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The multiphoton excitation pathways of plasmonic nanorod assemblies are described. By using dolmen structures formed from the directed assembly of three gold nanorods, plasmon-mediated three-photon excitation is resolved. These high-order multiphoton excitation channels were accessed by resonantly exciting a hybrid mode of the dolmen structure that was resonant with the 800-nm carrier wavelength of an ultrafast laser system. Rotation of the exciting field polarization to a non-resonant configuration did not generate third-order responses. Hence, the multiphoton excitation and resultant non-equilibrium electron distributions were generated by structure- and mode-selective excitation. Correlation between high-order and resonant plasmon excitation was achieved through sub-cycle time-resolved interferometric detection of incoherent nonlinear emission signals. The results illustrate the advantages of nonlinear optical interferometry and Fourier analysis for distinguishing plasmon-mediated processes from those that do not require plasmon excitation. [ABSTRACT FROM AUTHOR]

An average-case variant of the k-SUM conjecture asserts that finding k numbers that sum to 0 in a list of r random numbers, each of the order rk, cannot be done in much less than \(r^{\lceil k/2 \rceil }\) time. However, in the dense regime of parameters, where the list contains more numbers and many solutions exist, the complexity of finding one of them can be significantly improved by Wagner's k-tree algorithm. Such algorithms for k-SUM in the dense regime have many applications, notably in cryptanalysis. In this article, assuming the average-case k-SUM conjecture, we prove that known algorithms are essentially optimal for k= 3,4,5. For k> 5, we prove the optimality of the k-tree algorithm for a limited range of parameters. We also prove similar results for k-XOR, where the sum is replaced with exclusive or. Our results are obtained by a self-reduction that, given an instance of k-SUM that has a few solutions, produces from it many instances in the dense regime. We solve each of these instances using the dense k-SUM oracle and hope that a solution to a dense instance also solves the original problem. We deal with potentially malicious oracles (that repeatedly output correlated useless solutions) by an obfuscation process that adds noise to the dense instances. Using discrete Fourier analysis, we show that the obfuscation eliminates correlations among the oracle's solutions, even though its inputs are highly correlated. [ABSTRACT FROM AUTHOR]

A constraint satisfaction problem (CSP), \(\textsf {Max-CSP}(\mathcal {F})\) , is specified by a finite set of constraints \(\mathcal {F}\subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace\) for positive integers q and k. An instance of the problem on n variables is given by m applications of constraints from \(\mathcal {F}\) to subsequences of the n variables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (γ ,β)-approximation version of the problem for parameters 0 ≤ β ≤ γ ≤ 1, the goal is to distinguish instances where at least γ fraction of the constraints can be satisfied from instances where at most β fraction of the constraints can be satisfied. In this work, we consider the approximability of this problem in the context of sketching algorithms and give a dichotomy result. Specifically, for every family \(\mathcal {F}\) and every β < γ, we show that either a linear sketching algorithm solves the problem in polylogarithmic space or the problem is not solvable by any sketching algorithm in \(o(\sqrt {n})\) space. In particular, we give non-trivial approximation algorithms using polylogarithmic space for infinitely many constraint satisfaction problems. We also extend previously known lower bounds for general streaming algorithms to a wide variety of problems, and in particular the case of q=k=2, where we get a dichotomy, and the case when the satisfying assignments of the constraints of \(\mathcal {F}\) support a distribution on \([q]^k\) with uniform marginals. Prior to this work, other than sporadic examples, the only systematic classes of CSPs that were analyzed considered the setting of Boolean variables q = 2, binary constraints k =2, and singleton families \(|\mathcal {F}|=1\) and only considered the setting where constraints are placed on literals rather than variables. Our positive results show wide applicability of bias-based algorithms used previously by [47] and [41], which we extend to include richer norm estimation algorithms, by giving a systematic way to discover biases. Our negative results combine the Fourier analytic methods of [56], which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results. In particular, previous works used Fourier analysis over the Boolean cube to initiate their results and the results seemed particularly tailored to functions on Boolean literals (i.e., with negations). Our techniques surprisingly allow us to get to general q-ary CSPs without negations by appealing to the same Fourier analytic starting point over Boolean hypercubes. [ABSTRACT FROM AUTHOR]

A high-resolution, temperature oscillation-based probe of physical aging in complex systems is introduced. The Fourier analysis of the measured responses allows one to extract high-order, aging-related nonlinearities that are not accessible via traditional temperature-jump and temperature-ramp procedures. To demonstrate the potential of this oscillatory approach, we analyze the periodic time evolution of glycerol's structural relaxation using shear rheology as a vehicle. Thereby, we access up to the sixth harmonic and detect aging fingerprints within a resolution range of three orders of magnitude for temperature amplitudes of up to 4 K. The even harmonics are present since aging is not symmetrical with respect to the direction of temperature change. The high-order aging coefficients obtained for glycerol are described reasonably well within the Tool–Narayanaswamy–Moynihan formalism. [ABSTRACT FROM AUTHOR]

Recently, the sinosoidal output response in power series (SORPS) formalism was presented for system identification and simulation. Based on the concept of characteristic curves (CCs), it establishes a mathematical connection between power series and Fourier series for a first-order nonlinear system (Gonzalez in Sci Rep 13:1955, 2023). However, the system identification procedure discussed there, based on fast Fourier transform (FFT), presents the limitations of requiring a sinusoidal single tone for the dynamical variable and equally spaced time steps for the input–output dataset (DS). These limitations are here addressed by introducing a different approach: we use a power series-based model (referred to as model 1) for system modeling instead of FFT, where two hyperparameters A ^ 0 and A ^ 1 are optimally defined depending on the DS. Subsequently, two additional models are obtained from parameters obtained in model 1: another power series-based model (model 2) and a Fourier analysis-based model (model 3). These models are useful for comparing parameters obtained from different DSs. Through an illustrative example, we show that while the predicted values from the models are the same due to a mathematical equivalence, the parameters obtained for each model vary to a greater or lesser extent depending on the DS used for system estimation. Hence, the parameters of the Fourier analysis-based model exhibit notably less variation compared to those of the power series-based model, highlighting the reliability of using the Fourier analysis-based model for comparing model parameters obtained from different DSs. Overall, this work expands the applicability of the SORPS formalism to system identification from arbitrary input–output data and represents a groundbreaking contribution relying on the concept of CCs, which can be straightforwardly applied to higher-order nonlinear systems. The method of CCs can be considered as complementary to the commonly used approach (such as NARMAX-models and sparse regression techniques) that emphasizes the estimation of the individual parameter values of the model. Instead, the CCs-based methods emphasize the computation of the CCs as a whole. CCs-based models present the advantages that the system identification is uniquely defined, and that it can be applied for any system without additional algebraic operations. Thus, the parsimonious principle defined by the NARMAX-philosophy is extended from the concept of a model with as few parameters as possible to the concept of finding the lowest model order that correctly describe the input–output data. This opens up a wide variety of potential applications, covering areas such as vibration analysis, structural dynamics, viscoelastic materials, design and modeling of nonlinear electric circuits, voltammetry techniques in electrochemistry, structural health monitoring, and fault diagnosis. [ABSTRACT FROM AUTHOR]

