurately detect the amplitude and phase information of fundamental signal, which is beneficial to determine the start and end time, and the intensity of disturbance. With the increase of detection frequency, IST also has excellent energy concentration performance. Simulation and experimental results validated the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Let 풫 and P ′ be 3-dimensional convex polytopes in R 3 and S ⊆ R 3 be a non-empty intersection of an open set with a sphere. As a consequence of a somewhat more general result it is proved that 풫 and P ′ coincide up to translation and/or reflection in a point if | ∫ P e - i ⁢ s ⋅ x ⁢ dx | = | ∫ P ′ e - i ⁢ s ⋅ x ⁢ dx | for all s ∈ S . This can be applied to the field of crystallography regarding the question whether a nanoparticle modelled as a convex polytope is uniquely determined by the intensities of its X-ray diffraction pattern on the Ewald sphere. [ABSTRACT FROM AUTHOR]

This paper deals with the concept of the automated calibration design for inspection systems using laser sensors. The conceptual solution is based on using a laser sensor and its ability to scan 3D surfaces of inspected objects in order to create a representative point cloud. Problems of scanning are briefly discussed. The automated calibration procedure for solving problems of errors due to non-precise adjustment of the mechanical arrangement, possible tolerances in assembly, and their following elimination is proposed. The main goal is to develop a system able to measure and quantify the quality of produced objects in the environment of Industry 4.0. Laboratory measurements on the experimental stand, including the principal software solution for automated calibration of laser sensors suitable for gear wheel inspection systems are presented. There is described design of compensation eccentricity by Fourier transform and sinusoidal fitting to identify and suppress the first harmonic component in the data with high precision measuring. [ABSTRACT FROM AUTHOR]

A new software package, autoPX, for processing X‐ray diffraction data from biomacromolecular crystals is reported. This processing software package is designed on the basis of novel methods such as the location of diffraction spots by an improved Canny operator, indexing by a modified Fourier transform, a novel definition of mosaicity that expresses the dispersion state of reciprocal diffraction spots, and the correction of predicted diffraction spot coordinates by homography transform. New programming of some traditional algorithms necessary for integration and scaling is also included. Several examples of crystal structure determination using data from the SSRF beamlines reduced using autoPX, HKL‐2000, DIALS and XDS are also demonstrated, and indicate that autoPX is capable of processing diffraction data from biomacromolecular crystals and providing adequate solutions to problems encountered at the SSRF beamlines. [ABSTRACT FROM AUTHOR]

Let X be a ball quasi-Banach function space on R n and H X (R n) the associated Hardy space. In this article, under the assumptions that the Hardy–Littlewood maximal operator satisfies some Fefferman–Stein vector-valued inequality on X and is bounded on the associated space of X as well as under a lower bound assumption on the X-quasi-norm of the characteristic function of balls, the authors show that the Fourier transform of f ∈ H X (R n) coincides with a continuous function g on R n in the sense of tempered distributions and obtain a pointwise inequality about g and the Hardy space norm of f. Applying this, the authors further conclude a higher order convergence of the continuous function g at the origin and then give a variant of the Hardy–Littlewood inequality in the setting of Hardy spaces associated with X. All these results have a wide range of applications. Particularly, the authors apply these results, respectively, to mixed-norm Lebesgue spaces, variable Lebesgue spaces, and Orlicz spaces. Even in these special cases, the obtained results for variable Hardy spaces and Orlicz–Hardy spaces are totally new. [ABSTRACT FROM AUTHOR]

