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Multistep prediction of public parking spaces in the parking guidance and information system and parking reservation system has great benefits for intelligent parking. This study analyzes the C0 complexity of parking space occupancy time series from the frequency domain aspect. Results show that regular components account for the vast majority of parking space occupancy time series and can be considered a "quasiperiodic" series, which provides the theoretical basis for multistep prediction. This study combines the idea of Fourier transform (FT) and a machine learning method least squares support vector regression (LSSVR) together and proposes the Fourier transform–least squares support vector regression (FT–LSSVR) multistep prediction algorithm. As taking consideration of a predicting step threshold, this method has the power to predict single-step and multistep public parking spaces. Verification on two typical public parking lots in Hangzhou shows the great performance of FT–LSSVR. The prediction accuracy of proposed FT–LSSVR immensely outperforms the traditional LSSVR prediction after considering the step threshold. Moreover, the proposed method did not add the computational time complexity compared with the traditional LSSVR prediction. Thus, the proposed method is more suitable for real-time systems for its high prediction accuracy and less complex calculation. [ABSTRACT FROM AUTHOR]

In the present article, the authors study the heat equation in the form of the fractional wavelet transform with certain initial conditions, by exploiting the technique of fractional Fourier transform. The properties of the fundamental solution of heat equation are investigated and the relation between the fractional wavelet transform and fractional integrals obtained. The authors also study the computational aspect of the solution and heat flux of the heat equation as well as the Schrödinger equation. The graphical representations of both solutions and the heat flux for are shown and their values are compared with the classical solutions and found to have some better properties. [ABSTRACT FROM AUTHOR]

Index transforms with the product of the associated Legendre functions are introduced. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas are proved. The results are applied to solve a boundary value problem in a wedge for a third order partial differential equation. [ABSTRACT FROM AUTHOR]

Natural fibers have been focused by researches to develop high performance and eco-friendly reinforcement in polymer composites. The present work is deliberated on the characterization of nanoparticles of Aristida hystrix (AH) leaf fiber to confirm their compatibility as reinforcement in polymer composites. The macro leaf fiber is reduced to nanofiber particles by ball milling method. From the characterization results, the AH leaf nanoparticles had cellulose content of (61.21 wt %) and crystallinity index (58.37%). The thermal stability of AH nanofiber particles was studied under nitrogen and oxygen environment. From the results obtained, the thermal stability of this fiber was found to be closer to 298.6°C and 312.6°C respectively. The morphological analysis evidenced that the cellulosic particles were in nanoscale. The antibacterial activity of AH nanofiber particles against Escherichia coli, Acetino bacteria, Klebsiella pneumonia, and Staphylococcus aureus was determined by well diffusion method. The extracted AH nanopowder prepared by distilled water showed the maximum zone of inhibition against all tested bacterias in low concentrations (50 mg/50 µL). The zone of inhibition of AH fiber particles was better in Staphylococcus aureus bacteria, which is suitable for the medical applications. [ABSTRACT FROM AUTHOR]

We define the windowed Fourier transform, called also the Gabor transform, associated with singular partial differential operators. We establish Plancherel theorem, orthogonality property and inversion formula for this transform. Next, we define the localization operators , called also Gabor multipliers, associated with two windows and with symbol σ. First, we study the boundedness and compactness of the operators. Last, we define the Schatten-von Neumann class and we prove that the localization operators belong to. [ABSTRACT FROM AUTHOR]

