Search

The windowed coupled fractional Fourier transform was recently proposed in the literature. It may be considered as a generalized version of the windowed fractional Fourier transform. In this study, we first present various basic properties of the windowed coupled fractional Fourier transform including linearity, shifting, modulation, parity, orthogonality relation, and inversion formula. Further, the close relation of the windowed coupled fractional Fourier transform with the two‐dimensional Fourier transform and the windowed fractional Fourier transform is studied. By combining the properties and relation, we derive several versions of the uncertainty inequalities related to the windowed coupled fractional Fourier transform. [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]

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]

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]

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]

The high‐entropy‐alloy (HEA) nanoparticles with four, five or more metals significantly can yield the developments of functional materials with excellent performances in various reactions. However, the underlying reaction mechanisms of heterogeneous catalysis for HEA have been rarely investigated, due to their diverse elements and complex compositions. In this study, we successfully synthesized the homogeneously dispersed Ru−Rh−Pd−Pt HEA with adjustable compositions, as the multiple‐atom‐site catalysts (MASC). In the NOx reduction performance tests, Ru0.4 (Rh0.33Pd0.33Pt0.33)0.6 MASC showed the highest activity, which was significantly improved compared to that of the best monometal Rh, with the light‐off temperature decreasing by ca. 50 °C. The Fourier transform infrared measurements revealed that the outstanding activity of Ru−Rh−Pd−Pt MASC was attributable to the well‐coupled elementary steps of the CO adsorption, NO adsorption, NO dissociation and O spillover on the Ru, Rh, Rh−Pd and Pt sites, respectively, which explained the first clear reaction mechanism in heterogeneous catalysis for HEA. [ABSTRACT FROM AUTHOR]

The high‐entropy‐alloy (HEA) nanoparticles with four, five or more metals significantly can yield the developments of functional materials with excellent performances in various reactions. However, the underlying reaction mechanisms of heterogeneous catalysis for HEA have been rarely investigated, due to their diverse elements and complex compositions. In this study, we successfully synthesized the homogeneously dispersed Ru−Rh−Pd−Pt HEA with adjustable compositions, as the multiple‐atom‐site catalysts (MASC). In the NOx reduction performance tests, Ru0.4 (Rh0.33Pd0.33Pt0.33)0.6 MASC showed the highest activity, which was significantly improved compared to that of the best monometal Rh, with the light‐off temperature decreasing by ca. 50 °C. The Fourier transform infrared measurements revealed that the outstanding activity of Ru−Rh−Pd−Pt MASC was attributable to the well‐coupled elementary steps of the CO adsorption, NO adsorption, NO dissociation and O spillover on the Ru, Rh, Rh−Pd and Pt sites, respectively, which explained the first clear reaction mechanism in heterogeneous catalysis for HEA. [ABSTRACT FROM AUTHOR]

BACKGROUND: Sugar beet is one of the most produced industrial plants in the world, and during manufacturing it produces a large quantity of leaf waste. Because this waste is rich in protein, this study aimed to identify an efficient method for producing large‐scale protein concentrate from sugar beet leaves. RESULTS: Results showed that protein extraction from fresh leaves was more effective than from dried leaves. Maximum protein extraction was achieved at pH 9, compared with pH 7 or 8. Blanching as a pretreatment reduced protein yield during isoelectric precipitation, with a yield of 2.31% compared to 20.20% without blanching. Consequently, blanching was excluded from the extraction process. After extraction, isoelectric precipitation, heat coagulation, and isoelectric–ammonium sulfate precipitation were compared. Although the latter resulted in the highest protein yield, Fourier transform infrared analysis revealed that excessive salt was not removed during dialysis, making it unsuitable for scale‐up due to its additional cost and complexity. Therefore, isoelectric precipitation was selected as the appropriate method for protein precipitation from sugar beet leaves. To increase yield, extractions were assisted by ultrasound or enzyme addition. Ultrasound‐assisted extraction resulted in an increased protein yield from 20.20% to 28.60%, while Pectinex Ultra SP‐L‐assisted extraction was the most effective, increasing protein yield from 20.20% to 38.09%. CONCLUSION: Proteins were extracted from fresh sugar beet leaves using optimum conditions (50 °C, 30 min, pH 9) and precipitated at isoelectric point, with enzymatic‐assisted extraction yielding the maximum protein recovery. © 2023 The Authors. Journal of The Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry. [ABSTRACT FROM AUTHOR]

An integral geometry problem is considered on a family of n$n$‐dimensional surfaces of revolution whose vertices lie on a hyperplane and directions of symmetry axes are fixed and orthogonal to this plane, in Rn+1$\mathbb {R} ^{n+1}$. More precisely, the reconstruction of a function f(x,y)$f(\mathbf {x,}y)$, x∈Rn$\mathbf {x}\in \mathbb {R} ^{n}$, y∈R$y\in \mathbb {R}$, from the integrals of the form f(x,y)dx$f(\mathbf {x,}y) d\mathbf {x}$ extended over a chosen side of all surfaces of revolution of a given family is investigated. Unlike the usual Radon transform, the integrals considered here are not taken with respect to the surface area element. A Fourier slice identity and a backprojection‐type inversion formula are obtained with a method based on the Fourier and Hankel transforms. The reconstruction procedure and some analytical and numerical implementations of the obtained inversion formulas in the cases of n=1$n=1$ and n=2$n=2$ are provided. [ABSTRACT FROM AUTHOR]

In this study, three kinds of electrohydrodynamic atomization (EHDA) processes (electrospraying, electrospinning, and coaxial electrospinning) are implemented to create hydroxypropyl methylcellulose (HPMC) based ultra‐thin products for providing the fast dissolution of a poorly water‐soluble drug ketoprofen (KET). An EHDA apparatus, characterized by a novel spinneret, is homemade for conducting the three processes. The three types of products are electrospun nanofibers E1, electrosprayed microparticles E2, and core‐shell nanofibers E3. SEM and TEM results indicate that they have the anticipated morphologies and inner structures. X‐ray diffraction and Fourier Transform Infrared results verify that KET is mainly amorphous in all the composites due to its fine compatibility with HPMC. In vitro dissolution tests demonstrate that the drug rapid release performances has an order of E3>E1>E2≫KET powders. The fast dissolution mechanisms are suggested and the advantages of the three products are compared. The super performance of E3 in furnishing the rapid release is attributed to a synergistic action of small size (of the shell thickness), high porosity, amorphous state of drug, and the solubility of HPMC. EHDA nanostructures can support the development of nano drug delivery systems (DDSs) through tailoring the spatial distribution of drug molecules within the nano products. [ABSTRACT FROM AUTHOR]