This article presents selected physical diagnostic methods used in otorhinolaryngology and results of their application. In addition to the applications of methods using the capabilities of selective sensors, selected methods of hybrid diagnostics were also presented - for assessment of parameters of respiratory processes, with polysomnography as an example of using both typical diagnostic methods dedicated to otolaryngology, as well as standard EEG and ECG methods. It has been shown that in some special cases of respiratory disorders, measurements of the air flow in the respiratory tract can be supplemented with pressure measurements in selected positions within the airways. The presented optical methods and diagnostic systems are very often used in the diagnosis of diseases not specific for otolaryngology occurring in the area of the head and neck. The presented material is the second part of the study discussing both standard and widely used diagnostic methods. All presented methods are dedicated to otolaryngology. This text is a continuation of the material published in No 4 of 2021 [1]. [ABSTRACT FROM AUTHOR]

An effective corrosion monitoring technique is sought after by the engineers for assessing the steel bar corrosion at the early stage for the maintenance and repair works, especially in the corrosive environments, such as coastal and marine. In this work, tilted fiber Bragg grating (TFBG) with the optical sensor is employed in corrosion monitoring of a reinforced concrete structure. Taking advantage of the high sensitivity of TFBG cladding resonance wavelengths to the change in the surrounding medium, the sensor is mounted on the steel bar that is embedded in a concreted block during an accelerated corrosion process. The acquired transmission spectrum of the TFBG during the procedure is digitally processed using Fourier Transform to produce an index that is sensitive to the generated corrosion product surrounding the TFBG sensor. This eases the analysis of the sophisticated TFBG transmission spectra. The generated index can be used as an indicator (indicator J) for the corrosion process of the embedded steel bar in the concrete structure. This indicator J can act as an indicator to describe the corrosion activity and corrosion level at a specific point of the steel bar in concrete structures. [ABSTRACT FROM AUTHOR]

The growth process of soybean plants needs a lot of water. The rapid detection of canopy wilting of soybean under drought stress is of great significance for soybean variety breeding, cultivation regulation and fine management. Aiming at the problems of cumbersome and time-consuming when the traditional chemical technology was used to determine soybean wilting index, a calculation method of wilting index for soybean canopy was proposed in this study based on multispectral images' Fourier transform. Suinong 26, a northeast soybean variety, was taken as the object. First, four kinds of soybean multispectral images of green, red, red-edge and near-infrared channels were acquired by a Sequoia multispectral camera. Second, based on the multispectral reflection image preprocessed by median filter and mean filter, the target area of a multispectral image of the soybean canopy was extracted by the iterative threshold method and affine transformation algorithm, and the effective segmentation rate was 97.02%. In addition, Fourier transform was used to analyze the spectrum characteristics of the soybean canopy's multispectral image. When the spectrum radius of each channel was 50, the energy reached more than 98% and was concentrated in the low-frequency region of the spectrum center. Finally, according to the difference between the low-frequency DC component and the proportion of total energy in the spectral radius of the multispectral images under normal and drought treatment, a calculation model of the soybean wilting index was constructed based on the energy spectrum of Fourier transform. The results showed that the difference of the wilting index between normal and drought treatment for the four channels (green, near-infrared, red and red-edge) was 2.38, 3.11, 3.56 and 4.11, respectively. The effectiveness of the wilting index was verified and analyzed by using the average leaf inclination angle. The determination coefficient R2 of the four channels between the calculated wilting index and the average leaf inclination angle was more than 0.85. This calculation method can provide a quantitative basis and technical support for the scientific regulation of ecological and morphological phenotypic traits of soybean plants under drought stress. [ABSTRACT FROM AUTHOR]

The quaternion linear canonical transform is an important tool in applied mathematics and it is closely related to the quaternion Fourier transform. In this work, using a symmetric form of the two-sided quaternion Fourier transform (QFT), we first derive a variation on the Heisenberg-type uncertainty principle related to this transformation. We then consider the general two-sided quaternion linear canonical transform. It may be considered as an extension of the two-sided quaternion linear canonical transform. Based on an orthogonal plane split, we develop the convolution theorem that associated with the general two-sided quaternion linear canonical transform and then derive its correlation theorem. We finally discuss how to apply general two-sided quaternion linear canonical transform to study the generalized swept-frequency filters. [ABSTRACT FROM AUTHOR]