Fourier harmonic analysis (FHA) is a robust method for identification of minute changes in sperm nuclear shape that are indicative of reduced fertility. The current study was designed to develop a fertility prediction model for Nili-Ravi buffalo bulls through FHA of sperm. In experiment I, FHA technique was standardized, average sperm nuclear perimeter was measured and sperm nuclear shape plot of buffalo bull was constructed. Sperm of buffalo bulls (n = 10) were stained with YOYO-1 and Hoechst-33342 to differentiate live and dead, and digital images were captured using phase contrast and fluorescent microscopy. The images were analyzed by ImageJ software and 100 sperm/bull were evaluated. The results are described as mean ± SEM values of mean harmonic amplitude (mharm), skewness harmonic amplitude (skharm), kurtosis harmonic amplitude (kurharm) and variance harmonic amplitude (varharm) at Fourier frequencies 0–5 along with the cartesian and polar coordinate plots of buffalo bull sperm. In experiment II, a fertility prediction model was developed based on FHA of buffalo bull sperm. Semen samples of low (n = 6), medium (n = 3) and high (n = 8) fertility bulls were investigated for FHA of sperm and harmonic amplitudes (HA) were generated. Firstly, to determine if live and dead sperm population have unique nuclear shape distribution; the mean, skewness, kurtosis and variance HA 0–5 of 1700 live and 1294 dead spermatozoa of 17 bulls were evaluated. T-test signified a difference in the mharm0 (2.363 ± 0.01 vs. 2.439 ± 0.02), skharm0 (−0.0002 ± 0.07 vs. −0.266 ± 0.09), kurharm0 (−0.156 ± 0.07 vs. 0.260 ± 0.18), kurharm2 (0.142 ± 0.11 vs. 1.031 ± 0.32) and varharm4 (0.109 ± 0.00 vs. 0.082 ± 0.00) of live vs. dead sperm population (p < 0.05). Therefore, 100 live sperm/bull were further evaluated for mean, skewness, kurtosis and variance HA 0–5 values among high (n = 6) and low-fertility (n = 6) groups. Results of T-test showed higher values of mharm2 (0.739 ± 0.01 vs. 0.686 ± 0.00), mharm4 (0.105 ± 0.001 vs. 0.007 ± 0.001), and skharm0 (0.214 ± 0.109 vs. −0.244 ± 0.097) in high vs. low-fertility group (p < 0.05). In next step, five significantly different combinations of discriminant measures between high and low-fertility groups were obtained by discriminant analysis. In conclusion, mharm4, skharm0 and varharm2 correctly identified 91.7 % of bulls into their respective fertility groups, and upon cross validation the value of the canonical correlation was 0.928. • Fourier harmonic analysis (FHA) technique was standardized for Nili-Ravi buffalo sperm. • Average sperm nuclear perimeter was measured & sperm nuclear shape plot constructed. • FHA detected difference in live and dead sperm nuclear shape. • Sperm from high and low fertility bulls statistically differed in nuclear shape. • Discriminant analysis based on FHA defined an excellent fertility prediction model. [ABSTRACT FROM AUTHOR]

The linear axial expansion transport method avoids the negative source problem caused by transverse leakage in the traditional two-dimensional/one-dimensional (2D/1D) transport method and has better stability. However, stability is poor with the coarse-mesh finite difference (CMFD) accelerated linear axial expansion transport method. In this paper, the stability of the partial current–based coarse-mesh finite difference (p-CMFD) method, the optimally diffusive coarse-mesh finite difference (od-CMFD) method, and the linear prolongation coarse-mesh finite difference (lp-CMFD) method is studied based on Fourier analysis. The results of the Fourier analysis indicate that the problem is stable for axial coarse-mesh optical thickness less than 2 or larger than 50; the calculation diverges when the axial coarse-mesh optical thickness is between 2 and 50. The numerical results of the KUCA benchmark problem are the same as the results of the Fourier analysis. [ABSTRACT FROM AUTHOR]

This paper presents an innovative approach to efficiently perform deterministic direct whole-core transport calculations with multiphysics feedback for steady-state problems. Traditionally, Picard iteration combined with coarse mesh finite difference (CMFD) acceleration has been used, but it can suffer from instability and inefficiency in certain scenarios. In this work, we introduce the X-CMFD method, supported by Fourier analysis, to enhance the stability of the multiphysics iteration scheme. A new and efficient variation of the X-CMFD method for practical simulations is also present. Additionally, we explore the theoretical convergence rates of nonlinear fully coupled diffusion acceleration (NFCDA), a class of diffusion acceleration methods that formalizes similar ideas of previous research. NFCDA uses a low-order diffusion problem that is fully coupled with equivalent nonlinear multiphysics feedback to accelerate the high-order transport problem with feedback. The theoretical analysis shows that NFCDA offers similar convergence rates to nonlinear diffusion acceleration (NDA) in problems without feedback. This provides theoretical support for numerical experiments conducted by other researchers. X-CMFD, which is a discretized form of NFCDA, leverages typical coarse mesh concepts and operators from CMFD while applying feedback to cross sections in the low-order diffusion problem at each power iteration of the low-order problem. To reduce computational costs, we optimize the implementation of X-CMFD in MPACT by introducing an equivalent low-order approximation to the cross-section updates in the nonlinear low-order problem. Numerical results from pressurized water reactor problems demonstrate that X-CMFD, along with its practical implementation, outperforms current relaxed Picard iteration methods in terms of robustness and efficiency, irrespective of the presence of multiphysics feedback. [ABSTRACT FROM AUTHOR]

