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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]

The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used. [ABSTRACT FROM AUTHOR]

A theoretical model of pulsed photothermal radiometry based on conduction-radiation theory is introduced for a two-layered medium with a first layer having optical and thermal properties different from those of the semi-infinite substrate. This geometry closely represents the optical and thermal properties of biotissues, a major intended application. The theory derives the spatial distribution of the frequency spectrum of the pulsed photothermal signal from the composite two-layer boundary-value problem and matches the spectral frequency domain results to the measured photothermal transients through an efficient inverse Fourier transformation algorithm, which involves the optical, thermal, and geometric parameters of the experimental system. This approach avoids the complicated and computationally expensive analytical Laplace transform approach usually adopted in similar studies and yields a complete conduction–radiation description of photothermal signals without simplifying, yet restrictive, approximations encountered in the literature. Numerical and experimental tests of the model using intralipid solution as layer 1 and semi-infinite solid samples such black rubber and anodized aluminum as layer 2 of the medium are described. The radiation heat transfer coefficients from the air–intralipid and intralipid–solid interfaces were introduced to complement the conductive blackbody-radiated infrared signal component at the detecting camera. The best-fitted parameters and heat transfer coefficients are compared to theoretical and experimental data, and the results of these tests were found to be consistent with the theoretical model. [ABSTRACT FROM AUTHOR]

Fourier transform points out that a certain function that meets certain conditions can be decomposed into a linear combination of trigonometric functions (sine or cosine functions). The functions of high-order cumulant include suppressing the Gaussian noise, eliminating independent signal components, and identifying the phase coupling phenomenon of the signal. To prove this hypothesis, this study constructs a cosine signal with the phase coupling phenomenon based on Fourier transform theory which substitutes it into the third-order cumulant expression and performs detailed reasoning. The constructed signal is extended to the complex signal domain and the same conclusion is obtained. The number of coupled signals is expanded from three to a higher value. The results of the study give definite mathematical and physical meaning to the bispectral peaks. The collected mechanical vibration signals are given to demonstrate this conclusion. The demonstrated characteristics of high-order cumulants have made them widely used in many fields. [ABSTRACT FROM AUTHOR]

In this study, the plane continuous and discontinuous contact problems between a graded piezoelectric layer and a homogeneous piezoelectric half plane are considered. The layer is pressed by a rigid conducting flat punch with an electrical load. The problem is converted using Fourier integral transform into a singular integral equation. This equation is then solved numerically by applying the Gauss-Chebychev integration formula. The primary objective of this article is to investigate the effect of varying several parameters including the contact length, the mechanical and electrical loads, and the graded layer non-homogeneity parameter on the contact stresses and on the normal electric displacement. [ABSTRACT FROM AUTHOR]

• The accuracy of MODIS IR PWV is poor. • The GPS station and MODIS pixel points do not coincide completely in point position. • The problems of spatial interpolation and calibration model are considered in MODIS calibration process. • Compared with the original MODIS IR PWV, the accuracy of the new model is greatly improved in all aspects. • MODIS IR PWV of the new model is in good agreement with GPS PWV. The monitoring of precipitable water vapor (PWV) is of significant importance for meteorological research and rainstorm prediction. The moderate resolution imaging spectroradiometer (MODIS) is one of the most widely used remote sensing PWV instruments aboard the Terra and Aqua satellites. The main objective of this study is to develop a fused inverse distance weighting and the Fourier transform model (FIDWFT) to calibrate MODIS Infrared (IR) PWV. In this research, one year of ground observation data from 17 GPS stations were utilized to evaluate the accuracy of MODIS IR PWV in Hong Kong. Initially, the PWV obtained by one radiosonde was used to verify the GPS PWV. Comparison between GPS and radiosonde showed good agreement with an R-squared of 0.97. After the estimation of GPS PWV in the study area was evaluated, MODIS IR products in the study area were extracted for evaluation. The comparison between MODIS and GPS showed that the R-squared is 0.81 and the mean bias (MB) is −1.60 mm. Considering the spatial interpolation and calibration problems of MODIS products, new model used an inverse distance weighting method to make MODIS IR PWV and GPS PWV completely coincide in space, and fifteen MODIS pixel points were selected for interpolation. Then the MODIS IR PWV was calibrated by GPS PWV using Fourier transform model. Results showed that compared with the MODIS IR PWV before calibration, the R-squared increases from 0.81 to 0.94, the root mean square error decreases from 8.72 mm to 4.98 mm, and the MB decreases from −1.60 mm to −0.83 mm. Therefore, the method is feasible to estimate MODIS IR water vapor, and it achieves better results. [ABSTRACT FROM AUTHOR]