Leguminous and cereals are an important source of proteins actually having a large presence in the food industry; although, in recent years, there has been an increment in the use of pseudo cereals like quinoa. These types of proteins had shown physical properties could be taken as an advantage in developing new products. Hydrolysis is a process that enhance bio-active and functional attributes and that is why present research worked monitoring the hydrolysis process on proteins using infrared mid-range spectroscopy, to determine such structural changes. Enzymatic hydrolysis with endo or exo-protease, was made on three isolate proteins using Alcalasa® 2,4 L and Flavorzyme® from Sigma Laboratories. Correlation between enzyme/substrate was 5 %. Degree of Hydrolysis (DH) of 46 and 38,4 % were obtained for quinoa and rice isolate, respectively. Both, quinoa and soy hydrolysis monitoring took 60minutes with Alcalasa® 2,5 L, and 120 minutes con Flavorzima®. There were no significant differences of hydrolysis degree at 80 minutes after procedure. As a comparative view protein isolates and their hydrolysis were studied under 4000 cm-1 to 600 cm-1 infrared range to obtain information about the protein structure. Spectre deconvolution technique was applied through Fourier transform. Results showed significant differences on the secondary protein structure when compared to each configuration area. More relevant changes were observed on structural formation of β-sheet and β-turns structures. For an appropriate control of hydrolysis process will have repercussions over a steady protein, that might be used for developing new products. [ABSTRACT FROM AUTHOR]

Seismic data are often irregularly or insufficiently sampled along the spatial direction due to malfunctioning of receivers and limited survey budgets. Recently, machine learning techniques have begun to be used to effectively reconstruct missing traces and obtain densely sampled seismic gathers. One of the most widely used machine learning techniques for seismic trace interpolation is UNet with the mean-squared error (MSE). However, seismic trace interpolation with the UNet architecture suffers from aliasing, and the MSE used as a loss function causes an oversmoothing problem. To mitigate those problems in seismic trace interpolation, we propose a new strategy of using coarse-refine UNet (CFunet) and the Fourier loss. CFunet consists of two UNets and an upsampling process between them. The upsampling process is done by padding zeroes in the Fourier domain. We design the new loss function by combining the MSE and the Fourier loss. Unlike the MSE, the Fourier loss is not a pixelwise loss but plays a role in capturing relations between pixels. Synthetic and field data experiments show that the proposed method reduces aliased features and precisely reconstructs missing traces while accelerating the convergence of the network. By applying our strategy to realistic cases, we show that our strategy can be applied to obtain more densely sampled data from acquired data. [ABSTRACT FROM AUTHOR]

Conveyor belts are used in many industries, from food to mining and power generation. These conveyors consist of many subsystems, and these systems, like any mechanical system, are prone to failure. The failure of these systems can cause the conveyor to be stopped and repaired, and during this downtime, production is lost. Thermal cameras are the most using method to diagnose the faults in bearing that produce the heating than the healthy bearing. Acoustic gear and accelerometer are used to capture the idler sound and vibration to detect the current health of the idler. But, these diagnosis methods need an engineering presence near the belt and monitoring purposes. However, these sensors can be monitored by only a few idlers nearby, and the installation cost of these makes the monitoring system infeasible. A predictive maintenance framework and mathematical modelling of a belt conveyor have been proposed to identify the faults before the severe damage of the belt. The experimental results showed that the in-belt monitor could identify a faulty bearing even before failure occurred. This allows all the defective bearings to be identified and the needed stock can be purchased ahead of a planned outage, and all the faulty bearings can be replaced. One large, scheduled outage can be organized to replace all defective bearings and bearings showing signs of failure soon, reducing the number of short power failures that punctuate the conveyor feed. This form of monitoring is insufficient for estimating the remaining service life of the faulty bearings. [ABSTRACT FROM AUTHOR]