A subset A of a group G is called product-free if there is no solution to a = b c with a , b , c all in A . It is easy to see that the largest product-free subset of the symmetric group S n is obtained by taking the set of all odd permutations, i.e. S n ∖ A n , where A n is the alternating group. In 1985 Babai and Sós (Eur. J. Comb. 6(2):101–114, 1985) conjectured that the group A n also contains a product-free set of constant density. This conjecture was refuted by Gowers (whose result was subsequently improved by Eberhard), still leaving the long-standing problem of determining the largest product-free subset of A n wide open. We solve this problem for large n , showing that the maximum size is achieved by the previously conjectured extremal examples, namely families of the form { π : π (x) ∈ I , π (I) ∩ I = ∅ } and their inverses. Moreover, we show that the maximum size is only achieved by these extremal examples, and we have stability: any product-free subset of A n of nearly maximum size is structurally close to an extremal example. Our proof uses a combination of tools from Combinatorics and Non-abelian Fourier Analysis, including a crucial new ingredient exploiting some recent theory developed by Filmus, Kindler, Lifshitz and Minzer for global hypercontractivity on the symmetric group. [ABSTRACT FROM AUTHOR]

The key parameter in the printing process is the evenness of applying the ink layer on the printing substrate. It determines the quality of the produced prints. One of the many factors affecting the final evenness of the ink layer on the print is the phenomenon of mottling, which is caused by the non-uniform internal structure of the paper. The aim of this work was to analyze the influence of basic printing parameters on the value of the mottling index. The research showed a significant effect of the pressure in the printing unit of the offset machine and the thickness of the ink layer on the printing substrate on the value of the primary mottling index. In addition, the research revealed that the properties of the printing substrate have a significant impact on the value and nature of changes in the mottling index. In this work, using the Fourier analysis, the frequency of optical density fluctuations in solid tone area related to the mottling phenomenon was also studied. No influence of pressure changes in the Nip of the printing unit on this print parameter was found. [ABSTRACT FROM AUTHOR]

We report that the quantity measured in the L 2 norm of the solution itself of the generalized Rosenau equation, which was completely unknown in this equation, grows in the proper order at time infinity. It is also immediately apparent that this growth aspect does not occur in three or more spatial dimensions, so we will apply the results obtained in this study to provide another proof that Hardy-type inequalities do not hold in the case of one or two spatial dimensions. [ABSTRACT FROM AUTHOR]

A novel UV-curable rosin-based resin, named as DHTM, was synthesized through a Michael addition reaction involving a derivative of natural rosin (dehydroabietylamine, DHAA) and trimethylolpropane triacrylate (TMPTA). The reaction, conducted at a low temperature (50 °C) without solvents, achieved a high conversion rate exceeding 95%. Structural analyses via Fourier transform infrared (FTIR), nuclear magnetic resonance (1H NMR), and liquid chromatography-orthogonal time-of-flight mass spectrometry (LC-OTOF-MS) confirmed the chemical composition of DHTM. Subsequently, a multifunctional UV resin was formulated by combining DHTM with the diluent 4-acryloylmorpholine (ACMO) and cured under UV light. The resulting resin exhibited excellent thermal, mechanical, and microscopic properties, including notable crosslinking density, tensile strength, and adhesion. The addition of ACMO contributed to a smoother resin surface, achieving a higher crosslinking density of 57.04 × 103 mol/m3. In conclusion, the developed UV-curable rosin-based resins exhibit significant potential for applications in UV-curable materials, such as 3D printing and coatings. [ABSTRACT FROM AUTHOR]

This study empirically investigated the influence of freeze–thaw cycling on the dynamic splitting tensile properties of steel fiber reinforced concrete (SFRC). Brazilian disc splitting tests were conducted using four loading rates (0.002, 0.02, 0.2, and 2 mm/s) on specimens with four steel fiber contents (0%, 0.6%, 1.2%, and 1.8%) subjected to 0 and 50 freeze–thaw cycles. The dynamic splitting tensile damage characteristics were evaluated using acoustic emission (AE) parameter analysis and Fourier transform spectral analysis. The results quantified using the freeze–thaw damage factor defined in this paper indicate that the degree of damage to SFRC caused by freeze–thaw cycling was aggravated with increasing loading rate but mitigated by increasing fiber content. The percentage of low-frequency AE signals produced by the SFRC specimens during loading decreased with increasing loading rate, whereas that of high-frequency AE signals increased. Freeze–thaw action had little effect on the crack types observed during the early and middle stages of the loading process; however, the primary crack type observed during the later stage of loading changed from shear to tensile after the SFRC specimens were subjected to freeze–thaw cycling. Notably, the results of this study indicate that the freeze–thaw damage to SFRC reduces AE signal activity at low frequencies. [ABSTRACT FROM AUTHOR]

Based on partial Fourier series analysis, we adapt on a model case a new approach to classical results obtained in the literature describing the singularities of a family a solutions of a second‐order elliptic problems on open non‐convex planar sectors. The method allows the exhibition of singular and regular frequencies, explicit decomposition, and description of coefficients of singularities of the solution. As a main result, explicit and sharp estimates with respect to the opening angle parameter are obtained via this method. They are not uniform near π$$ \pi $$ where corners have opening angle generating a jump of singularity in Sobolev exponent, contrarily to the results obtained for harmonic and/or biharmonic problems on a family of convex planar sectors. [ABSTRACT FROM AUTHOR]

Mars' polar ice deposits are thought to preserve a record of climate throughout their evolution. In addition to the large north polar layered deposits (NPLD) at Mars' north pole, smaller ice deposits are preserved in craters nearby. These outlying deposits were potentially formed by the same mechanisms that drive NPLD formation, or may represent more local mechanisms. Distinguishing between these possibilities would help elucidate the spatial homogeneity of Martian climate processes. Here, we analyzed SHARAD radar depth profiles from 34 locations across the NPLD and 5 locations within the Korolev crater ice deposit using Fourier transform analysis and dynamic time warping to quantitatively assess the similarity between the internal layered stratigraphy of the two deposits. We identify broad stratigraphic similarities between the Korolev deposit and the NPLD, suggesting they likely formed due to the same climate forcing mechanism, with local variability also observed across the NPLD. Plain Language Summary: Mars has two large ice caps at its poles, which combined contain a similar volume of ice to Greenland on Earth. Near these large ice caps are craters that are also filled with ice, which may or may not have formed due to the same mechanisms that formed the large neighboring ice cap. Ground penetrating radar observations of ice on Mars can allow us to see layers of ice and dust that are present throughout the interior of these deposits, and represent climate events that have taken place during the deposit's formation and evolution. We analyze radar observations from two deposits near Mars' north pole and quantitatively show that these deposits have a similar pattern of layering. These results could indicate that they have shared a similar climate history, therefore implying the importance of regional‐scale climate processes on Mars in addition to local processes for forming these ice deposits. Key Points: We use Fourier transform analysis and dynamic time warping to assess the similarities between two ice deposits near Mars' north poleWe identified a periodic signal with an average wavelength of ∼45 m in radar observations of the ice mound in Korolev crater and the NPLDWe identify similar broad climate forcing for both Korolev and NPLD ice, with local variability across the NPLD also observed [ABSTRACT FROM AUTHOR]