In this study, 2 flexible and pre-organized tetraamide compounds derived from N-6-[(4- pyridylmethylamino)carbonyl]-pyridine-2-carboxylic acid methyl ester namely 1,2-bis[N,N'-6-(4- pyridylmethylamido)pyridyl-2-carboxyamido]pentane (L1) and 1,2-bis[N,N'-6-(4- pyridylmethylamido)pyridyl-2-carboxyamido]hexane (L2) have been successfully synthesized when reacted with diamines in 1:2 ratio. These new compounds were built from combination of 3 main components, as a trend requires for anion receptor which are (i) 2,6-pyridine dicarboxamide moieties as targeted anion binding host, (ii) amino methyl pyridine pendants arms as the flexible moieties and (iii) pentyl (-C5H10-) and hexyl (-C6H12-) unit as the spacer. Compounds L1-L2 were fully characterized by using elemental analyzer, Fourier transform infrared (FTIR) spectroscopy, gas chromatography-mass spectroscopy (GC-MS), ¹H, 2D NOESY and 13C Nuclear Magnetic Resonance (NMR) spectroscopies, and Ultraviolet-visible (UV-Vis) spectroscopies. In this study, anion titration methods were used to identify the affinity towards selected anions. The results showed that L1 (having a pentyl spacer) had the highest affinity towards phosphate anions as compared to L2, where the red shift changes were observed in the UV-vis spectrum at the amide region. [ABSTRACT FROM AUTHOR]

Tensor robust principal component analysis (TRPCA) aims at recovering the underlying low-rank clean tensor and residual sparse component from the observed tensor. The recovery quality heavily depends on the definition of tensor rank which has diverse construction schemes. Recently, tensor average rank has been proposed and the tensor nuclear norm has been proven to be its best convex surrogate. Many improved works based on the tensor nuclear norm have emerged rapidly. Nevertheless, there exist three common drawbacks: (1) the neglect of consideration on relativity between the distribution of large singular values and low-rank constraint; (2) the prior assumption of equal treatment for frontal slices hidden in tensor nuclear norm; (3) the missing convergence of whole iteration sequences in optimization. To address these problems together, in this paper, we propose a convex–concave TRPCA method in which the notion of convex–convex singular value separation (CCSVS) plays a dominant role in the objective. It can adjust the distribution of the first several largest singular values with low-rank controlling in a relative way and emphasize the importance of frontal slices collaboratively. Remarkably, we provide the rigorous convergence analysis of whole iteration sequences in optimization. Besides, a low-rank tensor recovery guarantee is established for the proposed CCSVS model. Extensive experiments demonstrate that the proposed CCSVS significantly outperforms state-of-the-art methods over toy data and real-world datasets, and running time per image is also the fastest. [ABSTRACT FROM AUTHOR]