This paper introduces an encoder–decoder-based attentional decoder network to recognize small-size lesions in chest X-ray images. In the encoder-only network, small-size lesions disappear during the down-sampling steps or are indistinguishable in the low-resolution feature maps. To address these issues, the proposed network processes images in the encoder–decoder architecture similar to U-Net families and classifies lesions by globally pooling high-resolution feature maps. However, two challenging obstacles prohibit U-Net families from being extended to classification: (1) the up-sampling procedure consumes considerable resources, and (2) there needs to be an effective pooling approach for the high-resolution feature maps. Therefore, the proposed network employs a lightweight attentional decoder and harmonic magnitude transform. The attentional decoder up-samples the given features with the low-resolution features as the key and value while the high-resolution features as the query. Since multi-scaled features interact, up-sampled features embody global context at a high resolution, maintaining pathological locality. In addition, harmonic magnitude transform is devised for pooling high-resolution feature maps in the frequency domain. We borrow the shift theorem of the Fourier transform to preserve the translation invariant property and further reduce the parameters of the pooling layer by an efficient embedding strategy. The proposed network achieves state-of-the-art classification performance on the three public chest X-ray datasets, such as NIH, CheXpert, and MIMIC-CXR. In conclusion, the proposed efficient encoder–decoder network recognizes small-size lesions well in chest X-ray images by efficiently up-sampling feature maps through an attentional decoder and processing high-resolution feature maps with harmonic magnitude transform. We open-source our implementation at https://github.com/Lab-LVM/ADNet. • We propose the AD-Net that utilizes a new encoder–decoder classification architecture. • We provide a harmonic magnitude transform that efficiently combines feature maps in a translation invariant manner, using minimal additional resources. • We achieve state-of-the-art performance on three widely-used chest X-ray datasets. [ABSTRACT FROM AUTHOR]

In the field of optics, there exist numerous chaotic processes like dissipative soliton dynamics, random laser generation, and laser scattering. It's very challenging to accurately capture the dynamics of these stochastic processes from the wavelength perspective with traditional spectrometers due to their slow signal integration speeds. Here, we propose a new approach, named time-delay Fourier transform spectrometer (TDFTS), to characterize the spectra of laser pulses with durations ranging from fs to ns with high speeds. Based on a fiber array with different lengths to impose frequency-dependent time delay, TDFTS efficiently maps the spectral distribution of light pulses to the temporal domain, and the spectrum can thus be detected with a photodiode and an oscilloscope. In experimental operation, the TDFTS provides spectral acquisition speeds up to 56 MHz frame rates and a bandwidth of tens of nanometers, while keeping comparable fidelity to traditional grating-scan spectrometers. While its spectral resolution of the current configuration is ∼0.1 nm, it can be further improved to 0.001 nm through optimizing the system. Based on its high speed, high spectral resolution, broad-bandwidth coverage, and compact configuration, TDFTS can be used to monitor nanosecond-scale spectral dynamics of non-repetitive optical processes. Numerous chaotic processes such as dissipative soliton dynamics, random laser generation and laser scattering contain rich and peculiar physical phenomena. Due to their fast occurrence and contingency, it is challenging to record their spectral changes with traditional spectrometers due to their slow signal integration speed. Therefore, developing a technology to capture the spectral dynamics of these stochastic processes has become a common concern for researchers. Existing real-time spectral measurement tools, e.g. dispersion Fourier transform (DFT), can hardly record ns-scale pulses due to too large amount of dispersion required. Other solution such as parametric spectro-temporal analyzer (PASTA) has the disadvantage of narrow measurement bandwidth. Here, we propose a new solution called Time-delay Fourier transform spectrometer (TDFTS), which makes use of specially designed fiber arrays (a bundle of fibers with different lengths) and a diffraction grating to achieve frequency-dependent time-delays. This method effectively maps the spectral distribution of light pulses to the temporal domain and the spectrum can be detected only with the combination of a detector and an oscilloscope. TDFTS has the advantages of high measurement speed (hundreds of MHz of frame rates), large operating bandwidth (can reach several hundreds of nanometers), simple configuration, and low cost. In particular, with the time-delay fiber array, it can measure the spectra of pluses with durations ranging from femtoseconds to nanoseconds. The TDFTS can not only be used for spectral measurement but is also expected to have wide applications in biomedical sensing, real-time continuous imaging and other fields. [ABSTRACT FROM AUTHOR]