In this paper, we study a few versions of the uncertainty principle for the short‐time Fourier transform on the lattice Zn×Tn$\mathbb {Z}^n \times \mathbb {T}^n$. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho–Stark's uncertainty principle, Benedicks‐type uncertainty principle, Heisenberg‐type uncertainty principle, and local uncertainty inequality for this transform on Zn×Tn$\mathbb {Z}^n \times \mathbb {T}^n$. Also, we obtain the Heisenberg‐type uncertainty inequality using the k$k$‐entropy of the short‐time Fourier transform on Zn×Tn$\mathbb {Z}^n \times \mathbb {T}^n$. [ABSTRACT FROM AUTHOR]

Chip‐based optical frequency combs address the demand for compact, bright, coherent light sources of equidistant phase‐locked lines. Traditionally, the Fourier Transform Spectroscopy (FTS) technique is considered a suboptimal choice for resolving comb lines in chip‐based sensing applications due to the requirement of long optical delays, and spectral distortion from the instrumental line shape. Here, a sub‐nominal resolution FTS technique is developed that extracts the comb's offset frequency in any spectral region directly from the measured interferogram without resorting to nonlinear f$f$‐to‐2f$2f$ interferometry. This in turn enables 10's of MHz resolution spectrometry with millimeter optical retardations currently limited by the emission linewidth and phase noise of the used lasers. Low‐pressure Doppler‐broadened absorption lines probed by widely‐tunable chip‐scale mid‐infrared optical frequen with electrical pumping are fully resolved over a span of tens of nanometers. This versatile technique paves the way for compact, electrostatically‐actuated, or even all‐on‐chip high‐fidelity FTS, and can be readily applied to boost the resolution of existing commercial instruments with compact interferometers several hundred times. [ABSTRACT FROM AUTHOR]

We generalize Beurling's theorem to the octonion Fourier transform for octonion‐valued functions. Despite challenges such as the failure of the octonion Fourier transform to change differentiation into multiplication and the absence of the octonionic Plancherel's theorem, we establish the octonionic Beurling theorem for Hermite functions on ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$ by introducing an integral condition involving the octonion Fourier transform. This extension of uncertainty principles by Hardy, Gelfand–Shilov, and Cowling–Price to the octonionic setting demonstrates that the function and its Fourier transform cannot have arbitrary Gaussian decay simultaneously. [ABSTRACT FROM AUTHOR]

An implementation of Slater‐type spherical scattering factors for X‐ray and electron diffraction for elements in the range Z = 1–103 is presented within the software Olex2. Both high‐ and low‐angle Fourier behaviour of atomic electron density and electrostatic potential can thus be addressed, in contrast to the limited flexibility of the four Gaussian plus constant descriptions which are currently the most widely used method for calculating atomic scattering factors during refinement. The implementation presented here accommodates the increasing complexity of the electronic structure of heavier elements by using complete atomic wavefunctions without any interpolation between precalculated tables or intermediate fitting functions. Atomic wavefunctions for singly charged ions are implemented and made accessible, and these show drastic changes in electron diffraction scattering factors compared with the neutral atom. A comparison between the two different spherical models of neutral atoms is presented as an example for four different kinds of X‐ray and two electron diffraction structures, and comparisons of refinement results using the existing diffraction data are discussed. A systematic but slight improvement in R values and residual densities can be observed when using the new scattering factors, and this is discussed relative to effects on the atomic displacement parameters and atomic positions, which are prominent near the heavier elements in a structure. [ABSTRACT FROM AUTHOR]

In this study, we propose a frequency‐domain autocorrelation as an imaging condition for time‐reversal imaging. The previous imaging conditions in time‐reversal imaging require time‐domain calculations such as inverse Fourier transform. The computational burden of these calculations is critical; therefore, time‐reversal imaging is not the proper method for real‐time event localization. We exclude these time‐domain calculations for efficiency. Instead, the maximum amplitude position of the frequency‐domain autocorrelation of the time‐reversal wavefield is determined as a source location. We conducted numerical tests to validate our imaging condition. The synthetic data test shows that our proposed algorithm provides a more credible source localization result than the conventional grid‐search method does in a noisy environment even using only one frequency component with many receivers. We also applied our algorithm to two real datasets acquired from the small monitoring network in Pohang. The real‐data test shows a comparable result with the result of the grid‐search method. [ABSTRACT FROM AUTHOR]

Temporal dispersion correction of second‐order finite‐difference time stepping for numerical wave propagation modelling exploits the fact that the discrete operator is exact but for the wrong frequencies. Mapping recorded traces to the correct frequencies removes the numerical error. Most of the implementations employ forward and inverse Fourier transforms. Here, it is noted that these can be replaced by a series expansion involving higher time derivatives of the data. Its implementation by higher‐order finite differencing can be sensitive to numerical noise, but this can be suppressed by enlarging the stencil. Tests with the finite‐element method on a homogeneous acoustic problem with an exact solution show that the method can achieve the same accuracy as higher‐order time stepping, similar to that obtained with Fourier transforms. The same holds for an inhomogeneous problem with topography where the solution on a very fine mesh is used as reference. The series approach costs less than dispersion correction with the Fourier method and can be used on the fly during the time stepping. It does, however, require a wavelet that is sufficiently many times differentiable in time. [ABSTRACT FROM AUTHOR]

There is a growing interest in quantum image processing (QIP) that rose from the desire to exploit the properties of quantum computing to improve the performance of classical techniques and their applications. Since the introduction of a quaternion by Hamilton in 1843, quaternions had been used in a lot of applications. We show how the quantum states and quantum operators work in the field of quaternions and how we can use it to extend the quantum complex Fourier transform (QCFT) to the quantum quaternion Fourier transform (QQFT). We propose for the first time the novel algorithm for the QQFT. We explain the impossibility of the use of convolution in quantum image processing; we design filters in the quaternion Fourier spectrum and the space domain an edge detector and a quantum median filter. [ABSTRACT FROM AUTHOR]