Background Atopic dermatitis (AD) is characterized by skin barrier defects that are often measured by biophysical tools that observe the functional properties of the stratum corneum (SC). Objectives To employ in vivo infrared spectroscopy alongside biophysical measurements to analyse changes in the chemical composition of the SC in relation to AD severity. Methods We conducted an observational cross-sectional cohort study where attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy measurements were collected on the forearm alongside surface pH, capacitance, erythema and transepidermal water loss (TEWL), combined with tape stripping, in a cohort of 75 participants (55 patients with AD stratified by phenotypic severity and 20 healthy controls). Common FLG variant alleles were genotyped. Results Reduced hydration, elevated TEWL and redness were all associated with greater AD severity. Spectral analysis showed a reduction in 1465 cm–1 (full width half maximum) and 1340 cm–1 peak areas, indicative of less orthorhombic lipid ordering and reduced carboxylate functional groups, which correlated with clinical severity (lipid structure r = –0.59, carboxylate peak area r = –0.50). Conclusions ATR-FTIR spectroscopy is a suitable tool for the characterization of structural skin barrier defects in AD and has potential as a clinical tool for directing individual treatment based on chemical structural deficiencies. [ABSTRACT FROM AUTHOR]

The aim of this work is to quantitatively assess the wavefront phase of keratoconic eyes measured by the ocular aberrometer t·eyede (based on WaveFront Phase Imaging Sensor), characterized by a lateral resolution of 8.6 µm without requiring any optical element to sample the wavefront information. We evaluated the parameters: root mean square error, Peak-to-Valley, and amplitude of the predominant frequency (Fourier Transform analysis) of a section of the High-Pass filter map in keratoconic and healthy cohorts. Furthermore, we have analyzed keratoconic eyes that presented dark–light bands in this map to assess their period and orientation with the Fourier Transform. There are significant statistical differences (p value < 0.001) between healthy and keratoconic eyes in the three parameters, demonstrating a tendency to increase with the severity of the disease. Otherwise, the quantification of the bands reveals that the width is independent of eye laterality and keratoconic stage as orientation, which tends to be oblique. In conclusion, the quantitative results obtained with t·eyede could help to diagnose and monitor the progression of keratoconus. [ABSTRACT FROM AUTHOR]

The influence of apparent slip on oscillatory shear measurements of a viscoplastic microgel [0.6 wt. % of poly(acrylic acid)] is analyzed by Couette and parallel-plate rheometry and particle image velocimetry (Rheo-PIV). We first provide direct evidence of a critical shear stress for the onset of slip of the microgel under oscillatory (σos) and nonoscillatory measurements (σs). Afterward, we describe the effect of slip on oscillatory measurements via waveforms, Bowditch–Lissajous curves, Fourier transform (FT) rheology, PIV, and as a sequence of physical processes (SPP). The effect of slip is mainly observed at low oscillating frequencies. For amplitudes of the oscillating stresses σ0 ≤ σos, the microgel exhibits linear viscoelastic behavior with in-phase strain response. For σos< σ0 ≤ yield stress (σy), slip introduces a phase shift in the strain response with a forward-tilted waveform and "mango" shape Bowditch–Lissajous curves. Meanwhile, FT rheology shows negligible even harmonics. The strain measured by the rheometer does not match the true strain determined by PIV in the presence of slip, resulting in waveforms that depend on how the displacement distribution is interpreted. This result indicates a break in the symmetry of the flow, that is, the microgel response no longer follows the imposed oscillation, which makes any attempt to correct oscillatory data for slip complex. This behavior arises from recoil of the slipping microgel after reaching its maximum displacement in a cycle. Finally, we provide an overall picture of the kinematics of the process of yielding in the presence of slip as an SPP. [ABSTRACT FROM AUTHOR]

We theoretically investigate the propagation properties of a Laguerre higher order cosh Gaussian beam (LHOchGB) in a fractional Fourier transform (FRFT) optical system. Based on the Collins formula and the expansion of the hard aperture function into a finite sum of Gaussian functions, we derive analytical expressions for a LHOchGB propagating through apertured and unapertured FRFT systems. The analysis of the evolution of the intensity distribution at the output plane has shown from the obtained expressions, using illustrative numerical examples. The results show that the intensity distribution of the considered beam propagating in FRFT is significantly influenced by the source beam parameters and the parameters of the FRFT system. It is possible to demonstrate the potential benefits of the results obtained for applications in laser beam shaping, optical trapping, and micro-particle manipulation. [ABSTRACT FROM AUTHOR]