We prove an operator-valued Laplace multiplier theorem for causal translation-invariant linear operators which provides a characterization of continuity from Hα(R,U)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H^\alpha ({\mathbb {R}},U)$$\end{document} to Hβ(R,U)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H^\beta ({\mathbb {R}},U)$$\end{document} (fractional U-valued Sobolev spaces, U a complex Hilbert space) in terms of a certain boundedness property of the transfer function (or symbol), an operator-valued holomorphic function on the right-half of the complex plane. We identify sufficient conditions under which this boundedness property is equivalent to a similar property of the boundary function of the transfer function. Under the assumption that U is separable, the Laplace multiplier theorem is used to derive a Fourier multiplier theorem. We provide an application to mathematical control theory, by developing a novel input-output stability framework for a large class of causal translation-invariant linear operators which refines existing input-output stability theories. Furthermore, we show how our work is linked to the theory of well-posed linear systems and to results on polynomial stability of operator semigroups. Several examples are discussed in some detail. [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(LlogL)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {O}(L{\text {log}}L)$$\end{document}. 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 inverse scattering problem is to reconstruct or recover some physical and/or geometric properties of an object from the measured scattered field in the process of illumination by an incident wave. The probing radiation can be an electromagnetic wave (e.g., microwave, optical wave, and X-ray), an acoustic wave, or some other waves. The inverse scattering problem is important when detailed information about the structure and composition of an object is required, but it cannot be obtained directly from the measurements. The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties of an anisotropic medium with respect to electromagnetic waves are defined by the tensors, which give the relation between the inductions and the fields. The tensor Fourier diffraction theorem derived in the paper can be considered as a useful tool for studying tensor fields in inverse problems of electromagnetic scattering. The Fourier diffraction theorem is obtained in a coordinate-free representation by the use of tensor (dyadic) analysis techniques. The method of inversion is based on the first Born approximation. [ABSTRACT FROM AUTHOR]

Let { S d } d = 0 2 N − 1 be an iterated function system defined by S d (x) = (− 1) d ρ (x + d) , x ∈ R , where 0 < ρ < 1 and N is a positive integer. Let μ ρ , D 2 N be a self-similar measure defined by μ ρ , D 2 N (⋅) = 1 2 N ∑ d = 0 2 N − 1 μ ρ , D 2 N (S d − 1 (⋅)). We show that μ ρ , D 2 N is a spectral measure if and only if ρ = p − 1 for some nature number p and 2 N divides p. Moreover, we introduce a useful way to determine the spectrality of the convolution of two infinitely supported measures. [ABSTRACT FROM AUTHOR]

We propose a method for frequency domain feature analysis of point clouds based on the multilayer perceptron paradigm (MLP), named PFFA-MLP. By leveraging the Fourier transform and the latest MLP as a replacement for the transformer mechanism, PFFA-MLP maps point clouds to the frequency domain using a three-dimensional (3D) discrete Fourier transform. PFFA-MLP employs lightweight stacked DGCNN modules for initial feature extraction on multi-scale point cloud signals. It also includes a frequency domain feature analysis module, based on the MLP, which analyzes and aggregates the extracted multi-scale point cloud features. Point cloud understanding experiments are conducted on the ModelNet40, ScanObjectNN, and ShapeNet Part benchmarks. On ModelNet40, PFFA-MLP achieves an accuracy of 98% compared to PointMLP, while improving the detection speed by 7.2 times. On ScanObjectNN, the accuracy reaches 94% of PointMLP, while the detection speed is improved by 3.2 times. On ShapeNet Part, it achieves 97% of PointMLP. The experimental results demonstrate that PFFA-MLP achieves a favorable trade-off between training and inference speed. This method is applicable in scenarios that require efficient point cloud analysis while maintaining remarkable detection precision. [ABSTRACT FROM AUTHOR]