The present work investigates fluorescent polymer dispersion in the cholesteric liquid crystal (LC) as a function of temperature and concentration of polymer. The dielectric parameters of the cholesteric LC are determined by measuring capacitance and inductance with the function of the frequency and temperature. The material used for doping is a polymer‐poly[(4,4′‐hexafluoroisopropylidene) diphthalic anhydride‐alt‐3,6‐diaminoacridine hemisulfate] and it is one concentration doped in pure cholesteryl stearate. The temperature dependence of dielectric permittivity has been discussed for the pure and polymer‐doped system. In addition to this Fourier transform infra‐red (FTIR) spectroscopy has also been performed to understand the interaction between cholesteric LC and polymer molecules. [ABSTRACT FROM AUTHOR]

In the present study, poly(N‐Isopropylacrylacrylamide‐co‐N‐tertiarybutylacrylamide‐co‐hydroxyethylcrylamide) (NIPAM‐co‐NTBA‐co‐HEAAm) hydrogels are prepared with variation of molar ratio of hydrophilic HEAAm and hydrophobic NTBA. The prepared hydrogels are characterized with elemental analysis and Fourier transform infrared (FTIR) spectroscopy. The thermodynamics of swelling properties of poly(NIPAM‐co‐NTBA‐co‐HEAAm) hydrogels have also been discussed. The experimental C/N ratios are comparable with the theoretical value. The enthalpy change of mixing ∆Hmix, entropy change of mixing ∆Smix, free energy change of mixing ∆Gmix are determined for swelling of hydrogels at 25 °C. The value of total free energy of hydrogel swelling is found to be negative which confirms the lower critical solution temperature (LCST) exhibited in all hydrogels and the volume change transition shows the thermoresponsive behavior. The values of ∆Smix increase and ∆Gmix decrease with increasing amount of hydrophobic NTBA content in the hydrogels. The values of free energy change of elasticity (∆Gel) are found to be increased with increasing the hydrophobic NTBA content followed by decrease in swelling percentage. Also, the transition temperature of the hydrogel is found to be decreased with increasing the hydrophobic NTBA. [ABSTRACT FROM AUTHOR]

BACKGROUND: In the present study, the insoluble fraction of Persian gum (IFPG) was modified with octenyl succinic anhydride (OSA) and its various properties were assessed. In addition, the effect of OSA‐IFPG on the rheological and textural properties of dairy cream was investigated. RESULTS: Suitable conditions for achieving a degree of substitution (DS) of 0.023 were found at pH 9, IFPG concentration 4 wt%, OSA concentration 10 wt% and a temperature of 40 °C, within 120 min. The carbonyl group attachment in OSA‐IFPG was also confirmed via Fourier transform infrared and H‐nuclear magnetic resonance spectroscopy (1H‐NMR). While the X‐ray diffraction test indicated no significant changes in the structure of the IFPG after modification with OSA, esterification increased the negative charge density, decreased thermal decomposition temperature and increased the emulsifying capacity to 100%, which was obtained for the first time. The use of OSA‐modified IFPG in creams augmented the complex viscosity, loss and storage modulus, while also demonstrating the creation of a pseudo‐gel network. The hardness and adhesiveness of the texture increased, which can be explained by the formation of a compact structure and reduced particle size. CONCLUSION: Overall, OSA‐IFPG with hydrophilic and hydrophobic sections may function as an emulsifier and be recommended as a safe source of hydrocolloids for emulsion stability. It can also provide a positive physical structure when added to dairy cream, even if the fat concentration is lower than usual. © 2023 Society of Chemical Industry. [ABSTRACT FROM AUTHOR]

Two‐stage polymerizing‐then‐degrading networks are achieved by exposure to a single near UV light source, by sequentially performing thiol–ene photopolymerization and radical‐mediated thioaminal scission. To understand the mechanisms involved, synthesis of model thioaminal small molecules shows photo‐activated thioaminal scission produces thioamide moieties, identifiable by distinct NMR singlets at 3.29 and 3.26 ppm and a Fourier Transform IR (FTIR) peak ≈1530 cm−1. The scission process is proposed to occur via ß‐scission of the carbon next to the sulfur atom and is found to be influenced by thiol substitution on the thioaminal, leading to scission conversion increasing from 5 ± 1 to 39 ± 3% and scission time decreasing from 6 to 2 min as the thiols become progressively more substituted. Thioaminal scission occurs semi‐orthogonally with radical‐mediated thiol–ene reactions; the thiol–ene reaction achieves near quantitative yield within the first 0.5 min while thioaminal scission requires a further 5–15 min. This semi‐orthogonality is exploited to create two‐stage polymerizing‐then‐degrading networks, with both regimes dependent on total light dose from a single light source and the transition occurring ≈2 J cm−2 under these exposure and polymerization conditions. This work establishes thioaminals as a new photo‐mediated scission chemistry and a means to create multi‐stage, light‐activated networks. [ABSTRACT FROM AUTHOR]

A recently developed linear convolution filter based on Hirschman theory has shown its advantage in saving computations compared with other convolution filters. Here, the Hirschman convolution filter is improved with the use of the split‐radix algorithm and explore its latency‐reduced advantage for the first time. A comparison of hardware resources in Field Programmable Gate Array (FPGA) between the proposed Hirschman‐based filter and other convolution filters is presented. Simulation results indicate that the split‐radix Hirschman convolution filter achieves a promising reduction in latency by 18.15% on average with an acceptable power consumption rise by about 3.05%. In the case of a device capacity limited implementation, the proposed Hirschman convolution filter is still computationally attractive as it uses a small‐size originator function instead of larger Fourier transform. [ABSTRACT FROM AUTHOR]

