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Interference is widely regarded as a foundational attribute of quantum mechanics. However, for a given experimental arrangement, interference can either contribute or not contribute to the outcome depending upon the basis in which it is measured. This observation is both foundational and particularly relevant to coherent control of molecular processes, an approach based upon quantum interference. Here, we address this issue and its relevance to controlling molecular processes via the "coherent control scattering (CCS) matrix," a formalism that allows for an analysis of modifications in an interference structure resulting from a change of basis. This analysis reveals that the change in the interference structure can be attributed to the non-commutativity of the transformation matrix with the CCS matrix and the non-orthogonality of the transformation. Additionally, minimal interference is shown to be associated with the CCS eigenbasis and that the Fourier transform of the eigenvectors of the CCS matrix provides the maximal interference and hence the best coherent control. The change of controllability through a change of basis is illustrated with an example of 85Rb+ 85Rb scattering. In addition, the developed formalism is applied to explain recent experimental results on He + D2 inelastic scattering demonstrating the presence or absence of interference depending on the basis. [ABSTRACT FROM AUTHOR]

A frequency-dependent dielectric constant characterizes the dielectric response of a medium and also represents the time scale of system's collective dynamics. Although it is valuable not only academically but also practically for developing advanced devices, getting the value of a solution at the interface with a solid or electrode surface is challenging both experimentally and computationally. Here, we propose a computational method that imitates the dielectric spectroscopy and AC impedance measurement. It combines a time-dependent voltage applied molecular dynamics simulation with an equivalent circuit representation of a system composed of a solution confined between two identical electrodes. It gives the frequency-dependent dielectric constants of the bulk solution and the interface simultaneously. Unlike the conventional method, it does not require computation of a dipole autocorrelation function and its Fourier transformation. Application of the method on a system of water confined between polarizable Pt electrodes gives the static dielectric constant and the relaxation time of the bulk water in good agreement with previous simulation results and experimental values. In addition, it gives a much smaller static dielectric constant at the interface, consistent with previous observations. The outline of the dielectric dispersion curve of the interface seems similar to that of the bulk, but the relaxation time is several times faster. [ABSTRACT FROM AUTHOR]

A new free-energy functional is proposed for inhomogeneous associating fluids. The general formulation of Wertheim's thermodynamic perturbation theory is considered as the starting point of the derivation. We apply the hypotheses of the statistical associating fluid theory in the classical density functional theory (DFT) framework to obtain a tractable expression of the free-energy functional for inhomogeneous associating fluids. Specific weighted functions are introduced in our framework to describe association interactions for a fluid under confinement. These weighted functions have a mathematical structure similar to the weighted densities of the fundamental-measure theory (i.e., they can be expressed as convolution products) such that they can be efficiently evaluated with Fourier transforms in a 3D space. The resulting free-energy functional can be employed to determine the microscopic structure of inhomogeneous associating fluids of arbitrary 3D geometry. The new model is first compared with Monte Carlo simulations and previous versions of DFT for a planar hard wall system in order to check its consistency in a 1D case. As an example of application in a 3D configuration, we then investigate the extreme confinement of an associating hard-sphere fluid inside an anisotropic open cavity with a shape that mimics a simplified model of zeolite. Both the density distribution and the corresponding molecular bonding profile are given, revealing complementary information to understand the structure of the associating fluid inside the cavity network. The impact of the degree of association on the preferential positions of the molecules inside the cavity is investigated as well as the competition between association and steric effect on adsorption. [ABSTRACT FROM AUTHOR]

The linear double-diffusivity (D-D) model of Aifantis, comprising two coupled Fick-type partial differential equations and a mass exchange term connecting the diffusivities, is a paradigm in modeling mass transport in inhomogeneous media, e.g., fissures or fractures. Uncoupling of these equations led to a higher order partial differential equation that reproduced the non-classical transport terms, analyzed independently through Barenblatt's pseudoparabolic equation and the Cahn–Hilliard spinodal decomposition equation. In the present article, we study transport in a nonlinearly coupled D-D model and determine the regime-switching of the associated diffusive processes using a revised formulation of the celebrated Lux method that combines forward Fourier transform with a Laplace transform followed by an Inverse Fourier transform of the governing reaction–diffusion (R–D) equations. This new formulation has key application possibilities in a wide range of non-equilibrium biological and financial systems by approximating closed-form analytical solutions of nonlinear models. [ABSTRACT FROM AUTHOR]

Ultrafast spectroscopy is a powerful technique that utilizes short pulses on the femtosecond time scale to generate and probe coherent responses in molecular systems. While the specific ultrafast methodologies vary, the most common data analysis tools rely on discrete Fourier transformation for recovering coherences that report on electronic or vibrational states and multi-exponential fitting for probing population dynamics, such as excited-state relaxation. These analysis tools are widely used due to their perceived reliability in estimating frequencies and decay rates. Here, we demonstrate that such "black box" methods for parameter estimation often lead to inaccurate results even in the absence of noise. To address this issue, we propose an alternative approach based on Bayes probability theory that simultaneously accounts for both population and coherence contributions to the signal. This Bayesian inference method offers accurate parameter estimations across a broad range of experimental conditions, including scenarios with high noise and data truncation. In contrast to traditional methods, Bayesian inference incorporates prior information about the measured signal and noise, leading to improved accuracy. Moreover, it provides estimator error bounds, enabling a systematic statistical framework for interpreting confidence in the results. By employing Bayesian inference, all parameters of a realistic model system may be accurately recovered, even in extremely challenging scenarios where Fourier and multi-exponential fitting methods fail. This approach offers a more reliable and comprehensive analysis tool for time-resolved coherent spectroscopy, enhancing our understanding of molecular systems and enabling a better interpretation of experimental data. [ABSTRACT FROM AUTHOR]