Air pollution has become a growing problem owing to its harmful effects on human health, making accurate air quality prediction an important task to avoid serious environmental impacts. Recently, graph-neural-network-based methods have emerged as promising approaches to modeling the spatial dependencies between adjacent stations. However, they have limitations in capturing the hierarchical temporal features of the time series, which include trends, and periodic components. They also overlook dynamic correlations between stations and multiple types of connections, resulting in generated graphs that lack dynamics. In this paper, we proposed a spatiotemporal hierarchical transmit neural network for the prediction of air quality by extracting long-term periodic features and short-term spatiotemporal dependencies. It incorporates a periodic feature extraction component (PFEC), a scene dynamic graph module (SDGM), a spatiotemporal extraction component (STEC), and a transmit attention (TransATT) component. The PFEC applies discrete Fourier transform and trend decomposition techniques to extract long-term periodic features from the spatiotemporal graph. The SDGM generates dynamic graphs by combining node features of time series with predefined graphs to encode diverse station relationships. The STEC comprises of two convolutional operations and attention mechanisms, enabling the model to capture the short-term spatiotemporal dependencies. TransATT integrates the extracted short-term spatiotemporal dependencies and long-term periodic features, allowing the model to transmit with short- and long-term features. To demonstrate the effectiveness of the proposed model, we conducted experiments on three real-world datasets and found that our approach outperforms state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this note, we discuss the validity of formula (4.54) in Grabisch's book from 2016. This equation expresses the Choquet integral of nonnegative functions w.r.t. a game in the form of linear invertible transform of set functions. However, the formula (erroneously) excludes the empty set, which has consequences for deriving Choquet integral representations in the literature using this approach. We point out that results for several transforms (e.g. Möbius, or co-Möbius transform) are not affected, but it is not the case of others (e.g. Fourier transform). In this spirit, we also provide a new formula for the Choquet integral representation via the Shapley interaction transform. [ABSTRACT FROM AUTHOR]

• A fast and highly accurate frequency estimation algorithm based on the union of amplitude-phase is proposed to redundant calculations and errors arising from the fast fourier transform process are reduced. • The size of the drive data is only 1 × 12 dimensions. • The neural network has simple structure, fast training and low calculation cost, which is conducive to the implementation in embedded system. • The model has strong universality and can be used to change of load power, cable length, load type, cable parameters and other working conditions. • According to the existing proposed low voltage AC series arc fault location methods, the method proposed in this paper has the highest positioning accuracy and the widest application range. In recent years, the safety of civil electricity has been seriously affected by low-voltage AC series arc faults. However, for indoor distribution lines (220 V/50 Hz), only a few researchers pay attention to the research of AC series arc fault location. Therefore, a fault location method of low-voltage AC series arc based on RBF neural network is proposed. Firstly, a fast and highly accurate frequency estimation algorithm based on the union of amplitude-phase is proposed to redundant calculations and errors arising from the Fast Fourier Transform (FFT) process are reduced. The proposed method extracts the voltage and current signals in the 0∼3 kHz frequency band. The current amplitude difference per meter of the line is calculated. However, influenced by the dynamic arc resistance, the minor differences no longer correspond to the actual fault point. The arc fault location model is trained by integrating the RBF neural network, and the deviation is eliminated. The performance of the model has also been verified in a variety of operating conditions with actual measurement data. The results show that the established localization model is generic and can be applied to complex indoor cable scenarios. [ABSTRACT FROM AUTHOR]