Taking the megacity of Beijing as an example, a short‐time Fourier transform (STFT) method was employed to extract the multi‐timescale evolution pattern of the canopy urban heat island intensity (CUHII) during 2000–2020. The STFT of CUHII showed a close relationship between the evolution of the CUHII in Beijing and the background meteorological forcing at intra‐annual, weather and intra‐daily scales. The intra‐annual‐scale spectrum of CUHII exhibited an increasing trend with obvious seasonal variation of the canopy urban heat island (CUHI). The intra‐daily‐scale spectrum of CUHII showed an increasing trend with the nighttime CUHI developing faster. Increasing Western Pacific Subtropical High intensity can enhance the seasonal and diurnal fluctuations of CUHII. The weather‐scale spectrum of CUHII is controlled by weather system evolution, showing that the frequency of cold/heat waves (CWs/HWs) in Beijing was significantly negatively correlated with the weather‐scale spectral intensity of the CUHII. CWs and HWs can increase the CUHII for a long duration. Plain Language Summary: The canopy urban heat island (CUHI) phenomenon can affect human health and the ecological environment, and its multi‐timescale variability brings great uncertainty to the study of urban climates worldwide. In this study, taking the megacity of Beijing as an example, a novel short‐time Fourier transform (STFT) method was used to extract the multi‐timescale pattern of the CUHI intensity (CUHII) during 2000–2020. The STFT of CUHII showed a close relationship between the CUHI and the background meteorological forcing at intra‐annual, weather and intra‐daily scales. The intra‐annual spectrum of CUHII showed an increasing trend with a V‐shaped mode. The local climatic backgrounds of different cities can lead to differences in the seasonal development of the CUHI. The intra‐daily spectrum of CUHII showed an increasing trend due to the asymmetry in the day/night development of the CUHI. Increasing Western Pacific Subtropical High Intensity can enhance the seasonal and diurnal fluctuations of CUHII. The weather‐scale spectrum of CUHII was mainly controlled by weather system evolution, showing that cold waves and heat waves can increase the CUHII over a long duration. Our findings indicate that the evolution of CUHII is a nonlinear and complex process that is directly related to multi‐timescale background climate forcing. Key Points: Using a short‐time Fourier transform to study the multi‐timescale evolution of the canopy urban heat island intensity (CUHII)Close relationships existed between CUHII and the background meteorological forcing at intra‐annual, intra‐daily, and weather scalesThe frequency of cold/heat waves in Beijing showed a significant negative correlation with the weather‐scale spectral intensity of the CUHII [ABSTRACT FROM AUTHOR]

In this paper, we introduce a fuzzy Fourier sine transform decomposition as an analytical solution of a fuzzy wave equation under generalized Hukuhara partial differentiability. Since the fuzzy transforms have already been proven to solve several problems in different fields, they propel us to utilize them as a practical and appropriate way to solve the wave equation. The theorems and properties are demonstrated in detail, then the efficiency of the proposed approach is confirmed through solving several examples. [ABSTRACT FROM AUTHOR]

The influence of ion irradiation on intrinsic lattice stress and phase transition is closely related to the irradiation resistance of high‐entropy ceramics. In this study, the ion‐induced response of high‐entropy‐stabilized o‐(ZrHfTiSn)O2 ceramic was investigated under Au2+ irradiation with different fluences. The results revealed that high‐fluence irradiation caused the minimal (orthorhombic‐to‐triclinic) phase transformation underneath the ion‐induced amorphous layer via. fast fourier transformation (FFT) pattern. The cation recombination led to cation rearrangement followed by the increase of lattice expansion induced stress. The lattice stability of residual crystal grains in the mixed layer was significantly improved after lattice rearrangement. This was evidenced by the fact that the X‐ray diffraction profile of the lattice remained unchanged, whereas the selected area electron diffraction (SAED) image exhibited drastic variations with the increase of irradiation fluence. Therefore, irradiation‐induced lattice rearrangement seems to be a reliable way to improve radiation resistance of high‐entropy ceramics. [ABSTRACT FROM AUTHOR]

The Lp$L_p$ Busemann–Petty problem for 00$\varepsilon >0$ small enough, if K is an Lp$L_p$ intersection body and L is a star body such that for any u∈Sn−1$u\in S^{n-1}$, the following inequality: ∥u∥IpK−p≤∥u∥IpL−p+ε$$\begin{equation*} \Vert u\Vert _{I_pK}^{-p}\le \Vert u\Vert _{I_pL}^{-p}+\varepsilon \end{equation*}$$implies V(K)n−pn≤V(L)n−pn+Cε,$$\begin{equation*} V(K)^{\frac{n-p}{n}}\le V(L)^{\frac{n-p}{n}}+C\varepsilon , \end{equation*}$$where ∥·∥IpK$\Vert \cdot \Vert _{I_pK}$ is the Minkowski functional of IpK$I_pK$, and C is a positive number depending only on p and n. Moreover, we also prove the linear stability and separation results for the negative answer of the Lp$L_p$ Busemann–Petty problem. [ABSTRACT FROM AUTHOR]

Regularization and interpolation of 3D offset classes prior to imaging are an important and challenging step in the marine seismic data processing flow. Here we describe how to perform this task using a deep neural network, and we explain how to overcome the challenge of creating a suitable training data set. The training data set is generated by de‐migrating stacked pre‐stack depth migration images. For each offset class volume, we de‐migrate the pre‐stack depth migrated stacked image into two configurations: (i) the original survey configuration consisting of the recorded source/receiver positions and (ii) an 'Ideal' survey configuration with constant offset and azimuth for each 3D offset class. The training creates a 3D convolutional encoder–decoder model that will regularize and interpolate seismic data. The convolutional encoder–decoder is trained on 3D sliding windows in each 3D offset cube to map from (i) to (ii), i.e. to map the original survey configuration with irregular and sparse sampling into the fully sampled regular offset cubes suitable for offset‐based migration, such as Kirchhoff migration. Such migration algorithms rely on regular and sufficiently dense sampling to achieve constructive interference to image the structures and destructive interference to suppress migration noise. We test the new method on one synthetic and one field data example and show that it performs better than a standard regularization/interpolation method based on anti‐leakage Fourier transform, especially for the smallest offset classes. On the synthetic data, we also demonstrate that the convolutional encoder–decoder method preserves the amplitude versus offset as well as the standard method. [ABSTRACT FROM AUTHOR]