A comparison is made between the three principal methods for the analysis of neutron and x-ray diffraction data from noble gas fluids by direct Fourier transform. All three methods (standard Fourier transform, Lorch modification, and Soper–Barney modification) are used to analyze four different sets of diffraction data from noble gas fluids. The results are compared to the findings of a full-scale real-space structure determination, namely, Empirical Potential Structure Refinement. Conclusions are drawn on the relative merits of the three Fourier transform methods, what information can be reliably obtained using each method, and which method is most suitable for the analysis of different kinds of diffraction data. The mathematical validity of the Lorch method is critically analyzed. [ABSTRACT FROM AUTHOR]

The first finite basis set implementation of the real-time time-dependent self-consistent field method in a dynamic (time-dependent) magnetic field using London atomic orbitals (LAOs) is presented. The accuracy of the finite basis approach using LAOs is benchmarked against numerical results from the literature for the hydrogen atom and H2 in the presence of rapidly oscillating magnetic fields. This comparison is used to inform the choice of appropriate basis sets for studies under such conditions. Remarkably, relatively modest compact LAO basis sets are sufficient to obtain accurate results. Analysis of electron dynamics in the hydrogen atom shows that LAO calculations correctly capture the time evolution of orbital occupations. The Fourier transformation of the autocorrelation function yields a power spectrum exhibiting harmonics associated with coherent emission, which closely matches the literature and further confirms the accuracy of this approach. The dynamical response of the electron density in H2 for a magnetic field parallel to the internuclear axis shows similar behavior to benchmark studies. The flexibility of this implementation is then demonstrated by considering how the dynamical response changes as a function of the orientation of the molecule relative to the applied field. At non-parallel orientations, the symmetry of the system is lowered and numerical benchmark data, which exploit cylindrical symmetry, are no-longer readily available. The present study demonstrates the utility of LAO-based calculations for extreme dynamic magnetic fields, providing a stress-test on the choice of basis. Future applications of this approach for less extreme dynamic magnetic fields are briefly discussed. [ABSTRACT FROM AUTHOR]

Non-impact effects in the absorption spectra of HCl in various collision-partners are investigated both experimentally and theoretically. Fourier transform spectra of HCl broadened by CO2, air, and He have been recorded in the 2-0 band region at room temperature and for a wide pressure range, from 1 to up to 11.5 bars. Comparisons between measurements and calculations using Voigt profiles show strong super-Lorentzian absorptions in the troughs between successive lines in the P and R branches for HCl in CO2. A weaker effect is observed for HCl in air, while for HCl in He, Lorentzian wings are in very good agreement with measurements. In addition, the line intensities retrieved by fitting the Voigt profile on the measured spectra decrease with the density of the perturber. This perturber-density dependence decreases with the rotational quantum number. For HCl in CO2, the decrease in the retrieved line intensity can reach 2.5% per amagat for the first rotational quantum numbers. This number is about 0.8% per amagat for HCl in air, while for HCl in He, no density dependence of the retrieved line intensity is observed. Requantized classical molecular dynamics simulations have been performed for HCl–CO2 and HCl–He in order to simulate the absorption spectra for various perturber-density conditions. The density dependence of the intensities retrieved from the simulated spectra and the predicted super-Lorentzian behavior in the troughs between lines are in good agreement with experimental determinations for both HCl–CO2 and HCl–He. Our analysis shows that these effects are due to incomplete or ongoing collisions, which govern the dipole auto-correlation function at very short times. The effects of these ongoing collisions strongly depend on the details of the intermolecular potential: they are negligible for HCl–He but significant for HCl–CO2 for which a line-shape model beyond the impact approximation will be needed to correctly model the absorption spectra from the center to the far wings. [ABSTRACT FROM AUTHOR]

This paper proves the existence of R$$ \mathcal{R} $$‐bounded solution operator families of the resolvent problem of Navier–Stokes–Korteweg model in half‐space (R+N)$$ \left({\mathbf{R}}_{+}^N\right) $$ with slip boundary condition. Especially we investigate the model for arbitrary constant viscosity and capillarity. We employ the R$$ \mathcal{R} $$‐bounded solution operators of the model obtained from the whole space cases and partial Fourier transform techniques to analyze the model. [ABSTRACT FROM AUTHOR]

Rhamnus prinoides, an indigenous Ethiopian traditional medicinal plant, has been used for treating various ailments including skin conditions in traditional formulations. In this study, plant leaf extract has been incorporated into polycaprolactone (PCL) nanofibers through electrospinning at concentrations of 1%, 3%, 5%, 7% wt/vol for the first time. The presence of extract in the nanofiber was analyzed using Fourier transform infrared. The in vitro antibacterial activity, release, contact angle, thermal, and mechanical properties of the nano mats were characterized. The scanning electron microscopy (SEM) analysis revealed that the produced mats are continuous, smooth, bead‐less, and inter connected. The examination of SEM images using ImageJ revealed that the fiber diameter ranged from 219 ± 47 nm to 284 ± 114 nm. The mats showed excellent anti‐bactericidal activity against both Staphylococcus aureus and Escherichia coli. During the 72‐h in vitro release investigation, an initial burst release was observed within the first 12 h, followed by sustained release of the extract over long period of time. The contact angle analysis showed, addition of leaf extract to the PCL nanofiber increased hydrophilicity. Furthermore, the nanofiber membranes had favorable mechanical properties. Overall, these findings suggested that R. prinoides leaf extract‐functionalized PCL nanofibers could be effective wound dressings with broad‐spectrum antimicrobial activity. [ABSTRACT FROM AUTHOR]

To enhance the safety of autonomous vehicles in mixed traffic and connected environment, it is crucial to recognize the lane-changing intentions (LCIs) of human-driven vehicles for autonomous vehicles. This paper presents a novel method for LCI recognition, which extracts features from the driving state and relative motion of the target vehicle and its neighbors. The method applies short-time Fourier transform, Gramian angular summation field, and Gramian angular difference field to the time-series data, and generates three grayscale images, which are merged into one information fusion image (IFI) by image processing techniques. The IFIs are then classified into three categories: lane keeping, lane-changing left, and lane-changing right, using the Vision Transformer model with transfer learning to speed up convergence and reduce training cost. The experimental results demonstrate that the proposed method outperforms the traditional methods, achieving an accuracy of 95.65% for recognizing LCI 3s before the lane change point. [ABSTRACT FROM AUTHOR]