A hydro-elastic frame has been considered to investigate the proliferation of waves over small base deformation on an infinitely extended flexible seabed. The flexible base surface is assumed as a thin elastic plate of very small thickness and it depends on the Euler–Bernoulli beam equation. For any particular frequency, there are two different modes of time-harmonic propagating wave exists rather than one mode of propagating wave along the positive horizontal direction. The waves with smaller wavenumber spread along the free-surface of the sea (say, free-surface mode) and the waves with higher wavenumber spread along the flexible base surface (say, flexural mode). A simplified perturbation approach is utilised to bring down the entire equations which govern the original boundary value problem (bvp) to a less complex bvp for the first-order velocity potential function. The first-order potential function along with the first-order reflection and transmission coefficients for both modes are calculated by a procedure based upon Fourier transform approach. A shape of sinusoidal swells flexible base surface is taken as an example to approve the scientific results. It is observed that when the train of normal incident propagating wave spreads over base distortion because of either the free-surface unsettling influence or the flexural wave movement in the sea, the reflected and transmitted energy are always feasible to be exchanged from one particular wave mode to another wave mode. Furthermore, we notice that the realistic changes in the flexural rigidity behaviour on the flexible base surface of the sea have a significant effect on the problem of water wave proliferation over small base deformation. Moreover, the energy conservation equation is derived with the help of the Green's integral theorem. The results for the values of reflection and transmission coefficients obtained for both the free-surface unsettling influence as well as flexural wave movement in the fluid are found to satisfy the energy conservation equation almost accurately. [ABSTRACT FROM AUTHOR]

In the present paper, we discuss about extension of the wavelet transform on distribution space of compact support and develop the Paley–Wiener–Schwartz type theorem for the wavelet transform on the same. Furthermore, Paley–Wiener–Schwartz type theorem for the wavelet transform is also established using the relation between the wavelet transform and double Fourier transform. [ABSTRACT FROM AUTHOR]

Image fusion is an important part of image processing because it can collaboratively use image information from different sensors for the same scene. Image fusion outputs the images, which are more suitable for human visual perception or computer processing and analysis; furthermore, it can obviously improve the shortcomings of a single sensor, as well as improve the image definition and packet content, making it conducive to accurately, reliably and comprehensively obtaining information regarding the target or scenarios. To improve the fusion precision of infrared and visible images, a new image fusion method for infrared and visible images is proposed in this paper. The proposed method is partitioned into three parts. First, anisotropic diffusion is used to decompose the source images into base and detail layers. Additionally, singular-value decomposition and principal-component analysis are adopted to calculate the final base and detail layers, respectively. Then, final detail and base layers are fused using the Fourier transform method. Finally, experiments with various infrared and visible images are conducted to evaluate the proposed method. Experimental and contrastive results show that the new algorithm has a good subjective visual effect; in addition, the objective evaluation index is improved significantly in terms of definition, mutual information and entropy. [ABSTRACT FROM AUTHOR]

Inspired by some works of Kirkby, J. L. [2015. Efficient option pricing by frame duality with the fast Fourier transform. SIAM Journal on Financial Mathematics 6(1), 713-747; 2016. An efficient transform method for Asian option pricing. SIAM Journal on Financial Mathematics 7(1), 845-892], we present a systematic study on effectively computing the Gerber-Shiu function in the Lévy risk model, where the frame duality projection is used for approximation. By introducing an auxiliary function, we provide a smooth extension of the Gerber-Shiu function, which has closed-form Fourier transform and is differentiable over the whole real line under some conditions. The objective function is approximated by its frame duality projection onto a Riesz basis, and the projection coefficients are readily computed by the fast Fourier transform algorithm. Error analysis is made and the effectiveness of our results will be further illustrated in the numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, using the Mellin transform of Wright function we derive an addition formula for the Wright function. In some special cases, addition formulas for the Hermite, Bessel and Mittag-Leffler functions are also given and the Green's function of two-dimensional time-fractional diffusion equation is presented in the whole plane. [ABSTRACT FROM AUTHOR]

A two-dimensional model has been developed to investigate the dynamic response of pavement-embankment-subsoil system considering the rise of water table. The ground consists of pavement, embankment, topsoil, saturated soil under the natural water table and semi-infinite substratum. Above the natural water table, the material is assumed to be dry and viscoelastic. Below the natural water table, the soil is saturated and modelled as poroviscoelasitc material. The semi-infinite substratum is assumed to be water-resistant and taken as a viscoelastic half-space. When the water table rises, the submerged part is then saturated and taken as poroviscoelastic medium. Biot’s theory and Fourier transform are employed to describe the problem, and some improvements are made based on traditional stiffness matrix method to give semi-analytical solution to the problem. The solution has been verified using a simplified problem reported by existing research. The influences of load characteristics and rise of water table are investigated. Resonance load frequency exists, at which the maximum surface vertical displacement of the pavement reaches its largest value. The rise of water table decreases the resonance frequency and generally increases the maximum surface vertical displacement of the pavement. The pore water pressure and pore water velocity are also substantially affected by the rise of water table. In general, the rise of water table has an amplifying effect on the vibration of the pavement system and increases the damage risk, which needs to be considered in the design and maintenance of highways. [ABSTRACT FROM AUTHOR]