The utilization of handwritten electronic signatures has expanded in various application scenarios, leading to an increased demand for identification. Unlike handwriting signatures, handwritten electronic signatures offer the advantage of extracting dynamic feature data, including writing pressure, velocity, and acceleration. In this study, the Fourier transform was employed to extract 18 characteristics from the time domain and frequency domain of writing pressure, velocity, and acceleration. The experimental findings revealed distinguishable differences between genuine signatures and random forgeries in writing pressure. However, no statistically significant differences were observed in writing velocity and writing acceleration. Moreover, significant differences were detected in most characteristics when comparing genuine signatures with freehand imitation forgeries and tracing imitation forgeries. The canonical discriminant analysis was performed between the genuine and Non‐genuine signatures; the cross‐validation estimated the discriminating power of these characteristics with a satisfactory result. The study proposed a new approach to analyzing handwritten electronic signatures using time‐domain and frequency‐domain characteristics and demonstrated its effectiveness in the examination. [ABSTRACT FROM AUTHOR]

Tridentinosaurus antiquus represents one of the oldest fossil reptiles and one of the very few skeletal specimens with evidence of soft tissue preservation from the Cisuralian (Early Permian) of the Italian Alps. The preservation and appearance of the fossil have puzzled palaeontologists for decades and its taphonomy and phylogenetic position have remained unresolved. We reanalysed T. antiquus using ultraviolet light (UV), 3D surface modelling, scanning electron microscopy coupled with energy dispersive spectroscopy (SEM‐EDS), micro x‐ray diffraction (μ‐XRD), Raman and attenuated total reflectance Fourier transformed infrared (ATR‐FTIR) spectroscopy to determine the origin of the body outline and test whether this represents the remains of organically preserved soft tissues which in turn could reveal important anatomical details about this enigmatic protorosaur. The results reveal, however, that the material forming the body outline is not fossilized soft tissues but a manufactured pigment indicating that the body outline is a forgery. Our discovery poses new questions about the validity of this enigmatic taxon. [ABSTRACT FROM AUTHOR]

To solve the problem of target recognition for flying‐birds and biomimetic flapping‐wing unmanned aerial vehicles (UAVs), a rectangular‐trapezoidal composite scattering model for lidar detection of bird wings has been proposed and established. According to the model, the influence of different line‐of‐sight angles on the time–frequency distribution characteristics of laser micro‐Doppler under the same flapping wing motion was simulated and studied. Then, the flapping‐wing frequency and maximum frequency shift are extracted based on the two‐dimensional Fourier transform and the least squares method. When signal noise ratio = 5 dB, the accuracy rate of flapping‐wing frequency extraction can reach at 100%, the maximum relative error of frequency shift for inner contour extraction is less than 3.0%, and the maximum relative error of frequency shift for outer contour extraction is less than 7.2%. [ABSTRACT FROM AUTHOR]

In this paper, mechanic–electric–circuit coupling algorithm based on the finite‐difference time‐domain (FDTD) method is proposed to analyze a one‐order microwave bulk acoustic wave (BAW) filter. FDTD method is used to solve the coupled mechanic–electric–circuit system equations to obtain the voltage and current at port position of the BAW filter in the time domain. Then S parameters of the BAW filter in the frequency domain are calculated using the Fourier transform. In our work, a one‐order BAW filter consists of two film bulk acoustic resonators (FBARs) by means of series and parallel. These two FBARs in the BAW filter are coupled together through an equivalent electrical connection. Similarly, multiphysical mechanic–electric–circuit analysis of the BAW filter is implemented in the commercial software COMSOL, which is realized by the time‐domain finite element method. The accuracy of the proposed method is verified by comparison with simulation results in COMSOL. In addition, the computational time and memory of the proposed method have obvious advantages over those of COMSOL. [ABSTRACT FROM AUTHOR]

Summary: Jaggery, a natural unrefined sweetener, is considered as a nutraceutical due to richness in minerals and phytochemicals. The present study intended to utilise liquid jaggery at 0–100% levels in place of refined sugar (sucrose) to develop a pumpkin‐based functional toffee. Five different formulations were prepared and impact of sugar replacement was assessed by evaluating quality characteristics of prepared toffees. Compared to control, jaggery incorporation significantly (P < 0.05) increased the physicochemical parameters, except total sugars while enhancing bioactive constituents (ascorbic acid, carotenoids, and total phenols) and mineral elements which was also confirmed using Fourier transform infrared analysis and ICP‐AES analysis. Jaggery‐based formulations presented a significantly (P < 0.05) lower hardness and darker appearance compared to control. Among the various formulations, toffee containing intermediate replacement percentage (50%) showed the highest overall acceptability (8.09 on a 9‐point hedonic scale) which suggested that sugar replacement up to 50% with liquid jaggery was highly desirable. [ABSTRACT FROM AUTHOR]

Nuclear magnetic resonance (NMR) spectral analysis of biofluids can be a time‐consuming process, requiring the expertise of a trained operator. With NMR becoming increasingly popular in the field of metabolomics, there is a growing need to change this paradigm and to automate the process. Here we introduce MagMet, an online web server, that automates the processing and quantification of 1D 1H NMR spectra from biofluids—specifically, human serum/plasma metabolites, including those associated with inborn errors of metabolism (IEM). MagMet uses a highly efficient data processing procedure that performs automatic Fourier Transformation, phase correction, baseline optimization, chemical shift referencing, water signal removal, and peak picking/peak alignment. MagMet then uses the peak positions, linewidth information, and J‐couplings from its own specially prepared standard metabolite reference spectral NMR library of 85 serum/plasma compounds to identify and quantify compounds from experimentally acquired NMR spectra of serum/plasma. MagMet employs linewidth adjustment for more consistent quantification of metabolites from higher field instruments and incorporates a highly efficient data processing procedure for more rapid and accurate detection and quantification of metabolites. This optimized algorithm allows the MagMet webserver to quickly detect and quantify 58 serum/plasma metabolites in 2.6 min per spectrum (when processing a dataset of 50–100 spectra). MagMet's performance was also assessed using spectra collected from defined mixtures (simulating other biofluids), with >100 previously measured plasma spectra, and from spiked serum/plasma samples simulating known IEMs. In all cases, MagMet performed with precision and accuracy matching the performance of human spectral profiling experts. MagMet is available at http://magmet.ca. [ABSTRACT FROM AUTHOR]