In this paper, the robust arbitrary trajectory tracking problem of multiple heterogeneous Euler–Lagrange (EL) systems with disturbances under a directed graph is investigated via a novel fully distributed event‐triggered control (ETC) strategy. Firstly, for an arbitrary tracked trajectory, the Fourier transform technique is employed to approximately obtain its linear form, which represents the leader of multiple EL systems. Since the dynamics and state of the leader are not available to all followers, fully distributed adaptive ETC‐based observers are proposed for each follower to reconstruct the leader's trajectory, where the global information requirements are avoided, and the Zeno behavior is excluded by giving the minimum triggering intervals. Armed with the observed information, a robust adaptive ETC protocol is further developed such that the position‐like state of each follower can track the leader with the intermittent controller updating, where a minimum control update interval is obtained theoretically. Moreover, the adaptive technique is used to eliminate the influence of the parameter uncertainties of multiple EL systems, thus the tracking is achieved asymptotically. Finally, simulation results are illustrated to show the feasibility and effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic response of an infinite Euler beam that was mounted on a fractional-order Pasternak viscoelastic foundation subjected to a moving point load was investigated. An analytical solution to the problem was derived using Fourier and Laplace transforms. Numerical results obtained by numerical Laplace inversion were analyzed to explore the impact of various parameters on the system's response. The findings indicated that increasing system damping led to a decrease in maximum deflection and a more visible deformation hysteresis with an increase in fractional derivative orders. Additionally, all parameters of the foundation and shear layer were observed to have a significant effect on the deflection. The study confirmed that the fractional-order model predicted damping and dynamic deflection more accurately than the conventional integer-order foundation model. The research contributed to the understanding of the behavior of Euler beams mounted on viscoelastic foundations and provided valuable insights into the design of such systems. [ABSTRACT FROM AUTHOR]

Rationale: Natural monomer flavors can modify the taste of cigarettes. However, no report was published to establish the quality control method for their chemical compositions. Methods: In this study, licorice, a traditional natural monomer flavor used in tobacco aroma processing, was selected, and the fingerprint was developed by high‐performance liquid chromatography (HPLC). Next, the chemical markers of samples from different places of origin were discovered by multivariate statistical analysis. Then, its chemical constituents were identified by combination of HPLC‐Fourier transform ion cyclotron resonance mass spectrometry (FT‐ICR‐MS), direct infusion FT‐ICR‐MS (DI‐FT‐ICR‐MS), and the technology of isotopic fine structures (IFSs). Moreover, its characteristic constituents were quantitatively analyzed using HPLC. Results: The 14 common peaks were assigned in the fingerprint, and 8 of them were considered as qualitative markers by multivariate statistical analysis. A total of 42 chemical constituents were detected using HPLC‐FT‐ICR‐MS, and 13 of them were unambiguously identified by references. Meanwhile, the elemental compositions of other eight unknown chemical components were decisively determined using IFSs. Subsequently, the contents of five characteristic constituents in 11 batches of samples were determined. Conclusions: The integration strategy established here can discover and quantify the chemical markers for improving the quality control standard of natural monomer flavor of licorice. It is expected that the strategy will be valuable for further quality control of other natural monomer flavors in Chinese tobacco industry. [ABSTRACT FROM AUTHOR]

To model several engineering and physical models, the approach of the fractional derivative is highly anticipated. As compared to the ordinary derivatives, the fractional derivatives with more flexibility can estimate the data due to the involvement of the fractional-order derivatives. Due to these advantages of the fractional approach, this study communicates with the determination of the fractional-based exact outcomes of an oscillatory rectangular duct problem of a generalized second-grade fluid. The approach of the fractional operator is involved in the relationship of the constitutive equations. For cosine oscillation of the rectangular duct, exact results of the magnetized unsteady flow problem are evaluated through the technique of Laplace transform with double finite Fourier sine transform. This study concludes that the velocity field exhibits escalating behavior relative to the improved fractional parameter. Moreover, the magnetic parameter with increasing values declines the flow field while the accelerating values of the fluid parameter enhance the velocity field. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to develop a new algorithm for computing a nonnegative low multi‐rank tensor approximation for a nonnegative tensor. In the literature, there are several nonnegative tensor factorizations or decompositions, and their approaches are to enforce the nonnegativity constraints in the factors of tensor factorizations or decompositions. In this paper, we study nonnegativity constraints in tensor entries directly, and a low rank approximation for the transformed tensor by using discrete Fourier transformation matrix, discrete cosine transformation matrix, or unitary transformation matrix. This strategy is particularly useful in imaging science as nonnegative pixels appear in tensor entries and a low rank structure can be obtained in the transformation domain. We propose an alternating projections algorithm for computing such a nonnegative low multi‐rank tensor approximation. The convergence of the proposed projection method is established. Numerical examples for multidimensional images are presented to demonstrate that the performance of the proposed method is better than that of nonnegative low Tucker rank tensor approximation and the other nonnegative tensor factorizations and decompositions. [ABSTRACT FROM AUTHOR]

This paper proposes an Interpolated Discrete-Time Fourier Transform (LIpDTFT) estimator for complex-valued noisy sinewave frequency based on the Linearization of the DTFT module behavior around the spectrum peak. It belongs to a class of LIpDTFT estimators that compensate the poor Discrete Fourier Transform (DFT) frequency resolution by interpolating two DTFT samples located very close to an initial frequency estimate. As compared with other DTFT-based frequency estimators recently proposed in the literature, the proposed LIpDTFT estimator ensures a smaller interpolation error and a lower processing effort. Moreover, if the rectangular window is adopted, it almost attains the unbiased Cramér-Rao Lower Bound (CRLB) even if a very small number of samples is analyzed. The accuracies ensured in different operating conditions by the proposed frequency estimator and other state-of-the-art DTFT-based algorithms are compared to each other through computer simulations. [ABSTRACT FROM AUTHOR]