Power quality is one of the key features in developing electric networks. It has been noticed because of its impact on economy and reliability of electrical networks. There are several power quality phenomena which are categorised in recent standards and literatures. Among them, voltage sag is more common and destructive for electric networks and consumers. This article presents a new detection method to monitor voltage sag in different electric network conditions. Goertzel algorithm is shown to be effective and simple for sag measurement compared to available sag detection methods. In order to increase the detection speed and response time, the Goertzel algorithm is modified. This modification will add to the speed of sag detection. The feasibility of the proposed method is justified through a measurement set-up developed using the dSPACE R1104 Digital Signal Processor Platform. The experimental results prove that sag measurement speed is improved by twice using the proposed modified Goertzel algorithm in comparison with the original method and some established methods. The results also verify that the sag detection of the proposed method is not affected by harmonic distortion of the voltage waveform. [ABSTRACT FROM AUTHOR]

Estimating an inverse regression space is especially important in sufficient dimension reduction. However, it typically requires a tuning parameter, such as the number of slices in a slicing method or bandwidth selection in a kernel estimation approach. Such a requirement not only affects the accuracy of estimates in a finite sample, but also increases difficulties for multivariate models. In this paper, we use a Fourier transform approach to avoid such difficulties and incorporate multivariate models. We further develop a Fourier transform approach to deal with variable selection, categorical predictor variables, and large p, small n data. To test the dimension, asymptotic results are obtained. Simulation studies and data analysis show the efficacy of our proposed methods. [ABSTRACT FROM AUTHOR]

Long-term Moderate Resolution Imaging Spectroradiometer (MODIS) Enhanced Vegetation Index (EVI) data have inherent noise due to clouds and poor atmospheric conditions that limit its applicability for environmental applications. This study was carried out with an objective of noise removal and reconstruction of time series MODIS EVI data (16 day) for the period 2010-2014 using de-noising algorithms. Relative evaluation of de-noising algorithms for smoothing temporal data with ideal noise free data is not possible in actual scenario. Hence, synthetic signals were generated and introduced Gaussian noise at different variance levels for evaluation purpose. Spatial analysis was carried out by introducing noise at different variance levels into the noise free EVI images from the raw EVI stacked image. Spatio-temporal analyses of noise signals in the reconstructed EVI images were evaluated in terms of performance indicators, namely Peak Signal-to-Noise Ratio and Mean Square Error. [ABSTRACT FROM AUTHOR]

The algebraic differentiators introduced by Mboup, Join and Fliessare studied in the frequency domain. The study complements the time-domain developments of the previous reference where a least-squares interpretation has allowed to explain the main properties of the method and also to devise efficient differentiators. The frequency-domain analysis gives answers to the central question of the choice of the algebraic differentiator parameters. Also, an interpretation of the algebraic differentiators in terms of wavelet decomposition is given. [ABSTRACT FROM AUTHOR]

One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et al proposed a dual-frequency method based on the Fourier transform profilometry, yet the low-frequency lobes are close to each other for accurate band-pass filtering. In the light of this problem, a novel dual-frequency pattern based on the spatial-temporal fringes (STF) method is developed in this paper. Three fringe patterns with two different frequencies are required. The low-frequency phase is obtained from two low-frequency fringe patterns by the STF method, so the signal lobes can be extracted accurately as they are far away from each other. The high-frequency phase is retrieved from another fringe pattern without the impact of the DC component. Simulations and experiments are conducted to demonstrate the excellent precision of the proposed method. [ABSTRACT FROM AUTHOR]