In this study, an effect that we will call entanglement closed loop (ECL) and that results from the implementation of entangled states through quantum Fourier transform (QFT) blocks, is presented. The dual-channel Bell test can be implemented using two linear polarizers (LP) or two half-wave plates (HWP). ECL allows us to verify that the arbitrary relocation of both the LPs and the HWPs is indifferent when it comes to reproducing the results of quantum mechanics. Implementations of two conspicuous relocations of the LPs on an optical table experimentally prove the existence of the entanglement closed loop. Finally, a new interpretation of quantum mechanics based on ECL, which explains the operation of a new family of quantum communications protocols, is presented. [ABSTRACT FROM AUTHOR]

BACKGROUND: Carboxymethylpachymaran (CMP) is created by carboxymethylating pachyman (PM), which increases its water solubility and enhances a number of biological activities. Traditional polysaccharides modified by carboxymethylation employ strong chemical techniques. Carboxymethylcellulose (CMC) has been used previously for liquid fermentation to carboxymethyl modify bacterial polysaccharides. This theory can be applied to fungal polysaccharides because Poria cocos has the ability to naturally utilize cellulose. RESULTS: CMC with different degrees of substitution (DS) (0.7, 0.9 and 1.2) were added to P. cocos fermentation medium, and CMPs with different DS (0.38, 0.56 and 0.78, respectively) were prepared by liquid fermentation. The physical and chemical properties and biological activities of the CMPs were determined. Their structures were confirmed by Fourier transform infrared (FTIR) spectroscopy and monosaccharide composition. With the increase of DS, the viscosity and viscosity‐average molecular weight of CMPs decreased, whereas polysaccharide content and water solubility increased, although the triple helix structure was not affected. The results of bioactivity assay showed that the higher the DS of CMPs, the higher the 2,2‐diphenyl‐1‐picrylhydrazyl radical scavenging ability, and the stronger the bacterial inhibition ability. CONCLUSION: The present study has developed a method for producing CMPs by P. cocos liquid fermentation. The results of the study confirm that enhancing the DS of CMP could effectively enhance its potential biological activity. The findings provide safe and reliable raw materials for creating CMP‐related foods and encourage CMP application in the functional food industry. © 2024 Society of Chemical Industry. [ABSTRACT FROM AUTHOR]

We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit δ (f ; Ω) which measures by how much the STFT of a function f ∈ L 2 (R) fails to be optimally concentrated on an arbitrary set Ω ⊂ R 2 of positive, finite measure. We then show that an optimal power of the deficit δ (f ; Ω) controls both the L 2 -distance of f to an appropriate class of Gaussians and the distance of Ω to a ball, through the Fraenkel asymmetry of Ω . Our proof is completely quantitative and hence all constants are explicit. We also establish suitable generalizations of this result in the higher-dimensional context. [ABSTRACT FROM AUTHOR]

This paper proposes a digital morphological filtering method based on a novel structuring element (SE) formulated using fractional Fourier transform (FrFT) and cross-convolution of window functions. The highlighting feature of this newly formulated filter is its flexibility in adding an adaptive nature to classical morphological filtering. Until now, every method listed in the literature makes a convenient assumption that noises corrupting ECG signal are Gaussian and model the filter around this assumption. Addressing this shortcoming, the first-of-its-kind filter adopts the α -stable distribution model (of which Gaussian distribution is a special case) of noise to better replicate the real-time noises interfering with ECG signals. The designed filter can suppress the noise and adapt to the changes in ECG signal morphology for better reconstruction. The proposed filter is tested on MIT-BIH Arrhythmia Database. The simulation results show improved performance in several quantitative metrics, demonstrating the superiority of our suggested method over the currently used state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