Modern radar systems often face various interference signals in complex and rapidly changing electronic environments. The task of suppressing this interference in the radar echo signal to extract vital information is challenging. A radar interference suppression method is proposed based on a generative adversarial network (GAN). This method effectively recovers the target signal from the echo signal, which contains interference and noise, by leveraging the powerful fitting ability of GAN. Specifically, this method was tested using coherent suppression interference, smart noise interference, and noise frequency modulation suppression interference. We compared the proposed GAN method with recurrent neural network, short‐time Fourier transform time‐varying filtering, short‐time fractional Fourier transform time‐varying filtering algorithms and RNN approach. The results show that the interference suppression algorithm based on GAN is superior to the other three algorithms. [ABSTRACT FROM AUTHOR]

Near-range radar imaging (NRRI) has evolved into a vital technology with diverse applications spanning fields such as remote sensing, surveillance, medical imaging and non-destructive testing. The Pseudopolar Format Matrix (PFM) has emerged as a promising technique for representing radar data in a compact and efficient manner. In this paper, we present a comprehensive PFM description of near-range radar imaging. Furthermore, this paper also explores the integration of the Fractional Fourier Transform (FrFT) with PFM for enhanced radar signal analysis. The FrFT—a powerful mathematical tool for signal processing—offers unique capabilities in analysing signals with time-frequency localization properties. By combining FrFT with PFM, we have achieved significant advancements in radar imaging, particularly in dealing with complex clutter environments and improving target detection accuracy. Meanwhile, this paper highlights the imaging matrix form of FrFT under the PFM, emphasizing the potential for addressing challenges encountered in near-range radar imaging. Finally, numerical simulation and real-world scenario measurement imaging results verify optimized accuracy and computational efficiency with the fusion of PFM and FrFT techniques, paving the way for further innovations in near-range radar imaging applications. [ABSTRACT FROM AUTHOR]

The spindle rotation error of computer numerical control (CNC) equipment directly reflects the machining quality of the workpiece and is a key indicator reflecting the performance and reliability of CNC equipment. Existing rotation error prediction methods do not consider the importance of different sensor data. This study developed an adaptive weighted deep residual network (ResNet) for predicting spindle rotation errors, thereby establishing accurate mapping between easily obtainable vibration information and difficult-to-obtain rotation errors. Firstly, multi-sensor data are collected by a vibration sensor, and Short-time Fourier Transform (STFT) is adopted to extract the feature information in the original data. Then, an adaptive feature recalibration unit with residual connection is constructed based on the attention weighting operation. By stacking multiple residual blocks and attention weighting units, the data of different channels are adaptively weighted to highlight important information and suppress redundancy information. The weight visualization results indicate that the adaptive weighted ResNet (AWResNet) can learn a set of weights for channel recalibration. The comparison results indicate that AWResNet has higher prediction accuracy than other deep learning models and can be used for spindle rotation error prediction. [ABSTRACT FROM AUTHOR]

Rapid and cost‐effective techniques for soil analysis are essential to guide sustainable land management and production agriculture. This study aimed at evaluating the performance and consistency of portable handheld Fourier‐transform near‐infrared spectrometers and the NeoSpectra scanners in estimating 12 common soil physical and chemical properties including pH; organic carbon (OC); inorganic carbon (IC); total nitrogen (TN); cation exchange capacity (CEC); clay, silt, and sand fractions; and exchangeable potassium (K), phosphorus (P), calcium (Ca), and magnesium (Mg). A diverse set of samples (n = 600) were retrieved from a national‐scale soil archive of the Kellogg Soil Survey Laboratory of USDA‐NRCS and scanned with five NeoSpectra scanners. Predictive models for the soil properties were developed using partial least squares regression (PLSR), Cubist, and memory‐based learning (MBL). Cubist outperformed PLSR and MBL, with the best prediction performance for clay, OC, and CEC (R2 > 0.7), followed by IC, sand, silt, and Mg (R2 > 0.6), and then pH, TN, and Ca (R2 > 0.5). K and P were predicted somewhat poorly with R2 of 0.48 and 0.22. All five NeoSpectra yielded comparable near‐infrared (NIR) spectral data and the PLSR models for the soil properties (in terms of model regression coefficients). However, the consistency assessment showed that the model performance was significantly decreased when the training and testing spectra were from different NeoSpectra scanners. It is concluded that NeoSpectra scanners could be rapid and cost effective for estimating certain soil properties, and calibration transfer should be considered for applications where multiple devices are involved and high estimation accuracy from NIR data is required. Core Ideas: Soil samples (n = 600) were retrieved from Kellogg Soil Survey Laboratory and analyzed with 5 NeoSpectra scanners.Partial least squares regression (PLSR), Cubist, and memory‐based learning (MBL) were employed to estimate 12 soil properties from NIR data.Cubist outperformed PLSR and MBL, with 10 of 12 properties having R2 > 0.5.The five NeoSpectra scanners yielded comparable NIR spectral data and PLSR models.Cross‐device assessment suggested that calibration transfer is needed to maintain higher accuracy of NIR models. [ABSTRACT FROM AUTHOR]