We report an Arase‐all sky imager (ASI) conjugate event in which the pulsating aurora (PsA) has a one‐to‐one correspondence with chorus bursts. Wavelet analysis displayed three peaks at ∼0.3 Hz, 4 Hz, and >10 Hz, corresponding to the main pulsation, internal modulation, and fast modulation, respectively. These correspond to the old terms of ∼5–15 s pulsations, chorus risers/elements and subelements/subpackets, respectively. Electron "microbursts" correspond to the 4‐Hz peak. The internal and fast modulations are further verified by the analysis based on fast Fourier transform analyses. Moreover, the spatial distributions of the Fourier spectral amplitude show that the internal and fast modulations are well‐structured within auroral patches. The above results indicate a paradigm shift away from quasilinear theory which implicitly assumes diffuse wave generation. The three time‐scale modulations are consistent with coherent chorus which has been theoretically argued to lead to pitch angle transport three orders of magnitude faster. Plain Language Summary: Pulsating aurora exhibit irregular patches of brightness with quasiperiodic on‐off transitions (∼2–20 s). More rapid modulations, such as internal modulation (∼3–4 Hz) or fast modulation (>10 Hz), have been detected within the pulsation "on" time. However, due to the measurement limitations, the simultaneous observation of three time‐scale modulations has never been reported. In this study, we analyze the conjugate observations of the pulsating aurora (PsA) and chorus recorded by the ground‐based Arase‐all sky imager and the Arase satellite, which demonstrates the coexistence of three time‐scale modulations in the PsA. The spatial distributions of Fourier spectral amplitude show that the internal and fast modulations are well‐structured within the aurora patches. The three time scales of chorus modulation have been previously called chorus 5–15 s pulsations, risers/elements and subelements/subpackets corresponding to the three aurora peaks. This study verifies the existence of internal and fast modulations in PsA, implying an extremely rapid electron loss mechanism. Quasilinear theory cannot explain any of the three time‐scale modulations. The discovery that chorus is coherent and will lead to pitch angle transport 1,000 times faster than diffuse waves is consistent with the fast modulations shown in this paper. A new theory of chorus generation is needed to update that of quasilinear theory. Key Points: We report a conjugate event in which the pulsating aurora (PsA) has a one‐to‐one correspondence with chorus burstsThe frequency spectra of auroral intensities obtained by wavelet analysis and fast Fourier transform (FFT) show the coexistence of ∼0.3 Hz, 4 Hz, and >10 Hz modulationsSpatial distributions show that the internal and fast modulations are well‐structured within aurora patches [ABSTRACT FROM AUTHOR]

In this paper we focus on two aspects. First we study the initial-value problem of the Timoshenko-Fourier system with memory-type dissipation. By using the method of energy estimate combined with the technique of Fourier analysis, we obtain the decay estimates of solutions to the problem. Then we deal with the open problem proposed by N. Mori and S. Kawashima in the paper [18] entitled "Decay property of the Timoshenko-Cattaneo system" from the point view of energy estimate. [ABSTRACT FROM AUTHOR]

Seals, sea lions, and other aquatic animals rely on their whiskers to identify and track underwater targets, offering valuable inspiration for the development of low-power, portable, and environmentally friendly sensors. Here, we design a single seal-whisker-like cylinder and conduct experiments to measure the forces acting on it with nine different upstream targets. Using sample sets constructed from these force signals, a convolutional neural network (CNN) is trained and tested. The results demonstrate that combining the seal-whisker-style sensor with a CNN enables the identification of objects in the water in most cases, although there may be some confusion for certain targets. Increasing the length of the signal samples can enhance the results but may not eliminate these confusions. Our study reveals that high frequencies (greater than 5 Hz) are irrelevant in our model. Lift signals present more distinct and distinguishable features than drag signals, serving as the primary basis for the model to differentiate between various targets. Fourier analysis indicates that the model's efficacy in recognizing different targets relies heavily on the discrepancies in the spectral features of the lift signals. [ABSTRACT FROM AUTHOR]

Power quality is a critical issue in power systems that can affect the performance and reliability of sensitive equipment. The dynamic voltage restorer (DVR) is a widely used technology for improving power quality, but it mainly focuses on mitigating voltage sags and often neglects the issue of harmonic distortion. This paper proposes a DVR voltage compensation strategy based on the discrete Fourier transform (DFT). This strategy utilizes the DFT to analyze the voltage waveform, separating the fundamental and desired harmonic components. With this strategy, the DVR can effectively compensate for voltage sag and achieve selective harmonic compensation, thereby improving the power quality of the power system. Additionally, a method utilizing hardware circuitry and an LED as a timestamp is proposed to dynamically estimate digital siginal processor (DSP) resource occupancy rate in real‐time, ensuring effective compensation while minimizing resource occupancy. A 3 kW DVR experimental prototype was constructed and tested to evaluate the practicality of the proposed strategy. The simulation and experimental results show that the method proposed in this paper successfully realizes the compensation of voltage sag and harmonics in the power system, and improves the stability and reliability of the power system. [ABSTRACT FROM AUTHOR]

An in‐depth study and analysis of the stability of one‐dimensional Linear System of PDEs via Caputo time fractional derivative (LSCFD) was presented. We proved some stability results for the LSCFD in different Hilbert spaces. Indeed, by using Fourier analysis method and the properties of the Mittag–Leffler Function (MLF), some polynomial stability results for LSCFD have been established. Finally, as an application, we used finite difference methods well suited to integer and fractional order derivatives, and performed some numerical experiments to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