The cognition radar utilizes the dynamic waveform configuration to adapt to the environment to improve tracking performance. A novel tracking algorithm based on waveform selection is proposed to address the maneuvering aircraft tracking problem in clutter. Based on the modified current statistical (MCS) model, the modified probabilistic data association filter (MPDAF) is integrated with the square-root cubature Kalman filter (SCKF) to deal with the nonlinear measurement and the clutter. Additionally, the waveform library is established by applying the fractional Fourier transform (FRFT) to a base waveform, and a direct method is proposed to select the optimal waveform to minimize the posterior state error covariance matrix. The simulation results showed that, compared with the filters with the fixed waveform as well as the state-of-the-art algorithms, the proposed algorithm achieved higher estimation precision and lower track loss percentage while maintaining a low computational burden. [ABSTRACT FROM AUTHOR]

Titania is a functional oxide used as a catalyst and photocatalyst, which has various applications. Modifying the surface morphology and creating micro patterns on titania can significantly enhance its catalytic efficiency and utility in semiconductor devices. This study focuses on the fabrication of submicron patterns on titania using thermal nanoimprinting. The process involves the preparation of a high-viscosity sol consisting of 2-butoxyethanol, titanium butoxide, ethylene glycol, and water, followed by drying on a substrate to obtain a printable titania gel. We investigated the structural characteristics of this printable titania gel using Fourier transform infrared thermal analysis and high-energy X-ray diffraction. These structural analyses shed light on the critical factors affecting the growth of the Ti–O network within the gel and the effect of the organic content of the gel on its properties. [ABSTRACT FROM AUTHOR]

• Size-dependent near-surface response of FG elastic layer is investigated. • Size effects induced by material microstructures are modeled by couple stress elasticity theory. • Solution of surface loaded layer is derived in closed-form via Fourier transform method. • Efficient numerical scheme is implemented for layer under frictionless contacts. • Effects of length scale and model's parameters on contact response are highlighted. This paper focuses on a theoretical examination of the mechanical behavior of elastic layers made of functionally graded (FG) materials. It particularly highlights the impact of material microstructures by utilizing the couple stress theory to introduce FG characteristics of the coating material across the thickness direction, along with size effects. The study distinctively addresses both surface loading and contact problems, employing various indenter shapes and eccentric indentation forces. The Fourier transform is utilized to solve for displacements and stress fields resulting from surface tractions. The method for approximating the pressure distribution under the indenter is based on a collocation method with a simple discretization of the contact pressure. Brent's method is applied to determine the unknown contact region when using indenters with non-sharp edges. The results demonstrate that the shear modulus ratio and the intrinsic material length scale significantly influence the pressure intensity, highlighting a substantial dependence on the mechanical properties of materials under indentation force. The research also shows that the effect of the length scale and shear modulus ratio affects the limit eccentricity and tilt angle. The results highlight the necessity of considering both the size effect and material gradation when analyzing FG materials under mechanical stress. [ABSTRACT FROM AUTHOR]

Digital speech recognition is a challenging problem that requires the ability to learn complex signal characteristics such as frequency, pitch, intensity, timbre, and melody, which traditional methods often face issues in recognizing. This article introduces three solutions based on convolutional neural networks (CNN) to solve the problem: 1D-CNN is designed to learn directly from digital data; 2DS-CNN and 2DM-CNN have a more complex architecture, transferring raw waveform into transformed images using Fourier transform to learn essential features. Experimental results on four large data sets, containing 30,000 samples for each, show that the three proposed models achieve superior performance compared to well-known models such as GoogLeNet and AlexNet, with the best accuracy of 95.87%, 99.65%, and 99.76%, respectively. With 5-10% higher performance than other models, the proposed solution has demonstrated the ability to effectively learn features, improve recognition accuracy and speed, and open up the potential for broad applications in virtual assistants, medical recording, and voice commands. [ABSTRACT FROM AUTHOR]

Layered transition metal oxides are extensively considered as appealing cathode candidates for potassium‐ion batteries (PIBs) due to their abundant raw materials and low cost, but their further implementations are limited by slow dynamics and impoverished structural stability. Herein, a layered composite having a P2 and P3 symbiotic structure is designed and synthesized to realize PIBs with large energy density and long‐term cycling stability. The unique intergrowth of P2 and P3 phases in the obtained layered oxide is plainly characterized by X‐ray diffraction refinement, high‐angle annular dark field and annular bright field‐scanning transmission electron microscopy at atomic resolution, and Fourier transformation images. The synergistic effect of the two phases of this layered P2/P3 composite is well demonstrated in K+ intercalation/extraction process. The as‐prepared layered composite can present a large discharge capacity with the remarkable energy density of 321 Wh kg−1 and also manifest excellent capacity preservation after 600 cycles of K+ uptake/removal. [ABSTRACT FROM AUTHOR]