Background: Oscillating x‐ray attenuation in the lungs provides an opportunity to evaluate pulmonary perfusion without contrast. Recent intensity‐based methods have been compared to pulmonary scintigraphy and CT angiography but lack rigorous phantom studies. Purpose: A new method to quantify the periodic signal amplitude was employed using spectral analysis. Performance was characterized using a water phantom capable of creating an oscillating x‐ray attenuation at physiologic amplitudes. Feasibility in detecting abnormal perfusion was performed on a volunteer with pulmonary vascular disease and compared to pulmonary angiography, the clinical gold standard. Methods: For each fluoroscopic acquisition, the normalized temporal signal from each pixel was decomposed into its frequency components using Fourier transformation, and the spectral amplitude, defined as the x‐ray pulsatility index (XPI), was determined at the desired frequency using a band‐pass filter. XPI was displayed as a pixel‐wise parametric colormap. Based on XPI maps generated using two human volunteers, a water bath phantom was constructed with a fluctuating fluid height and a 1 cm diameter pulsatility defect. Contrast‐to‐noise (CNR) of the defect was measured using fluoroscopy images acquired at variable fluid height fluctuation (0.1–1.9 mm) and oscillation frequency (30–60 bpm). Various sampling frame rates (3–30 fps) and acquisition durations (1.8–8 s) using truncated datasets were reconstructed from full datasets. Fluoroscopic images were obtained in a patient just prior to pulmonary angiography in the same projection. Results: XPI maps in human subjects showed high signal to background contrast with high central XPI measuring up to 0.5. Phantom experiments revealed CNR was linearly correlated to fluid height change (r2 = 0.998). CNR is proportional to increasing sampling frame rate and increasing acquisition duration as expected with Fourier analysis. XPI map displayed multifocal perfusion defects in good agreement with pulmonary angiography. Conclusion: Spectral analysis is an accurate and sensitive method to detect small changes in periodic x‐ray attenuation using a short fluoroscopic acquisition. This method demonstrated good agreement to pulmonary angiography and shows promise for clinical imaging of pulmonary perfusion using standard fluoroscopic methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the structural properties of Nevanlinna measures, that is, Borel measures that arise in the integral representation of Herglotz–Nevanlinna functions. In particular, we give a characterization of these measures in terms of their Fourier transform, characterize measures supported on hyperplanes including extremal measures, describe the structure of the singular part of the measures when some variable are set to a fixed value, and provide estimates for the measure of expanding and shrinking cubes. Corresponding results are stated also in the setting of the polydisc where applicable, and some of our proofs are actually performed via the polydisc. [ABSTRACT FROM AUTHOR]

This paper presents simple numerical solutions for electromagnetic plane waves in spatially homogenous time varying medium. The solution is based on converting the resulting second order differential equation into two combined ordinary differential equations which are solved numerically by using the built-in ode113 function in Matlab. By using this method, the time domain responses of the electric and magnetic fields at fixed point in space are obtained. The proposed method is applied on two cases: linearly time varying medium and sinusoidally time varying medium. The corresponding frequency domain response is obtained by using inverse Fourier transformation of the obtained time domain response. The proposed method is compared with FDTD solution. It is found that the proposed method has the same accuracy of FDTD with much less computational time. [ABSTRACT FROM AUTHOR]

Some fundamental properties of the Moritoh wavelet are discussed in this paper. The Moritoh transform is approximated for ultra-distributions in generalised Sobolev space. The adjoint formula of the Fourier transform is extended to the Moritoh transform. The convolution for quaternion-valued functions is defined for a modified representation of quaternions. Furthermore, the quaternionic Moritoh transform is defined with the help of convolution. The inner product relation and the uncertainty principle are also established for the quaternionic Moritoh wavelet transform. [ABSTRACT FROM AUTHOR]

Two chemists employed a three‐device rapid screening "toolkit" consisting of a handheld Raman spectrometer, transportable mass spectrometer, and portable Fourier transform infrared (FT‐IR) spectrometer at an international mail facility (IMF) satellite laboratory to examine unknown (unlabeled/mislabeled) products for the presence of active pharmaceutical ingredients (APIs). Phase I of this project previously demonstrated that this toolkit was the most effective collection of instruments for identifying APIs in product types collected at IMFs during a nationwide mail blitz and Phase II of this project previously demonstrated that results generated using the toolkit during a satellite laboratory pilot program were as reliable as those generated by a full‐service library when two or more of these instruments identify an API. This study (Phase III) described the results of the satellite laboratory toolkit during production mode and encompassed the period ranging from June 2021 through December 2022. During this study, a total of 858 products were examined on‐site at the IMF. The satellite laboratory yielded conclusive results for 726 (84.6%) products, which were used to support regulatory action, and identified 132 (15.4%) products that required additional full‐service laboratory analyses due to inconclusive results. The satellite and full‐service laboratory verified/confirmed at least one API/related substance in 617 (71.9%) products. A total of 709 APIs/related substances were found in the 617 products, and 202 of these 709 compounds were unique/different. Overall, during Phases I through III of this program, 350 different substances have been identified in products collected at IMFs. [ABSTRACT FROM AUTHOR]

We investigate the question: for which functions f (x 1 , ... , x n) , g (x 1 , ... , x n) the asymptotic expansion of the integral ∫ g (x 1 , ... , x n) e f (x 1 , ... , x n) + x 1 y 1 + ⋯ + x n y n ħ d x 1 ... d x n consists only of the first term. We reveal a hidden projective invariance of the problem which establishes its relation with geometry of projective hypersurfaces of the form { (1 : x 1 : ... : x n : f) } . We also construct various examples, in particular we prove that Kummer surface in P 3 gives a solution to our problem. [ABSTRACT FROM AUTHOR]

The exponential decay of lattice Green functions is one of the main technical ingredients of the Bałaban's approach to renormalization. We give here a self-contained proof, whose various ingredients were scattered in the literature. The main sources of exponential decay are the Combes–Thomas method and the analyticity of the Fourier transforms. They are combined using a renormalization group equation and the method of images. [ABSTRACT FROM AUTHOR]

For the octonion Fourier transform, we establish the real Paley‐Wiener theorem. It relates the mean of derivatives of a function with the support of its octonion Fourier transform via limm→∞‖∂mαf‖L2(ℝ3,핆)1/m=(2π)α‖wα‖L∞(suppF핆{f},핆)for any octonion‐valued Sobolev function f∈H∞(ℝ3,핆). [ABSTRACT FROM AUTHOR]

Wavelets on the sets of M -positive vectors in the Euclidean space are studied. These sets are multidimensional analogs of the half-line in the Walsh analysis. Following the ideas of the Walsh analysis, the space of M -positive vectors is equipped with a coordinate-wise addition. Harmonic analysis on this space is also similar to the Walsh harmonic analysis, and the Fourier transform is such that there exists a class of so-called test functions (with a compact support of the function itself and of its Fourier transform). Tight wavelet frames consisting of the test functions are studied. A complete description of the masks generating such frames is given, and an algorithmic method for constructing them is developed. These frames may be very useful for applications to signal processing because some examples of such systems on the half-line were already investigated in this aspect, and it appeared that they have an advantage over classical wavelet systems when used for processing fractal signals and images. [ABSTRACT FROM AUTHOR]