Small‐angle X‐ray scattering (SAXS) which records reciprocal‐space signals with characteristic Bessel‐type oscillations is a powerful technique for studying nanoparticles. However, the size polydispersity (or size distribution) of nanoparticles in an ensemble sample smears the oscillational peaks and valleys in the SAXS profile, making it difficult to extract accurate real‐space information (e.g. three‐dimensional geometry) on the nanoparticles. In this work, a method capable of eliminating the size‐distribution‐induced smearing effect from SAXS profiles by taking the known size‐distribution function into consideration has been developed. The method employs a penalized iterative regression to fit the pair distance distribution function (PDDF) derived from a SAXS profile, recovering the representative PDDF of the nanoparticles. The method has been evaluated with a series of nanoparticle systems of various shapes and size distributions, showing their PDDF profiles to have high fidelity to the reference ideal PDDF profiles. Inverse Fourier transformation of the recovered PDDF profiles gives SAXS profiles presenting the characteristic Bessel‐type oscillations, enabling reconstruction of the representative three‐dimensional geometry of the nanoparticles. This method will help in the use of SAXS to image synthesized colloidal nanoparticles where size polydispersity is inevitable. [ABSTRACT FROM AUTHOR]

Two novel oxygen‐containing imidazo[1,2‐d][1,2,4]oxadiazole heterocycle compounds 2 and 3 were successfully synthesized by oxidation of the aminofurazan group. Compounds 2 and 3 were fully characterized by Fourier Transform Infrared, multinuclear NMR spectroscopy, elemental analysis, and single‐crystal X‐ray diffraction. Their properties were evaluated by measured density, impact, and friction sensitivities, calculated heat of formation, and detonation performances. Compound 2 has high density (1.87 g cm−3), good detonation velocity and pressure (D:8690 m s−1, P: 33.3 GPa), acceptable sensitivity (IS: 12 J, FS: 144 N), and its overall performance is comparable to RDX. Compound 3 has a better sensitivity (IS: 28 J, FS: 252 N), but the detonation performance is average (D:8008 m s−1, P: 27.4 GPa), which may be caused by its low packing index (70.9%) affecting its density (1.78 g cm−3). [ABSTRACT FROM AUTHOR]

Chitosan (CH) is a very well‐known biopolymer that has been widely used for the development of biomaterials with a wide range of applications in the biomedical field, such as the preparation of hydrogels, owing to its outstanding anti‐inflammatory, antibacterial and antifungal properties, biocompatibility and biodegradability, although they present limited mechanical properties. Chemical crosslinking is one of the most recurrent strategies for the reinforcement of these structures and, above all, crosslinking with natural‐origin compounds that do not compromise their biocompatibility is considered a hot topic in this research field. D‐fructose (F), obtained from the hydrolyzation and further isomerization of starch, an abundant raw material and genipin (G), which is extracted from the fruits of Gardenia jasminoides Ellis are used as natural crosslinkers. Chitosan‐based hydrogels crosslinked with each crosslinking agent are prepared and characterized through Fourier transform infrared (FTIR) spectroscopy, crosslinking and swelling degree determination, rheological, microstructural, and biological studies. The results demonstrate that crosslinking with G is more beneficial for chitosan‐based hydrogels since these samples showed more compact structures and better rheological performance. Additionally, excellent biological in vitro behavior due to the crosslinking with G, unlike that of F. [ABSTRACT FROM AUTHOR]

Beginning with the work of Landau, Pollak and Slepian in the 1960s on time‐band limiting, commuting pairs of integral and differential operators have played a key role in signal processing, random matrix theory, and integrable systems. Previously, such pairs were constructed by ad hoc methods, which essentially worked because a commuting operator of low order could be found by a direct calculation. We describe a general approach to these problems that proves that every point W of Wilson's infinite dimensional adelic Grassmannian Grad$\operatorname{{\mathrm{Gr}^{\mathrm{ad}}}}$ gives rise to an integral operator TW$T_W$, acting on L2(Γ)$L^2(\Gamma)$ for a contour Γ⊂C$\Gamma \subset \mathbb {C}$, which reflects a differential operator with rational coefficients R(z,∂z)$R(z, \partial _z)$ in the sense that R(−z,−∂z)∘TW=TW∘R(w,∂w)$R(-z,-\partial _z) \circ T_W = T_W \circ R(w, \partial _w)$ on a dense subset of L2(Γ)$L^2(\Gamma)$. By using analytic methods and methods from integrable systems, we show that the reflected differential operator can be constructed from the Fourier algebra of the associated bispectral function ψW(x,z)$\psi _W(x,z)$. The exact size of this algebra with respect to a bifiltration is in turn determined using algebro‐geometric methods. Intrinsic properties of four involutions of the adelic Grassmannian naturally lead us to consider the reflecting property above in place of plain commutativity. Furthermore, we prove that the time‐band limited operators of the generalized Laplace transforms with kernels given by the rank one bispectral functions ψW(x,−z)$\psi _W(x,-z)$ always reflect a differential operator. A 90° rotation argument is used to prove that the time‐band limited operators of the generalized Fourier transforms with kernels ψW(x,iz)$\psi _W(x, iz)$ admit a commuting differential operator. These methods produce vast collections of integral operators with prolate‐spheroidal properties, associated to the wave functions of all rational solutions of the KP hierarchy vanishing at infinity, introduced by Krichever in the late 1970s. [ABSTRACT FROM AUTHOR]