A facile and rapid approach to immobilize nano-sized titanium dioxide (TiO2) using a renewable biopolymer (i.e. alginate) has been successfully demonstrated. TiO2 exhibits a positively charged surface in acidic environment due to the presence of hydroxyl groups. Meanwhile, alginate polymer is negatively charged at any pH due to the presence of carboxylic group in the polymer chain. The negatively charged alginate polymer and positively charged TiO2 formed composite instantaneously when the alginate polymer was introduced into the TiO2 nanoparticles suspension. The TiO2-alginate (TiO2-A) composite photocatalyst was characterized using thermogravimetric analysis (TGA), field emission-scanning electron microscopy (FE-SEM) coupled with energy dispersive X-ray (EDX) analysis and Fourier Transform Infrared (FTIR). Thermogravimetric analysis indicated that incorporating TiO2 into sodium alginate increases its decomposition temperature due to the stability of TiO2 at elevated temperatures, with the TiO2 content estimated in the composite being 55.6%, lower than the theoretical calculation of 62.8%. FTIR analysis revealed a shift in the peak of the carboxylic group of sodium alginate, suggesting composite formation through electrostatic interactions with TiO2 nanoparticles, while FESEM analysis showed that the TiO2-A composite surface exhibited more pores compared to protonated alginate. The TiO2-A composite was able to remove 90% of the Reactive Black 5 (RB5) in less than 200 min under Ultra-violet (UV) illumination. The optimal pH to remove RB5 was found to be pH 2 due strong electrostatic attraction of negatively charged RB5 on the positive surface of TiO2 nanoparticles. The photocatalyst can be recovered by simple separation method, i.e. gravitational settling, and reused for 10 consecutive cycles with efficiency greater than 90% consistently. The TiO2-A composite is a promising immobilized photocatalyst for practical application in wastewater treatment. [ABSTRACT FROM AUTHOR]

This paper investigates a high-order numerical method based on a spatial compact exponential scheme for solving the time-fractional Black–Scholes model. Firstly, the original time-fractional Black–Scholes model is converted into an equivalent time-fractional advection–diffusion reaction model by means of a variable transformation technique. Secondly, a novel high-order numerical method is constructed with (2 − α) accuracy in time and fourth-order accuracy in space based on a spatial compact exponential scheme, where α is the fractional derivative. The uniqueness of solvability of the derived numerical method is rigorously discussed. Thirdly, the unconditional stability and convergence of the derived numerical method are rigorously analyzed using the Fourier analysis technique. Finally, numerical examples are presented to test the effectiveness of the derived numerical method. The proposed numerical method is also applied to solve the time-fractional Black–Scholes model, whose exact analytical solution is unknown; numerical results are illustrated graphically. [ABSTRACT FROM AUTHOR]

The radio spectrum is a scarce and extremely valuable resource that demands careful real-time monitoring and dynamic resource allocation. Dynamic spectrum access (DSA) is a new paradigm for managing the radio spectrum, which requires AI/ML-driven algorithms for optimum performance under rapidly changing channel conditions and possible cyber-attacks in the electromagnetic domain. Fast sensing across multiple directions using array processors, with subsequent AI/ML-based algorithms for the sensing and perception of waveforms that are measured from the environment is critical for providing decision support in DSA. As part of directional and wideband spectrum perception, the ability to finely channelize wideband inputs using efficient Fourier analysis is much needed. However, a fine-grain fast Fourier transform (FFT) across a large number of directions is computationally intensive and leads to a high chip area and power consumption. We address this issue by exploiting the recently proposed approximate discrete Fourier transform (ADFT), which has its own sparse factorization for real-time implementation at a low complexity and power consumption. The ADFT is used to create a wideband multibeam RF digital beamformer and temporal spectrum-based attention unit that monitors 32 discrete directions across 32 sub-bands in real-time using a multiplierless algorithm with low computational complexity. The output of this spectral attention unit is applied as a decision variable to an intelligent receiver that adapts its center frequency and frequency resolution via FFT channelizers that are custom-built for real-time monitoring at high resolution. This two-step process allows the fine-gain FFT to be applied only to directions and bands of interest as determined by the ADFT-based low-complexity 2D spacetime attention unit. The fine-grain FFT provides a spectral signature that can find future use cases in neural network engines for achieving modulation recognition, IoT device identification, and RFI identification. Beamforming and spectral channelization algorithms, a digital computer architecture, and early prototypes using a 32-element fully digital multichannel receiver and field programmable gate array (FPGA)-based high-speed software-defined radio (SDR) are presented. [ABSTRACT FROM AUTHOR]

We give investigations on a kernel function approximation problem arising from learning theory and show the convergence rate from the view of classical Fourier analysis. First, we provide the general definition for a modulus of smoothness and a K -functional, and show that they are equivalent. In particular, we give explicit representation for some moduli of smoothness. Second, we establish some Jackson-type inequalities for the approximation error associated with some non-radial kernels. Also we apply these results to some concrete classical kernel function spaces and give Jackson-type inequalities for some concrete RKHS approximation problems. Finally, we apply these discussions to learning theory and describe the learning rates with the moduli of smoothness. The tools we used are Fourier analysis and the semigroup operator. The results show that the Jackson-type inequalities of approximation by some radial kernel functions on compact set with nonempty interiors cannot be expressed with the classical moduli of smoothness. [ABSTRACT FROM AUTHOR]

We propose a new method based on discrete Fourier analysis to analyze the time evolutionary algorithms spend on plateaus. This immediately gives a concise proof of the classic estimate of the expected runtime of the (1 + 1) evolutionary algorithm on the Needle problem due to Garnier et al. (Evol Comput 7:173–203, 1999). We also use this method to analyze the runtime of the (1 + 1) evolutionary algorithm on a benchmark consisting of n / ℓ plateaus of effective size 2 ℓ - 1 which have to be optimized sequentially in a LeadingOnes fashion. Using our new method, we determine the precise expected runtime both for static and fitness-dependent mutation rates. We also determine the asymptotically optimal static and fitness-dependent mutation rates. For ℓ = o (n) , the optimal static mutation rate is approximately 1.59/n. The optimal fitness dependent mutation rate, when the first k fitness-relevant bits have been found, is asymptotically 1 / (k + 1) . These results, so far only proven for the single-instance problem LeadingOnes, thus hold for a much broader class of problems. We expect similar extensions to be true for other important results on LeadingOnes. We are also optimistic that the Fourier analysis approach can be applied to other plateau problems as well. [ABSTRACT FROM AUTHOR]

We study a matrix analog of the Erdős-Falconer distance problems in vector spaces over finite fields. We provide lower bounds for the cardinality of a subset of the matrix algebra over a finite field such that its distance set is the whole matrix algebra. There arises an interesting analysis of certain quadratic matrix Gauss sums. [ABSTRACT FROM AUTHOR]