Lignin is a complex heteroaromatic polymer which is one of the most abundant and diverse biopolymers on the planet. It comprises approximately one third of all woody plant matter, making it an attractive candidate as an alternative, renewable feedstock to petrochemicals to produce fine chemicals. However, the inherent complexity of lignin makes it difficult to analyse and characterise using common analytical techniques, proving a hindrance to the utilisation of lignin as a green chemical feedstock. Herein we outline the tracking of lignin degradation by an alkaliphilic laccase in a semi-quantitative manner using a combined chemical analysis approach using Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) to characterise shifts in chemical diversity and relative abundance of ions, and NMR to highlight changes in the structure of lignin. Specifically, an alkaliphilic laccase was used to degrade an industrially relevant lignin, with compounds such as syringaresinol being almost wholly removed (95%) after 24 hours of treatment. Structural analyses reinforced these findings, indicating a >50% loss of NMR signal relating to β-β linkages, of which syringaresinol is representative. Ultimately, this work underlines a combined analytical approach that can be used to gain a broader semi-quantitative understanding of the enzymatic activity of laccases within a complex, non-model mixture. [ABSTRACT FROM AUTHOR]

Spatial‐variant micro/nano‐structures are widely utilized in metasurfaces to modulate optical wave‐fronts into arbitrary shapes, performing as a new generation of flat optics. To flexibly fabricate micro/nano‐structures in real time, an optical Fourier transform system modulated by a diaphragm and a binary optical element (BOE) is proposed. Theoretical analysis shows that light field at image plane is a multiple result of twice Fourier transform of diaphragm and BOE's transmission field, with its amplitude and phase distribution independently manipulated by diaphragm and BOE. Inversely, diaphragm and BOE can be designed to get customized interference fields, where four fields with different vectors are generated for instance. Utilizing these four fields for time division multiplexing exposure, fringes inside circle/ring shapes with variant orientations are produced in photoresist film. Furthermore, multiple spatial variant fields can be obtained simultaneously while more symmetric distributed apertures acted as diaphragm, which shows great potential for the fabrication of segmented or interleaved spatial‐variant micro/nano‐structures in addition. [ABSTRACT FROM AUTHOR]

Modulation instability of one-dimensional plane wave is demonstrated in nonlinear Kerr media with sine-oscillatory nonlocal response function and pure quartic diffraction. The growth rate of modulation instability, which depends on the degree of nonlocality, coefficient of quartic diffraction, type of the nonlinearity and the power of plane wave, is analytically obtained with linear-stability analysis. Different from other nonlocal response functions, the maximum of the growth rate in media with sine-oscillatory nonlocal response function occurs always at a particular wave number. Theoretical results of modulation instability are confirmed numerically with split-step Fourier transform. Modulation instability can be controlled flexibly by adjusting the degree of nonlocality and quartic diffraction. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for the diagnosis of electrical system conditions using fractional-order integral transforms for feature extraction. This work proposes three feature extraction algorithms using the Fractional Fourier Transform (FRFT), the Fourier Transform combined with the Mittag-Leffler function, and the Wavelet Transform (WT). Each algorithm extracts data from an electrical system to obtain a set of features that are classified by an Artificial Neural Network to determine the system's condition. The algorithms are utilized in diagnosing two types of electrical machine faults, one in a photovoltaic system, and another in classifying the power quality disturbances (PQDs). An optimization algorithm is suggested to find the optimal orders of integral transforms. The obtained results demonstrate the system's effective diagnosis, displaying superior performance in classifying the faults and PQDs with complex signals. [ABSTRACT FROM AUTHOR]