Brain‐inspired optical neural computing (ONC) is the state‐of‐the‐art scheme in modern computing, offering robust strategies to execute advanced inference with a high throughput and large‐scale parallelism. However, the hitherto prevalent diffractive ONC networks have watered‐down competence, which is mostly a phase‐only methodology but fails to precisely handle the Fourier transform of complex fields, thus forfeiting the integrity of the architecture and half the volume of available training weights. Here, a novel neural meta‐transformer (ONM) enabled by an optical rotation‐isolator‐assisted paradigm is proposed, whose meta‐neurons utilize structural birefringence and polarization rotation to achieve independently arbitrary tailoring of full Fourier components, that is the complete learnable parameters of diffractive ONC. The full‐Fourier‐component ONM has great merits over phase‐only counterparts in all representative cases: being a classifier, it improves the recognition accuracy, especially for input with more high‐frequency features; acting as an imager, the background noise of output is effectively diminished; and when engineering as an encoder, both near‐field grayscale nanoprinting and neural meta‐holography are yielded. The mechanism is minimalist, compact, and compatible with nonlinear activation, opening the route to fully parametric intelligent meta‐devices, with far‐reaching implications for optical computing, display, encryption, etc. [ABSTRACT FROM AUTHOR]

A novel phthalazine‐based phthalonitrile resin was prepared by two different curing procedures. The phthalonitrile monomer, namely, 4,4′‐(((phthalazine‐1,4‐diylbis(oxy))bis(3,1‐phenylene))bis(oxy))diphthalonitrile (PDOP), was synthesized from the reaction of 1, 4‐dichloropthalazine, resorcinol, and 4‐nitrophthalonitrile. Its curing behavior and curing kinetics with 4‐(4‐aminophenoxy)phthalonitrile (APPH) were investigated by Differential Scanning Calorimetric (DSC). Isoconversional method based on Starink was applied to analyze the curing process of PDOP/APPH. The PDOP monomer exhibits a low melting point (89 °C) and a wide processing window (146 °C). The PDOP polymer mainly forms triazine, isoindoline, and phthalocyanine structure, as revealed by Fourier Transform Infrared (FTIR) spectroscopy, and its properties improved with the increase of post‐curing temperature and curing time. After post‐curing at 350 °C, the polymer has high storage modulus (3313 MPa), high glass‐transition temperature (380 °C), and outstanding thermal stability and thermal oxidation stability. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the theory of a generalized Fourier transform in order to solve differential equations with a generalized fractional derivative, and we state its main properties. In particular, we obtain the new corresponding convolution, inverse and Plancherel formulas, and Hausdorff–Young type inequality. We show that this generalized Fourier transform is useful in the study of several fractional differential equations (both ordinary and partial differential equations). [ABSTRACT FROM AUTHOR]

Taking into account a wavelet transform associated with the quadratic‐phase Fourier transform, we obtain several types of uncertainty principles, as well as identify conditions that guarantee the unique solution for a class of integral equations (related with the previous mentioned transforms). Namely, we obtain a Heisenberg–Pauli–Weyl‐type uncertainty principle, a logarithmic‐type uncertainty principle, a local‐type uncertainty principle, an entropy‐based uncertainty principle, a Nazarov‐type uncertainty principle, an Amrein–Berthier–Benedicks‐type uncertainty principle, a Donoho–Stark‐type uncertainty principle, a Hardy‐type uncertainty principle, and a Beurling‐type uncertainty principle for such quadratic‐phase wavelet transform. For this, it is crucial to consider a convolution and its consequences in establishing an explicit relation with the quadratic‐phase Fourier transform. [ABSTRACT FROM AUTHOR]

The study of soil organic matter (SOM) can benefit from the use of Fourier‐transform infrared spectroscopy, an analytical method that complements traditional fractionation and extraction methods. This review provides guidance on the use of diffuse reflectance infrared Fourier transform (DRIFT) in the mid‐infrared region (MIR: 4000–400 cm−1). Two distinct applications of DRIFT spectroscopy are reviewed: soil organic matter (1) characterization and (2) quantification. Characterization of SOM involves the qualitative to semi‐quantitative measurement of functional groups that constitute organic matter, and quantification employs chemometrics to predict fractions of SOM. Guidance on decision‐making in how methods are conducted based on sample type and research question, and on interpretation of results are provided. Core Ideas: Fourier‐transform infrared (FTIR) spectroscopy can be used to characterize and quantify soil organic matter (SOM).Diffuse reflectance infrared Fourier transform in the mid‐infrared region of 4000–400 cm−1 is reviewed.Organic functional groups detected by FTIR spectroscopy complement other structural analytical techniques.FTIR spectroscopy can also be used to quantify SOM fractions using chemometrics. [ABSTRACT FROM AUTHOR]

The present article considers an anti‐plane stress problem of three cracks at different orthotropic materials' interfaces. According to the geometry of the problem, the governing equations and mixed boundary conditions have been formulated. Fourier integral transformation is used to convert the mixed boundary value problem into dual integral equations, which gives two equations containing infinite series. The investigation of the problem concerning anti‐plane cracks subjected to static loadings is done with the help of the Schmidt method to satisfy the given boundary conditions. The difference in displacements is expanded to proceed further in the problem, which becomes zero outside the cracks. Numerical computations are carried out for the graphical representation of stress intensity factors (SIFs) at all cracks' tips. The Interaction among the cracks as those are in close proximity to each other or move away are represented pictorially. Detailed numerical results and discussion are done for the considered materials, which include aluminium, epoxy and graphite epoxy. The novelty of the present article is the numerical analysis and pictorial presentation of SIFs at the tips of interfacial offset parallel cracks for various crack lengths and normalised heights for different combinations of materials. The authors have obtained variations in SIFs for the cracks at the interfaces of dissimilar composite materials. [ABSTRACT FROM AUTHOR]

We carried out an integrated interpretation of available geophysical data (gravity and electrical data) in Sidi Bou Aouane–Khadhkhadha Pb–Zn province, located in a Neogene basin south of the Alpine thrust‐belt front in northern Tunisia. The interpretive approach of gravity data was done based on the Fourier transformation and spectral analysis to extract the residual component. Furthermore, edge enhancement techniques (tilt angle, total horizontal derivative) were applied to image the underlying lineaments in the study area. The computed gravity maps reveal multiple NE–SW hidden faults considered potential mineralization targets, referring to geological information. Detrital formations, known as containers of disseminated Pb–Zn mineralization, are expressed by low gravity responses. Resistivity and chargeability 3D inversion was conducted concurrently through on an iterative approach based on the conventional least‐squares algorithm and "incomplete Gauss‐Newton" as an optimization method. The initial model was defined based on drill‐hole data and geological knowledge. Inverted resistivity confirms the basin architecture expressed by gravity data. The combined interpretation of inverted resistivity and chargeability correlated to borehole and outcrops allows the definition of different electrical ranges associated to different lithologies and mineralization type and contents. A new potential target, expressing the same electrical signature of mineralization, is evidenced northward Khadhkhadha old mine. In addition, a potential copper concentration area was proven based on its electrical responses south Sidi Bou Aouane mine. 2.5D gravity modelling supports the evidenced interpreted target. The revealed results provided evidence for future interpretations of further geological structures, along with evaluations of mineral resources. [ABSTRACT FROM AUTHOR]