In an effort to estimate the number of true nulls in large scale multiplicity problems (the normal means problem), we generalize the current Fourier transform based oracle estimator with a Laplace transform based estimator. Our interest in this problem stems from the application of r-power which requires knowledge of the number of nulls (Dasgupta et al. in Sankhya B 78(1):96–118, 2016). We analytically show that our method is consistent and theoretically has lower mean squared error than the existing competitor (Jin in J R Stat Soc Ser B (Stat Methodol) 70(3):461–493, 2008). We follow up by a numerical example and a simulation study that ratifies our theoretical results. [ABSTRACT FROM AUTHOR]

Monitoring and classifying cognitive workload in real time is vital for optimizing human–machine interactions and enhancing performance while ensuring safety, particularly in industrial scenarios. Considering this significance, the authors aim to formulate a cognitive workload monitoring system (CWMS) by leveraging the deep gated neural network (DGNN), a hybrid model integrating bi-directional long short-term memory (Bi-LSTM) and gated recurrent unit (GRU) networks. In our experimental setup, each of the four virtual users is equipped with a Raspberry Pi Zero W module to ensure efficient data transmission, thereby enhancing the reliability and efficacy of the monitoring process. This seamless monitoring framework utilizes the constrained application protocol (CoAP) and the Things Board platform to evaluate cognitive workload in real time. The most popular EEG benchmark dataset, the STEW is utilized for workload classification in this study. We employ the short-time Fourier transformation (STFT) to extract frequency bands corresponding to users in both high and low cognitive workload modes. The proposed DGNN models achieve a perfect accuracy of 99.45%, outperforming every previous state-of-the-art model. We meticulously monitored critical parameters, including latency, classification processing time, and cognitive workload levels. This research demonstrates the importance of continuous monitoring for increasing productivity and safety in industries by introducing a novel method of real-time cognitive workload monitoring. The implementation codes for each experiment are documented and made available for reproducibility. [ABSTRACT FROM AUTHOR]

The Chirp-Fourier transform is one of the most important tools of the modern signal processing. It has been widely used in the fields of ultrasound imaging, parameter estimation, and so on. The key to its application lies in the sampling and fast algorithms. In practical applications, nonuniform sampling can be caused by sampling equipment and other reasons. For the nonuniform sampling, we utilized function approximation and interpolation theory to construct different approximation forms of Chirp-Fourier transform kernel function, and proposed three fast nonuniform Chirp-Fourier transform algorithms. By analyzing the approximation error and the computational complexity of these algorithms, the effectiveness of the proposed algorithms was proved. [ABSTRACT FROM AUTHOR]

Short‐term wind speed prediction is essential for economical wind power utilization. The real‐world wind speed data are typically intermittent and fluctuating, presenting great challenges to existing shallow models. In this paper, we present a novel deep hybrid model for multistep wind speed prediction, namely, LR‐FFT‐RP‐MLP/LSTM (linear fast Fourier transform rank pooling multiple‐layer perceptron/long short‐term memory). Our hybrid model processes the local and global input features simultaneously. We leverage RP for the local feature extraction to capture the temporal structure while maintaining the temporal order. Besides, to understand the wind periodic patterns, we exploit FFT to extract global features and relevant frequency components in the wind speed data. The resulting local and global features are, respectively, integrated with the original data and are fed into an MLP/LSTM layer for the initial wind speed predictions. Finally, we leverage a linear regression layer to collaborate these initial predictions to produce the final wind speed prediction. The proposed hybrid model is evaluated using real wind speed data collected from 2010 to 2020, demonstrating superior forecasting capabilities when compared with state‐of‐the‐art single and hybrid models. Overall, this study presents a promising approach for improving the accuracy of wind speed forecasting. [ABSTRACT FROM AUTHOR]

The main objective of this article is to study how a finite crack interacts with horizontally polarized shear (SH) waves in a nonlocal isotropic medium when a magnetic field is present. The study aims to understand the effects of various parameters, including the magnetic field, non-locality, frequency of SH waves, on the behavior of the crack. Here, we are concerned with Griffith's theory of a brittle fracture crack mechanism. The article starts by formulating the governing equations for the propagation of SH waves in the given medium. These equations are converted into dual integral equations using Fourier transformation. Subsequently, an Abel transformation is applied to obtain a Fredholm integral equation of the second kind. Daubechies wavelet family has been used to find an approximate solution for the integral equation. The article aims to determine specific physical quantities including stress intensity factor (SIF), shear stress, and crack energy related to the behavior of the crack. These parameters are essential in understanding how the crack responds to the external conditions. The application of Daubechies wavelets in this context is a relatively new and innovative approach. The study performed a comprehensive analysis of the effects of various factors on the crack behavior. The findings are presented in graphical form to help illustrate the conclusions. To assess the accuracy of the proposed method, the obtained results are compared with known results from the literature for local media. This is an important step in demonstrating the reliability and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a quantum secure multi-party summation scheme with a third party based on quantum Fourier transform (QFT) is put forward, where the third party cannot be permitted to cooperate with others but is allowed for all kinds of attacks. Under the help of third party, N users can calculate the addition modulo d of their private integer strings. The third party generates two-level single qubit and its product state as the initial quantum resource, produces the traveling particles with QFT and the controlled-not (CNOT) operations, and sends the traveling particles out to the first users; then, N users encode their private integer sequences by performing the phase shifting operations on the travelling particles one after another; and finally, the third party decodes out the summation of the private integer sequences from N users through CNOT operations and inverse quantum Fourier transform (IQFT). This protocol only adopts two-level single particle state and its product state as initial quantum resource, only needs d-level single particle measurement and does not need to perform quantum entanglement swapping. Security analysis indicates that this protocol can overcome not only the outside attack but also the participant attack. [ABSTRACT FROM AUTHOR]