Although great success has been achieved in various computer vision tasks, deep neural networks (DNNs) suffer dramatic performance degradation when evaluated on out-of-distribution data. Domain generalization (DG) is proposed to handle this problem by learning domain-agnostic information from multiple source domains to generalize well on unseen target domains. Several methods resort to Fourier transform due to its simplicity and efficiency. They argue that amplitude spectra imply domain-specific information, which should be suppressed, while phase counterparts imply domain-agnostic information, which should be preserved. However, these methods only suppress the domain-specific information in source domains and neglect the relationship with target domains, leading to the persistence of the domain gap. Besides, these methods preserve domain-agnostic information by keeping phase components unchanged, causing them to be underutilized. In this paper, we propose Dual Branch Augmentation Module (DBAM) by leveraging Fourier transform and taking advantage of both amplitude and phase spectra. For the amplitude branch, we propose Inner-domain Amplitude Distribution Rectification (IADR) and Cross-domain Amplitude Dirichlet Mixup (CADM) to stabilize the training process and explore more feature space. In addition, we propose Test-time Amplitude Prototype Calibration (TAPC) to construct the connection between source and target domains during evaluation to further mitigate the domain gap. For the phase branch, we propose Random Symmetric Phase Perturbation (RSPP) to enhance the robustness for recognizing domain-agnostic information. With the combined contributions of the two branches, DBAM significantly surpasses other state-of-the-art (SOTA) methods. Extensive experiments on four benchmarks and further analysis demonstrate the effectiveness of DBAM. [ABSTRACT FROM AUTHOR]

The paper concerns problems of the recovery of operators from noisy information in weighted L q -spaces with homogeneous weights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson type inequalities with several weights and problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in the L p -metric. [ABSTRACT FROM AUTHOR]

The product q · q in Section 4 and Appendix should be replaced by qq. [ABSTRACT FROM AUTHOR]

An infinitely smooth symmetric convex body K ⊂ R d is called k -separably integrable, 1 ≤ k < d , if its k -dimensional isotropic volume function V K , H (t) = H d ({ x ∈ K : dist (x , H ⊥) ≤ t }) can be written as a finite sum of products in which the dependence on H ∈ Gr k (R d) and t ∈ R is separated. In this paper, we will obtain a complete classification of such bodies. Namely, we will prove that if d − k is even, then K is an ellipsoid, and if d − k is odd, then K is a Euclidean ball. This generalizes the recent classification of polynomially integrable convex bodies in the symmetric case. [ABSTRACT FROM AUTHOR]

In this paper, we announce a result that generalizes the first Beurling–Malliavin theorem. In other words, we give a new sufficient condition on a function guaranteeing that it belongs to the Beurling–Malliavin class of majorants. It is also shown that the main result of this article is sharp in many senses. [ABSTRACT FROM AUTHOR]

Isolation piles are widely used to increase the horizontal resistance of high‐speed railway under adjacent loading in soft soils. This study proposes a theoretical model for horizontal additional stress of pile‐reinforced area subjected to adjacent loading. The isolation piles and the soil between piles in the reinforcement area are equivalent to a uniform medium in the proposed model. The Heaviside function is introduced to avoid the partition solution problem of pile‐reinforced area and the foundation soils. A combined method with the inverse Fourier transform, Gauss integral, Lagrange quadratic interpolation, and Simpson quadrature formula is employed in the calculation process. The theoretical model is validated by the finite element method. According to the calculated results, the distribution of horizontal additional stress is obtained. The horizontal soil displacements at the location of the railway increases in the depth range of 0–2.5 m and then gradually decreases. The proposed model with engineering significance is available for preliminary design of isolation piles. [ABSTRACT FROM AUTHOR]

In this paper we study the local and global well posedness of a fractional dissipative Klein–Gordon–Schrödinger type system in dimension 1 and establish the existence of a global attractor. [ABSTRACT FROM AUTHOR]