Lysozyme, a common antimicrobial agent, is widely used in the food, biopharmaceutical, chemical, and medicine fields. Rapid and effective isolation of lysozymes is an everlasting topic. In this work, ethylene vinyl alcohol (EVOH) copolymer nanofibrous membranes with a gradient porous structure used for lysozyme adsorption were prepared through layer-by-layer nanofiber wet-laying and a cost-efficient ultraviolet (UV)-assisted graft-modification method, where benzophenone was used as an initiator and 2-acrylamide-2-methylpropanesulfonic acid as a modifying monomer. As indicated in the Fourier Transform Infrared (FTIR) and X-ray photoelectric energy spectrometer (XPS) investigation, sulfonic acid groups were introduced on the surface of the modified nanofibrous membrane, which possessed the ability to adsorb lysozyme. Compared with membranes with homogenous porous structures, membranes with a gradient porous structure present higher static (335 mg/g) and dynamic adsorption capacities (216.3 mg/g). Meanwhile, the adsorption capacity remained high after five cycles of the adsorption–desorption process. The results can be attributed to the gradient porous structure rather than the highest porosity and specific surface area. This suggests that the membrane with comprehensive separation performance can be designed from the view of the transmembrane porous structure, which is of significance for the development of next-generation advanced chromatographic membranes. [ABSTRACT FROM AUTHOR]

In this paper, a one-dimensional (1-D) range profile of the hypersonic target enveloped by a plasma sheath is investigated. Firstly, the non-uniform property of the plasma sheath is studied and its impact on the wideband electromagnetic (EM) wave is analyzed. A wideband radar echo model for the plasma-sheath-enveloped hypersonic target is constructed. Then, by exploiting the relationship among the incident depth, reflection intensity, and plasma velocity, it reveals that distinct scatter points in various areas of the target will suffer from varying reflection intensity and coupled velocity, leading to severe defocusing in the range profile. To tackle this issue, a novel focusing algorithm combing the Fractional Fourier Transform (FRFT) with the CLEAN technique is developed, which independently calculates the coupled plasma velocity and compensates for the phase error via a series of iterative procedures. Finally, the influence of the plasma sheath on the 1-D range profile and the effectiveness of the proposed focusing algorithm are validated through simulations. [ABSTRACT FROM AUTHOR]

The instantaneous frequency (IF) is an important feature for the analysis of nonstationary signals. For IF estimation, the time–frequency representation (TFR)-based algorithm is used in a common class of methods. TFR-based methods always need the representation concentrated around the "true" IFs and the number of components within the signal. In this paper, we propose a novel method to adaptively estimate the IFs of nonstationary signals, even for weak components of the signals. The proposed technique is not based on the TFR: it is based on the frequency estimation operator (FEO), and the short-time Fourier transform (STFT) is used as its basis. As we know, the FRO is an exact estimation of the IF for weak frequency-modulated (FM) signals, but is not appropriate for strong FM modes. Through theoretical derivation, we determine that the fixed points of the FEOwith respect to the frequency are equivalent to the ridge of the STFT spectrum. Furthermore, the IF of the linear chirp signals is just the fixed points of the FEO. Therefore, we apply the fixed-point algorithm to the FEO to realize the precise and reliable estimation of the IF, even for highly FM signals. Finally, the results using synthetic and real signals show the utility of the proposed method for IF estimation and that it is more robust than the compared method. It should be noted that the proposed method employing the FEO only computes the first-order differential of the STFT for the chirp-like signals, while it can provide a result derived using the second-order estimation operator. Moreover, this new method is effective for the IF estimation of weak components within a signal. [ABSTRACT FROM AUTHOR]