We utilize a Fourier transformation-based representation of Maxwell's equations to develop physics-constrained neural networks for electrodynamics without gauge ambiguity, which we label the Fourier–Helmholtz–Maxwell neural operator method. In this approach, both of Gauss's laws and Faraday's law are built in as hard constraints, as well as the longitudinal component of Ampère–Maxwell in Fourier space, assuming the continuity equation. An encoder–decoder network acts as a solution operator for the transverse components of the Fourier transformed vector potential, A ^ ⊥ (k , t) , whose two degrees of freedom are used to predict the electromagnetic fields. This method was tested on two electron beam simulations. Among the models investigated, it was found that a U-Net architecture exhibited the best performance as it trained quicker, was more accurate and generalized better than the other architectures examined. We demonstrate that our approach is useful for solving Maxwell's equations for the electromagnetic fields generated by intense relativistic charged particle beams and that it generalizes well to unseen test data, while being orders of magnitude quicker than conventional simulations. We show that the model can be re-trained to make highly accurate predictions in as few as 20 epochs on a previously unseen data set. [ABSTRACT FROM AUTHOR]

The article delves into the intricate phase transitions of 1-Octadecanol and n-Nonadecane within a binary system, unveiling dynamic structural changes under varying conditions. Through Fourier transform infrared (FTIR) analysis, specific molecular vibrations were identified, shedding light on the molecular composition and interactions. The study highlights the challenges in detecting subtle phase transitions and emphasises the individuality of molecular behaviours in closely related compounds. The findings underscore the complexity of phase transitions in binary systems and advocate for a nuanced approach to studying molecular structures and behaviours. [ABSTRACT FROM AUTHOR]

Geary's c is a prominent measure of spatial autocorrelation in univariate spatial data. It uses a weighted sum of squared differences. This paper develops Geary's c for multivariate spatial data. It can describe the similarity/discrepancy between vectors of observations at different vertices/spatial units by a weighted sum of the squared Euclidean norm of the vector differences. It is thus a natural extension of the univariate Geary's c. This paper also develops a local version of it. We then establish their properties. [ABSTRACT FROM AUTHOR]

High-frequency (HF) radar plays a crucial role in the detection of far-range, stealth, and high-speed targets. Nevertheless, the echo signal of such targets typically exhibits a low signal-to-noise ratio (SNR) and significant amplitude fluctuations because their radar cross-section (RCS) accounting for the HF band is in the resonance region. While enhancing detection performance often requires long-time integration, existing algorithms inadequately consider the impact of amplitude fluctuation. In response to this challenge, this article introduces an improved approach based on coherent and non-coherent integration. Initially, coherent integration, employing the generalized Radon Fourier transform (GRFT), is utilized to derive a candidate detection set of targets' range–time trajectories. This involves a joint solution for range migration (RM) and Doppler frequency migration (DFM) through a multi-parameter motion model search. Subsequently, the removal of low SNR pulses, followed by non-coherent integration, is implemented to mitigate amplitude fluctuation, referred to as Amplitude Fluctuation Suppression (AFS), and refine the detection outcomes. Both simulation and experiment results are provided to prove the effectiveness of the proposed AFS-GRFT algorithm. [ABSTRACT FROM AUTHOR]

Chipless RFID tags have attractive low-cost advantages. However, traditional RFID anti-collision algorithms cannot be applied due to a lack of computing and processing capabilities. Problems with multitag detection must be solved to commercialize chipless RFID tags. In this paper, an innovative method for frequency-domain chipless RFID tag detection is proposed. The tags' scattered signals are processed via wavelet analysis, and a time–frequency plot that can read the code is obtained. When the distance between tags is too close to distinguish in the time–frequency plot, independent component analysis is used to separate individual scattered signals from mixed echo signals; then, the code is read by means of wavelet analysis. To validate the proposed method, C-shaped frequency-domain chipless RFID tag models and a multitag detection simulation scenario were constructed in selected software. The short-time matrix pencil method (STMPM), short-time Fourier transform (STFT), and the proposed method were compared. When the tag spacing is 0.05 m, the code can be read successfully. Compared with the STMPM, the proposed method greatly reduces the computational quantity and shortens the reading time. Furthermore, adjustment of the window width and search step parameters is avoided. [ABSTRACT FROM AUTHOR]

Of the early Eocene amber deposits known across the world, Belgian amber has been mostly absent from the relevant literature. We reinvestigated amber held in the palaeobotanical collection of the Royal Belgian Institute of Natural Sciences, Brussels, which derived from three localities in Belgium that originated from two geographical areas (Leval-Trahegnies and Orp-le-Grand). Using Fourier transform infrared (FTIR) spectroscopy we show the close chemical relationship of Belgian amber to the early Eocene Oise amber from the Paris Basin, and highlight the potential effect of weathering on the amber chemistry. The amber derives from a very similar botanical source as the Oise amber (Combretaceae or Leguminosae-Caesalpinioideae), but from different coeval basins. The two Leval-Trahegnies localities provided amber that exhibit different stages of weathering (heavily fissured and crazed, darkened) and lacking any inclusions. The Orp-le-Grand locality provided the least weathered amber, with one amber piece containing two inclusions: a mite and a new genus and species of hemipteran (Cativolcus uebruum gen. et sp. nov.), and a second one that preserved the impression of insect wings pressed into the surface. [ABSTRACT FROM AUTHOR]

CNN has demonstrated remarkable performance in EEG signal detection, yet it still faces limitations in terms of global perception. Additionally, due to individual differences in EEG signals, the generalization ability of epilepsy detection models is week. To address this issue, this paper presents a cross-patient epilepsy detection method utilizing a multi-head self-attention mechanism. This method first utilizes Short-Time Fourier Transform (STFT) to transform the original EEG signals into time-frequency features, then models local information using Convolutional Neural Network (CNN), subsequently captures global dependency relationships between features using the multi-head self-attention mechanism of Transformer, and finally performs epilepsy detection using these features. Meanwhile, this model employs a light multi-head attention mechanism module with an alternating structure, which can comprehensively extract multi-scale features while significantly reducing computational costs. Experimental results on the CHB-MIT dataset show that the proposed model achieves accuracy, sensitivity, specificity, F1 score, and AUC of 92.89%, 96.17%, 92.99%, 94.41%, and 96.77%, respectively. Compared to the existing methods, the method proposed in this paper obtains better performance along with better generalization. [ABSTRACT FROM AUTHOR]