We present a numerical scheme for obtaining guaranteed (reliable) and arbitrarily close two sided bounds to effective (homogenized) parameters of the linear elasticity problem. For the upper bounds, we use standard finite element (FE) discretization of the so‐called primal problem with preconditioning based on the fast discrete Fourier transformation (FFT). For the lower bounds, we use the dual formulation and some smoother FE approximation spaces. Moreover, instead of solving the discretized dual problem, we can only compute an L2‐orthogonal projection of an auxiliary field built from the primal solution. The projection can be computed easily by FFT and provides a lower bound of almost the same quality as that obtained as the exact solution of the discretized dual problem. In addition, a simple low‐dimensional optimization improves the projected solution. Numerical examples are presented to support the theoretical developments. [ABSTRACT FROM AUTHOR]

Summary: The effect of cooking time and the solid content was analysed in the techno‐functional properties of lentils and common beans aquafaba, and their powders obtained through spray‐drying. Foam drainage kinetic and emulsion destabilisation were successfully modelled showing that lentil aquafaba had better foaming capacity than beans, due to its higher protein content. Moreover, an increase in cooking time results in more liquid incorporated into the foam and a longer lag phase. Bean aquafaba had acceptable emulsifying capacity, attributable to higher soluble carbohydrates. Additionally, microstructure, Fourier Transform Infrared Spectrometry, rehydration capacity, and flowability of aquafaba powders were studied. Microscopy of dried lentil aquafaba showed damaged and collapsed particles, while bean powder consisted of spherical smooth particles. The dominant factor influencing aquafaba functional properties and powder characteristics was the legume type, attributed to their chemical compositions. These findings broaden the insights of alternative sources of aquafaba and enhance the industrial applicability of these residues through highly rehydratable and functional powders. [ABSTRACT FROM AUTHOR]

Analytical solutions for coupled problems are very significant for both understanding the physical mechanism and verifying the numerical methods. However, existing solutions usually focus on advection‐dispersion models without considering the coupling effect of contaminant transport or partial‐coupled models with the zero initial concentration (ZIC) condition, which are impractical in many engineering applications. This paper proposes novel analytical solutions to solve the non‐zero initial concentration (NZIC) problem for a fully‐coupled hydraulic‐mechanical‐chemical (HMC) model by Fourier transform. The proposed analytical solutions are highly competent and efficient compared with existing solutions from the literature. The solutions are applied to investigate the long‐term contaminant transport behavior and consequent deformation of clay liner under NZIC conditions. Results show that the presence of NZIC greatly promotes contaminant ions migration and shorten breakthrough time. The higher the initial concentration, the shorter the breakthrough time. When the initial concentration is increased by 3 and 5 times, the corresponding breakthrough time is reduced by 23.9 and 27.1 years, respectively. In practical engineering, neglecting the NZIC of contaminant can lead to an overestimation of performance efficiency of clay liners. [ABSTRACT FROM AUTHOR]

Orthogonal frequency division multiplexing (OFDM) technology has been increasingly applied to power line carrier communication (PLC). Discrete Fourier Transformation (DFT)‐based channel estimation algorithm is suitable for OFDM‐based PLC due to its low complexity. In view of the problem that the traditional DFT channel estimation does not consider the influence of noise inside cyclic prefix (CP), an improved DFT channel estimation based on signal‐to‐noise ratio (SNR) estimation is proposed. First, least‐square (LS) algorithm is performed and the frequency domain channel estimation is converted to the time domain through inverse DFT, and the average SNR of the system is estimated according to the pilot sequence. Second, the substitute SNR for each sample point inside CP is defined and used to filter impulse noise inside CP. Third, the average SNR is converted into the threshold of the useful signal energy inside CP, and the widespread background noise inside CP is filtered. The simulation results show that the proposed algorithm can obtain more accurate channel estimation than other DFT channel estimation algorithms because it can effectively filter out noise inside CP. In addition, compared with other similar algorithms, the proposed algorithm dose not result in a significant increase in complexity. [ABSTRACT FROM AUTHOR]

The objective of this work was to adapt the FT Raman spectroscopy analysis in the differentiation of haploid and diploid kernels in maize, developing a new efficient, agile, precise, and nondestructive methodology. The main difference observed in FT Raman readings was a peak in the region between 1600 and 1700 cm−1 in possibly haploid kernels. It was possible to correlate the characteristics of the kernels with the presence of the R1‐nj gene and the readings obtained in the Raman spectrometry technique. Most of the kernels previously classified as haploid showed positive values for principal component analysis (PCAs), indicating a correlation in the identification of haploids by the techniques adopted. The identification of haploids by R‐Navajo was superior to FT Raman. However, FT Raman spectroscopy is an agile analysis technique that enables the development of non‐invasive and non‐destructive analytical methods in maize kernels, in addition to providing relevant information about the chemical structures present in the composition of the samples. [ABSTRACT FROM AUTHOR]

In this paper, we determine the motivic class -- in particular, the weight polynomial and conjecturally the Poincaré polynomial -- of the open de Rham space, defined and studied by Boalch, of certain moduli spaces of irregular meromorphic connections on the trivial rank n bundle on ℙ¹. The computation is by motivic Fourier transform. We show that the result satisfies the purity conjecture, that is, it agrees with the pure part of the conjectured mixed Hodge polynomial of the corresponding wild character variety. We also identify the open de Rham spaces with quiver varieties with multiplicities of Yamakawa and Geiss-Leclerc-Schröer. We finish with constructing natural complete hyperkähler metrics on them, which in the four-dimensional cases are expected to be of type ALF. [ABSTRACT FROM AUTHOR]