In this paper, a numerical computation method for the Gierer–Meinhardt model in two-dimensional space diffusion with homogeneous Neumann boundary conditions, considering the interaction between activator and inhibitor substances, is proposed. First, a high-order compact finite difference scheme is constructed for the Gierer–Meinhardt model using the finite difference method. A fourth-order compact difference scheme is applied to the second-order spatial derivative terms, while the time derivative terms are discretized using Taylor series expansion and residual correction functions. Consequently, the difference scheme achieves fourth-order accuracy in space and second-order accuracy in time for the Gierer–Meinhardt model. In addition, the stability of the difference scheme is demonstrated using Fourier analysis. Finally, numerical simulations are conducted on the Gierer–Meinhardt model near its equilibrium point to explore the impact of the inhibitor degradation rate, denoted as E, on the pattern formation. The model exhibits distinct pattern structures with varying E, thereby revealing the relationship between tissue variability and pattern formation in biological systems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove the small data global existence of solutions to the semilinear damped wave equation$ \partial_t^2 u + Au + \partial_t u = |u|^{p-1}u $on a measure space $ X $ with a self-adjoint operator $ A $ on $ L^2(X) $. Under a certain decay estimate on the corresponding heat semigroup, we establish the linear estimates which generalize the so-called Matsumura estimates. Our approach is based on a direct spectral analysis analogous to the Fourier analysis. The self-adjoint operators treated in this paper include some important examples such as the Laplace operators on Euclidean spaces, the Dirichlet Laplacian on an arbitrary open set, the Robin Laplacian on an exterior domain, the Schrödinger operator, the elliptic operator, the Laplacian on Sierpinski gasket, and the fractional Laplacian. [ABSTRACT FROM AUTHOR]

Let n ∈ N and α > - 1 2 . The purpose of the present work is to show an analogue of a classic Titchmarsh theorem to higher differences of functions belonging to L α , n p (R +) where 1 < p ≤ 2 . [ABSTRACT FROM AUTHOR]

For the density of Galton-Watson processes in the Schröder case, we derive a complete left tail asymptotic series consisting of power terms multiplied by periodic factors. [ABSTRACT FROM AUTHOR]

Functional magnetic resonance imaging (fMRI) is a noninvasive and in-vivo imaging technique essential for measuring brain activity. Functional connectivity is used to study associations between brain regions, either while study subjects perform tasks or during periods of rest. In this paper, we propose a rigorous definition of task-evoked functional connectivity at the population level (ptFC). Importantly, our proposed ptFC is interpretable in the context of task-fMRI studies. An algorithm for estimating the ptFC is provided. We present the performance of the proposed algorithm compared to existing functional connectivity frameworks using simulations. Lastly, we apply the proposed algorithm to estimate the ptFC in a motor-task study from the Human Connectome Project. [ABSTRACT FROM AUTHOR]

We perform a multitracer full-shape analysis in Fourier space based on the effective field theory of large-scale structure (EFTofLSS) using the complete Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 luminous red galaxy (LRG) and emission line galaxy (ELG) samples. We study in detail the impact of the volume projection effect and different prior choices when doing the full-shape analysis based on the EFTofLSS model. We show that adopting a combination of Jeffreys prior and Gaussian prior can mitigate the volume effect and avoid exploring unphysical regions in the parameter space at the same time, which is crucial when jointly analysing the eBOSS LRG and ELG samples. We validate our pipeline using 1000 eBOSS EZmocks. By performing a multitracer analysis on mocks with comparable footprints, we find that cosmological constraints can be improved by |$\sim 10-35~{{\ \rm per\ cent}}$| depending on whether we assume zero stochastic terms in the cross power spectrum, which breaks the degeneracy and boosts the constraints on the standard deviation of matter density fluctuation σ8. Combining with the Big Bang Nucleosynthesis (BBN) prior and fixing the spectral tilt ns to Planck value, our multitracer full-shape analysis measures H 0 = 70.0 ± 2.3 km s−1Mpc−1, |$\Omega _m=0.317^{+0.017}_{-0.021}$|⁠ , |$\sigma _8=0.787_{-0.062}^{+0.055}$|⁠ , and |$S_8=0.809_{-0.078}^{+0.064}$|⁠ , consistent with the Planck 2018 results. In particular, the constraint on σ8 is improved beyond that obtained from the single tracer analysis by 18 per cent, or by 27 per cent when assuming zero stochastic terms in the cross power spectrum. [ABSTRACT FROM AUTHOR]

This paper explores the Fourier decomposition method to approximate the decomposition of electrocardiogram (ECG) signals into their component waveforms, such as the QRS-complex and T-wave. We compute expansion coefficients using the ℓ 1 Fourier transform and the traditional ℓ 2 Fourier transform. Numerical examples are presented, and the analysis focuses on ECG signals as a real-world application, comparing the performance of the ℓ 1 and ℓ 2 Fourier transforms. Our results demonstrate that the ℓ 1 Fourier transform significantly enhances the separation of ECG signal components, such as the QRS-complex and T-wave. This improvement is attributed to a notable reduction in the Gibbs phenomenon introduced by the Fourier-series expansion when using the ℓ 1 Fourier transform, as opposed to the traditional ℓ 2 Fourier transform. [ABSTRACT FROM AUTHOR]

Non-woven jute (NWJ) produced from carpet industry waste was oxidized by H2O2 or alkali-treated by NaOH and compared with water-washed samples. Changes in the structure of the NWJ, tracked by X-ray diffraction (XRD), showed that both chemical treatments disrupt hydrogen bond networks between cellulose Iβ chains of the NWJ fibers. Thereafter, nano-carbon nitride (nCN) was impregnated, using a layer-by-layer technique, onto water-washed jute samples (nCN-Jw), NaOH-treated samples (nCN-Ja) and-H2O2 treated samples (nCN-Jo). Analysis of the Fourier transform infrared spectroscopy (FTIR) spectra of the impregnated samples revealed that nCN anchors to the water-washed NWJ surface through hemicellulose and secondary hydroxyl groups of the cellulose. In the case of chemically treated samples, nCN is preferentially bonded to the hydroxymethyl groups of cellulose. The stability and reusability of prepared nCN-jute (nCN-J) samples were assessed by tracking the photocatalytic degradation of Acid Orange 7 (AO7) dye under simulated solar light irradiation. Results from up to ten consecutive photocatalytic cycles demonstrated varying degrees of effectiveness across different samples. nCN-Jo and nCN-Ja samples exhibited declining effectiveness over cycles, attributed to bond instability between nCN and jute. In contrast, the nCN-Jw sample consistently maintained high degradation rates over ten cycles, with a dye removal percentage constantly above 90%. [ABSTRACT FROM AUTHOR]