Let R k = diag (r k , 1 , r k , 2 , ... , r k , n) be the n × n expanding integer diagonal matrix, and let D k ⊂ Z n . We show that the sequence of Hadamard triples { (R k , D k , S k) } admits a spectrum of the associated Moran measure under specific situations. The results are new in all dimensions n greater than two. [ABSTRACT FROM AUTHOR]

The small‐angle neutron scattering data of nanostructured magnetic samples contain information regarding their chemical and magnetic properties. Often, the first step to access characteristic magnetic and structural length scales is a model‐free investigation. However, due to measurement uncertainties and a restricted q range, a direct Fourier transform usually fails and results in ambiguous distributions. To circumvent these problems, different methods have been introduced to derive regularized, more stable correlation functions, with the indirect Fourier transform being the most prominent approach. Here, the indirect Fourier transform is compared with the singular value decomposition and an iterative algorithm. These approaches are used to determine the correlation function from magnetic small‐angle neutron scattering data of a powder sample of iron oxide nanoparticles; it is shown that with all three methods, in principle, the same correlation function can be derived. Each method has certain advantages and disadvantages, and thus the recommendation is to combine these three approaches to obtain robust results. [ABSTRACT FROM AUTHOR]

In this work, we investigate using Fourier coefficients (FCs) for capturing useful information about viral sequences in a computationally efficient and compact manner. Specifically, we extract geographic submission location from SARS-CoV-2 sequence headers submitted to the GISAID Initiative, calculate corresponding FCs, and use the FCs to classify these sequences according to geographic location. We show that the FCs serve as useful numerical summaries for sequences that allow manipulation, identification, and differentiation via classical mathematical and statistical methods that are not readily applicable for character strings. Further, we argue that subsets of the FCs may be usable for the same purposes, which results in a reduction in storage requirements. We conclude by offering extensions of the research and potential future directions for subsequent analyses, such as the use of other series transforms for discreetly indexed signals such as genomes. [ABSTRACT FROM AUTHOR]

Fourier ptychography is an emerging computational microscopy technique that can generate gigapixel-scale images of biological samples. With only the addition of a low-cost LED array to a standard digital microscope and a reconstruction algorithm, Fourier ptychography overcomes the fundamental trade-off between a microscope's resolution and field-of-view without any moving parts. This article is the first in a three-part series that aims to introduce the fundamentals of the technology to the broader microscopy community and beyond, using intuitive explanations. [ABSTRACT FROM AUTHOR]

Recently, Liu and Zhang studied the rather challenging problem of time series forecasting from the perspective of compressed sensing. They proposed a no-learning method, named Convolution Nuclear Norm Minimization (CNNM), and proved that CNNM can exactly recover the future part of a series from its observed part, provided that the series is convolutionally low-rank. While impressive, the convolutional low-rankness condition may not be satisfied whenever the series is far from being seasonal, and is in fact brittle to the presence of trends and dynamics. This paper tries to approach the issues by integrating a learnable, orthonormal transformation into CNNM, with the purpose for converting the series of involute structures into regular signals of convolutionally low-rank. We prove that the resultant model, termed Learning-Based CNNM (LbCNNM), strictly succeeds in identifying the future part of a series, as long as the transform of the series is convolutionally low-rank. To learn proper transformations that may meet the required success conditions, we devise an interpretable method based on Principal Component Pursuit (PCP). Equipped with this learning method and some elaborate data argumentation skills, LbCNNM not only can handle well the major components of time series (including trends, seasonality and dynamics), but also can make use of the forecasts provided by some other forecasting methods; this means LbCNNM can be used as a general tool for model combination. Extensive experiments on 100,452 real-world time series from Time Series Data Library (TSDL) and M4 Competition (M4) demonstrate the superior performance of LbCNNM. [ABSTRACT FROM AUTHOR]