Rapid and minimally destructive methods for estimating the endogenous organic content of subfossil bone save time, lab consumables, and valuable ancient materials. Fourier transform infrared (FTIR) spectroscopy is an established method to estimate bone protein content, and portable spectroscopes enable field applications. We review the ability of benchtop and portable FTIR indices to predict %N and %collagen from 137 bone specimens drawn from eight taxa. We also explore associations of these indices with the endogenous DNA content estimated for 105 specimens. Bulk bone elemental abundance and crystallinity index data reflect diagenetic alteration of these specimens, which come from a variety of depositional environments in four countries (Madagascar, Greece, Monaco, and Germany). Infrared (IR) indices from benchtop and portable units perform similarly well in predicting observed sample N content and collagen yields. Samples that include little collagen (0–5 wt%) tend to have similar IR index values, and we present a Bayesian approach for the prediction of collagen yields. Bone type best explains variation in target species DNA content (endogenous DNA being particularly abundant in petrosals), but low IR index values were consistently associated with minimal DNA content. We conclude that, although portable FTIR fails to distinguish collagen preservation among poorly preserved samples, a simple approach with minimal sample preparation can effectively screen bone from a variety of taxa, elements, and environments for the extraction of organics. [ABSTRACT FROM AUTHOR]

This work is focused on the explosion performance of syngas/air premixed gas in a self-designed variable cross-section pipe under varying ignition positions (IP 1 , IP 2) and hydrogen volume fraction (α(H 2)). Results show that α(H 2) has a great influence on the propagation of the flame as well as the maximum flame front velocity (FFV max) and the maximum overpressure (P max). As α(H 2) in the syngas increases, the time the flame stays in the pipe is gradually reduced, the FFV max as well as the P max increase regardless of the ignition position. Differently, when α(H 2) < 50%, the t closed at IP 1 is shorter than that at IP 2. The opposite is true when α(H 2) ≥ 50%. This is attributed to the difference in flame velocity and the effect of film breakage. Both α(H 2) and variable cross-section chamber structure all affect the evolution of the flame morphology. When ignition at IP 2 , a "M" flame is observed for the first time at α(H 2) = 20%, and a flame resembling a "T" shape appears at α(H 2) = 70%. Ignition positions have a great influence on overpressure oscillation. In the case of α(H 2) = 15%, the Fourier transform is performed for the pressure curve. When ignited at IP 1 , secondary unstable oscillations occur during the later stage of flame propagation. However, when ignition at IP 2 , primary instability oscillations occur in both the early and late stages of flame propagation. The variable cross-section chamber structure plays a role in the flame front velocity (FFV) and overpressure. After the flame front enters the variable section chamber, the FFV reduces, and when the flame front leaves the variable section chamber, due to the sudden decrease of the cross-sectional area, the FFV increases significantly, and FFV max and P max are obtained at this moment. • A self-designed variable cross-section pipe is studied. • Open-end ignitions at varying positions are analyzed. • When ignition at IP 2 , a "M" flame is observed for the first time at α(H 2) = 20%. • Pressure oscillation frequency is different under different ignition positions. • When the flame front leaves the variable section, FFV max and P max will be obtained. [ABSTRACT FROM AUTHOR]

Medical images contain sensitive information and are prone to various attacks during network transmission. Therefore, it is essential to develop a robust algorithm to ensure the safety of transmitting medical images. In this paper, we propose an efficient and secure color medical image encryption system utilizing the FRFT-DRPE optical transformation and 2D-SICM hyperchaos system. The encryption process in our system considers the specific characteristics of each channel in the HSI color model. First, the image is converted from RGB space to HSI space. Subsequently, different encryption methods are applied to the hue and saturation components, including S-box replacement, scrambling, and diffusion operations. For the intensity component, scrambling and FRFT-DRPE optical encryption operations are performed. Additionally, the order of 2D-FRFT serves as an additional key to enhance the security of the encryption system. Finally, the three channels are merged to complete the overall encryption process. Simulations and performance analysis have confirmed the high-security level of our algorithm. It effectively protects the privacy of medical images during transmission. [ABSTRACT FROM AUTHOR]

Laser-based light detection and ranging (LIDAR) offers a powerful tool to real-timely map spatial information with exceptional accuracy and owns various applications ranging from industrial manufacturing, and remote sensing, to airborne and in-vehicle missions. Over the past two decades, the rapid advancements of optical frequency combs have ushered in a new era for LIDAR, promoting measurement precision to quantum noise limited level. For comb LIDAR systems, to further improve the comprehensive performances and reconcile inherent conflicts between speed, accuracy, and ambiguity range, innovative demodulation strategies become crucial. Here we report a dispersive Fourier transform (DFT) based LIDAR method utilizing phase-locked Vernier dual soliton laser combs. We demonstrate that after in-line pulse stretching, the delay of the flying pulses can be identified via the DFT-based spectral interferometry instead of temporal interferometry or pulse reconstruction. This enables absolute distance measurements with precision starting from 262 nm in single shot, to 2.8 nm after averaging 1.5 ms, in a non-ambiguity range over 1.7 km. Furthermore, our DFT-based LIDAR method distinctly demonstrates an ability to completely eliminate dead zones. Such an integration of frequency-resolved ultrafast analysis and dual-comb ranging technology may pave a way for the design of future LIDAR systems. Here the authors develop a dispersive Fourier transform (DFT) based LIDAR method utilizing phase-locked Vernier dual soliton laser combs and demonstrate improved precision in the measurements. [ABSTRACT FROM AUTHOR]

This article describes the mechanism of telecommunication problems caused by conducted disturbance in AC (alternating current) power lines and case studies of troubleshooting investigated by the Technical Assistance and Support Center, NTT EAST. This is the eighty-second article in a series on telecommunication technologies. [ABSTRACT FROM AUTHOR]