Aiming at the problem that it is difficult to effectively characterize the operation status of hydropower units with a single vibration signal feature under the influence of multiple factors such as water–machine–electricity coupling, a multidimensional fusion feature extraction method for hydroelectric units based on time–frequency analysis and unsupervised learning models is proposed. Firstly, the typical time–domain and frequency–domain characteristics of vibration signals are calculated through amplitude domain analysis and Fourier transform. Secondly, the time–frequency characteristics of vibration signals are obtained by combining the complementary ensemble empirical mode decomposition and energy moment calculation methods to supplement the traditional time–domain and frequency–domain characteristics, which have difficulty in comprehensively reflecting the correlation between nonlinear non–stationary signals and the state of the unit. Finally, in order to overcome the limitations of shallow feature extraction relying on artificial experience, a Stacked Denoising Autoencoder is used to adaptively mine the deep features of vibration signals, and the extracted features are fused to construct a multidimensional feature vector of vibration signals. The proposed multidimensional information fusion feature extraction method is verified to realize the multidimensional complementarity of feature attributes, which helps to accurately distinguish equipment state types and provides the foundation for subsequent state identification and trend prediction. [ABSTRACT FROM AUTHOR]

Simple Summary: Based on the differences in otolith morphology and skeletal morphology, this study presents an investigation of the evolution of three Schizothoracinae species from two major river systems in Northwest China. A total of 138 samples were collected, and the morphological factors, morphological indices and Fourier transform coefficients of the otoliths were measured and analyzed to compare the morphological differences between the otoliths and bones. Morphological analysis of the otoliths of the three Schizothoracinae species revealed significant differences and cluster analysis further confirmed this relationship. At the same time, their skeletal morphology showed significant differences in the number of tentacles, pharyngeal teeth and vertebrae, as well as in the shape of several key bone blocks. The unique morphological characteristics and skeletal differences of the three Schizothoracinae species during their evolution are closely related to the geological changes in and water system evolution of the Qinghai-Tibet Plateau. This study not only deepens our understanding of the evolution of plateau fishes and other species but also provides a scientific basis for understanding the conservation and evolutionary mechanism of plateau fishes, which is highly important for ecological protection and biodiversity conservation. Schizothoracinae species are the largest group of Cypriniformes that readily adapt to the natural conditions of the Qinghai-Tibet Plateau. This group has habitat characteristics and distribution patterns centered on the Qinghai-Tibet Plateau. To study the evolution of three Schizothoracinae species in Northwest China, the evolutionary characteristics of these species were explored based on differences in otolith morphology and skeletal morphology. From 2020 to 2022, 138 samples (63 Aspiorhynchus laticeps, 35 Diptychus maculatus and 40 Schizothorax pseudaksaiensis) were collected from the Tarim River and Ili River, 6 basic morphological parameters of otoliths were measured and converted into 6 morphological factors and 7 morphological indices. A total of 77 Fourier transform coefficients of each otolith were selected The first three principal components accounted for 92.834% of the total variation in 13 otolith morphological indices of the three Schizothoracinae species, and the overall discrimination rate was 94.20%. According to the principal component analysis of 77 Fourier harmonic values of otoliths, the first 20 principal components explained 97.233% of the total variation, and the overall discrimination rate was 100%. The results of the cluster analysis directly reflected the relationships between related species. The differences in the bone morphology of the three Schizothoracinae species were particularly reflected in the number of whiskers, pharyngeal teeth and vertebrae, and there were also significant differences in the shapes of the sphenotic (SP), pterotic (PTE), preoperculum (PO), branchiostegal ray (BRA) and basibranchial (BB) bones. Their unique morphological and skeletal characteristics are closely related to geological changes and water system evolutionary trends. This study contributes to the understanding of species identification and the evolutionary status of plateau fishes, provides a reference for further evolutionary classification and for assessing the evolutionary mechanisms of plateau fishes, and provides a scientific basis for phylogeny and germplasm resource protection. [ABSTRACT FROM AUTHOR]

There have been archaeological and ethnographic reports of artificially modified crania from all continents. Archaeological excavations at the late fifth millennium BCE cemetery of Tol‐e Chega Sofla, located southwest of the Iranian plateau, also revealed these crania. This paper uses the morphometric approach to study Tol‐e Chega Sofla's modified crania. The outlines of normal and modified crania of Chega Sofla and Khuzestan residents' specimens were considered. How accurate is the morphometric approach in identifying and recognizing Chega Sofla's modified skulls from normal ones? Can it recognize small variations in the skull's morphology, such as the flattening of the squamous part of the occipital bone? The results of this method can be compared with descriptive studies. Finally, it is shown that the morphometric approach based on Elliptic Fourier Analysis can identify the deformed skull of Chega Sofla and its intensity, as well as the flattening of the squamous part of the occipital bone. [ABSTRACT FROM AUTHOR]

Herein, the effect of elastic strain on a Mach–Zehnder (MZ) interferometer created by graphene p–n junction in quantum Hall regime is investigated. It is demonstrated that a Gaussian‐shaped nanobubble causes detuning of the quantum Hall conductance oscillations across the p–n junction, due to the strain‐induced local pseudo‐magnetic fields (PMFs). By performing a machine‐learning‐based Fourier analysis, the nanobubble‐induced Fourier component from the conductance oscillations originating from the external magnetic fields is differentiated. It is shown that the detuning of the conductance oscillations is due to the altered pathway of quantum Hall interface channels caused by the strain‐induced PMFs. In the presence of the nanobubble, a new Fourier component for a magnetic flux Φ0/2$\left(\Phi\right)_{0} / 2$ appears, and the corresponding MZ interferometry indicates that the enclosed area is reduced by half due to the strain‐mediated pathway between two quantum Hall interface channels. In the findings, the potential of using graphene as a strain sensor is suggested for developments in graphene‐based device fabrications and measurements technologies. [ABSTRACT FROM AUTHOR]

The concept of Image Phase Congruency (IPC) is deeply rooted in the way the human visual system interprets and processes spatial frequency information. It plays an important role in visual perception, influencing our capacity to identify objects, recognize textures, and decipher spatial relationships in our environments. IPC is robust to changes in lighting, contrast, and other variables that might modify the amplitude of light waves yet leave their relative phase unchanged. This characteristic is vital for perceptual tasks as it ensures the consistent detection of features regardless of fluctuations in illumination or other environmental factors. It can also impact cognitive and emotional responses; cohesive phase information across elements fosters a perception of unity or harmony, while inconsistencies can engender a sense of discord or tension. In this survey, we begin by examining the evidence from biological vision studies suggesting that IPC is employed by the human perceptual system. We proceed to outline the typical mathematical representation and different computational approaches to IPC. We then summarize the extensive applications of IPC in computer vision, including denoise, image quality assessment, feature detection and description, image segmentation, image registration, image fusion, and object detection, among other uses, and illustrate its advantages with a number of examples. Finally, we discuss the current challenges associated with the practical applications of IPC and potential avenues for enhancement. [ABSTRACT FROM AUTHOR]

Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the stability estimate for the Helmholtz equation in a deterministic periodic structure is established. For the stochastic case, by introducing a variable transform, the variational formulation of the scattering problem in a random domain is reduced to that in a definite domain with random medium. Combining the stability result for the deterministic case with regularity and stochastic regularity of the scattering surface, Pettis measurability theorem and Bochner's Theorem further yield the stability result for the scattering problem by random periodic structures. Both stability estimates are explicit with respect to the wavenumber. [ABSTRACT FROM AUTHOR]

In this article we present a general method to rigorously prove existence of strong solutions to a large class of autonomous semi-linear PDEs in a Hilbert space Hl⊂Hs(Rm) (s≥1) via computer-assisted proofs. Our approach is fully spectral and uses Fourier series to approximate functions in Hl as well as bounded linear operators from L² to Hl. In particular, we construct approximate inverses of differential operators via Fourier series approximations. Combining this construction with a Newton-Kantorovich approach, we develop a numerical method to prove existence of strong solutions. To do so, we introduce a finite-dimensional trace theorem from which we build smooth functions with support on a hypercube. The method is then generalized to systems of PDEs with extra equations/parameters such as eigenvalue problems. As an application, we prove the existence of a traveling wave (soliton) in the Kawahara equation in H4(R) as well as eigenpairs of the linearization about the soliton. These results allow us to prove the stability of the aforementioned traveling wave. [ABSTRACT FROM AUTHOR]

In a deep, curved cavity, polymerization of a bulk fill composite can be challenging. The aim of this study was to investigate the solubility, water absorption, and conversion rate of bulk-fill composite samples prepared using molds with various slope angles. Bulk-fill composite resin (Filtek One Bulk Fill) was placed into cylindrical Teflon molds with a depth of 4 mm, angled at varying degrees (90°, 75°, 60°, 45°). Two different LED light-curing units (VALO Cordless, iLed Curing Light) were used to cure the samples. Polymerizations were performed at three different distances (0 mm, 2 mm, and 4 mm). Five samples per group were used, resulting in a total of 24 groups. The Fourier Transform Infrared Spectrometer was utilized to evaluate the conversion levels of the samples. Water sorption and solubility values were determined by storing the composites in distilled water at 37 °C for 21 days. The VALO light-curing unit applied closest to samples inserted in a 90° angulation mold had the highest mean degree of conversion (41.55%), while iLED light-curing unit group that applied from 4 mm to the samples inserted in a 45° angulation mold had the lowest mean conversion (8.97%). The angle of the cavity and the distance at which the light-curing unit is applied significantly affected bulk-fill composite resin conversion. In addition, the choice of light-curing unit impacted the conversion levels. However, with the tested conditions, the water sorption and solubility values of polymerized composite resin samples remain unaffected by these factors. [ABSTRACT FROM AUTHOR]

To address the prevalent genistein (GST) metabolism and inadequate intestinal absorption, an oral long-acting and gastric in-situ gelling gel was designed to encapsulate and localize the intestinal release of the loaded genistein-ginseng (GST-GNS) solid dispersion. Because of the high breast perfusion of GST upon oral absorption, the GST-GNS solid dispersion was developed to enhance GST's dissolution and penetration while offering a synergistic impact against breast cancer (BC). Physiochemical analysis of the GST-GNS solid dispersion, release analysis, gel characterizations, storage stability, penetration, and in vitro cytotoxicity studies were carried out. GST-GNS solid dispersion showed improved dissolution and penetration as compared to raw GST. GST-GNS solid dispersion homogenous shape particles and hydrophilic contacts were revealed by scanning electron microscopy and Fourier Transform-Infrared analysis, respectively. GST-GNS solid dispersion's diffractogram shows the amorphous character. A second modification involved creating a gastric in-situ gelling system loaded with GST-GNS solid dispersion. This system demonstrated improved GST penetration employing the solid dispersion, as well as the localizing of the GST release at the intestinal media and antitumor synergism against BC. For a better therapeutic approach for BC, the innovative oral GST long-acting gel encasing the GST-GNS solid dispersion would be recommended. [ABSTRACT FROM AUTHOR]

The Brundtland report has significantly influenced and guided sustainable development since its publication. There is abundant literature on how and to what degree the report and its incarnations (e.g. Agenda 21, Millennium Development Goals, Sustainable Development Goals) have been implemented at all spatial and governance scales. However, there is lesser literature on a quantitative determination and evaluation of the sustainability outcomes of implementing the report at a specified spatial–temporal scale. Therefore, this paper seeks to contribute towards remedying this, by determining and evaluating the indicated levels, nature, and dynamics of sustainability of the UK, for the period 2000–2018 from a Brundtland perspective. This is achieved by the application of the Sustainability Dynamics Framework to the results of the Sustainable Society Index. The results indicate that the sustainability of the UK improved from very weak to weak sustainability over the period. This was due to improvements in energy-related indicators which had a significant positive influence and impact upon sustainability outcomes. However, both the indicators of Population Growth and Public Debt were indicated as having a significant negative influence and impact upon the obtained levels and nature of sustainability. Furthermore, the Consumption indicator levels also had a significant detrimental influence upon the other indicators and sustainability over the period. The dynamics of sustainability occurring in the UK indicates the development of a more disturbed cycle of impacts upon the nature of the environment–human system and relationship. Therefore, unless corrective measures are taken through a fundamental transformational shift, then there is the realistic possibility of a systemic crisis occurring. [ABSTRACT FROM AUTHOR]

Abstract Power quality is a critical issue in power systems that can affect the performance and reliability of sensitive equipment. The dynamic voltage restorer (DVR) is a widely used technology for improving power quality, but it mainly focuses on mitigating voltage sags and often neglects the issue of harmonic distortion. This paper proposes a DVR voltage compensation strategy based on the discrete Fourier transform (DFT). This strategy utilizes the DFT to analyze the voltage waveform, separating the fundamental and desired harmonic components. With this strategy, the DVR can effectively compensate for voltage sag and achieve selective harmonic compensation, thereby improving the power quality of the power system. Additionally, a method utilizing hardware circuitry and an LED as a timestamp is proposed to dynamically estimate digital siginal processor (DSP) resource occupancy rate in real‐time, ensuring effective compensation while minimizing resource occupancy. A 3 kW DVR experimental prototype was constructed and tested to evaluate the practicality of the proposed strategy. The simulation and experimental results show that the method proposed in this paper successfully realizes the compensation of voltage sag and harmonics in the power system, and improves the stability and reliability of the power system.