Jamming recognition is a significant prior step to achieving effective jamming suppression, and the precise results of the jamming recognition will be beneficial to anti-jamming decisions. However, as the electromagnetic environment becomes more complex, the received signals may contain both suppression jamming and deception jamming, which is more challenging for existing methods focused on a single kind of jamming. In this paper, a recognition method for compound jamming based on a dual-channel neural network and feature fusion is proposed. First, feature images of compound jamming are extracted by the short-time Fourier transform and the wavelet transform. Feature images are then employed as inputs for the proposed network. During parallel processing in dual-channel, the proposed network can adaptively extract and learn task-relevant features via the attention modules. Finally, the output features in dual-channel are fused in the fusion subnetwork. Compared with existing methods, the proposed method can yield better recognition performance with less inference time. Additionally, compared with existing fusion strategies, the fusion subnetwork can further improve the recognition performance under low jamming-to-noise ratio conditions. Results with the semi-measured datasets also verify the feasibility and generalization performance of the proposed method. [ABSTRACT FROM AUTHOR]

Induction motors (IM) play a fundamental role in the industrial sector because they are robust, efficient, and low-cost machines. Changes in the environment, installation errors, or modifications to working conditions can generate faults in induction motors. The trend on IM fault detection is focused on the design techniques and sensors capable of evaluating multiple faults with various signals using non-invasive analysis. The methodology is based on processing electric current signals by applying the short-time Fourier transform (STFT). Additionally, the computation of the mean and standard deviation of infrared thermograms is proposed as main indicators. The proposed system combines both parameters by means of Support Vector Machine and k-nearest-neighbor classifiers. The development of the diagnostic system was done with digital hardware implementations using a Xilinx PYNQ Z2 card that integrates an FPGA with a microprocessor, thus taking advantage of the acquisition and processing of digital signals and images in hardware. The proposed method has proved to be effective for the classification of healthy (HLT), misalignment (MAMT), unbalance (UNB), damaged bearing (BDF), and broken rotor bar (BRB) faults with an accuracy close to 99%. [ABSTRACT FROM AUTHOR]

Long-term coherent integration (CI) can effectively improve the radar detection capability for high-speed targets. However, the range walk (RW) effect caused by high-speed motion significantly degrades the detection performance. To improve detection performance, this study proposes an improved algorithm based on the modified Radon inverse Fourier transform (denoted as IMRIFT). The proposed algorithm uses parameter searching for velocity estimation, designs a compensation function based on the relationship between velocity and distance walk and Doppler ambiguity terms, and performs CI based on the compensated signal. IMRIFT can achieve RW correction, avoid the blind-speed sidelobe (BSSL) effect caused by velocity mismatch, and improve detection performance, while ensuring low computational complexity. In addition, considering the relationship between energy concentration regions and bandwidth in the 2D frequency domain, a fast method based on IMIRFT is proposed, which can balance computational cost and detection capacity. Finally, a series of comparative experiments are conducted to demonstrate the effectiveness of the proposed algorithm and the fast method. [ABSTRACT FROM AUTHOR]

Activity recognition is one of the significant technologies accompanying the development of the Internet of Things (IoT). It can help in recording daily life activities or reporting emergencies, thus improving the user's quality of life and safety, and even easing the workload of caregivers. This study proposes a human activity recognition (HAR) system based on activity data obtained via the micro-Doppler effect, combining a two-stream one-dimensional convolutional neural network (1D-CNN) with a bidirectional gated recurrent unit (BiGRU). Initially, radar sensor data are used to generate information related to time and frequency responses using short-time Fourier transform (STFT). Subsequently, the magnitudes and phase values are calculated and fed into the 1D-CNN and Bi-GRU models to extract spatial and temporal features for subsequent model training and activity recognition. Additionally, we propose a simple cross-channel operation (CCO) to facilitate the exchange of magnitude and phase features between parallel convolutional layers. An open dataset collected through radar, named Rad-HAR, is employed for model training and performance evaluation. Experimental results demonstrate that the proposed 1D-CNN+CCO-BiGRU model demonstrated superior performance, achieving an impressive accuracy rate of 98.2%. This outperformance of existing systems with the radar sensor underscores the proposed model's potential applicability in real-world scenarios, marking a significant advancement in the field of HAR within the IoT framework. [ABSTRACT FROM AUTHOR]