New index transforms with Weber-type kernels, consisting of products of Bessel functions of the first and second kind, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on the wedge for a fourth-order partial differential equation. [ABSTRACT FROM PUBLISHER]

The study and quantification of the tympanic membrane (TM) displacements add important information to advance the knowledge about the hearing process. A comparative statistical analysis between two commonly used demodulation methods employed to recover the optical phase in digital holographic interferometry, namely the fast Fourier transform and phase-shifting interferometry, is presented as applied to study thin tissues such as the TM. The resulting experimental TM surface displacement data are used to contrast both methods through the analysis of variance and F tests. Data are gathered when the TMs are excited with continuous sound stimuli at levels 86, 89 and 93 dB SPL for the frequencies of 800, 1300 and 2500 Hz under the same experimental conditions. The statistical analysis shows repeatability inz-direction displacements with a standard deviation of 0.086, 0.098 and 0.080 μm using the Fourier method, and 0.080, 0.104 and 0.055 μm with the phase-shifting method at a 95% confidence level for all frequencies. The precision and accuracy are evaluated by means of the coefficient of variation; the results with the Fourier method are 0.06143, 0.06125, 0.06154 and 0.06154, 0.06118, 0.06111 with phase-shifting. The relative error between both methods is 7.143, 6.250 and 30.769%. On comparing the measured displacements, the results indicate that there is no statistically significant difference between both methods for frequencies at 800 and 1300 Hz; however, errors and other statistics increase at 2500 Hz. [ABSTRACT FROM PUBLISHER]

In this paper, we deal with a new class of non-local operators that we term integro-differential systems of mixed type. We study the behaviour of solutions of this system when the diffusion term involves higher order fractional powers of the Laplacian. Moreover, we prove that the solution of the system decays faster than a power with an exponent given by the smallest index of the fractional power of the Laplacian. [ABSTRACT FROM PUBLISHER]

The fractional Radon transform defined, based on the Fourier slice theorem and the fractional Fourier transform, has many potential applications in optics and the pattern-recognition field. Here we study many properties of the fractional Radon transform using existing theory of the regular Radon transform: the inversion formulas, stability estimates, uniqueness and reconstruction for a local data problem, and a range description. Also, we define the fractional exponential Radon transform and present its inversion. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the nonparametric estimation of the Gerber-Shiu function in a compound Poisson risk model perturbed by diffusion. We present a more efficient estimator based on Fourier-Sinc series expansion. Our estimator is easily computed and has a faster convergence rate. Some simulation examples are provided to show that the estimator performs well when the sample size is finite. [ABSTRACT FROM AUTHOR]

In this paper, we get three integral representations for the linear independent solutions of differential equationin terms of the quartic Lévy stable functions. We also present the products of these solutions with new integral representations including the Bessel functions. Finally, we obtain the Riesz fractional derivative of solutions. [ABSTRACT FROM PUBLISHER]

Phase wraps in a 2D wrapped phase map can be completely eliminated or greatly reduced by frequency shifting. But it usually cannot be optimally reduced using conventional fast Fourier transform (FFT) because the spectrum can be shifted only by a integer number in the frequency domain. In order to achieve a significant phase wrap reduction, we propose a fast and precise two-step method for phase wraps reduction in this paper, which is based on the iterative local discrete Fourier transform (DFT). Firstly, initial estimate of the frequency peak is obtained by FFT. Then sub-pixel spectral peak with high resolution is determined by iteratively upsampling the local DFT around the initial peak location. Finally, frequency shifting algorithm that operates in the spatial domain is used to eliminate phase wraps. Simulations and experiments are conducted to demonstrate the superb computing efficiency and overall performance of the proposed method. [ABSTRACT FROM AUTHOR]

We present a massively parallel algorithm for the fused lasso, powered by a multiple number of graphics processing units (GPUs). Our method is suitable for a class of large-scale sparse regression problems on which a two-dimensional lattice structure among the coefficients is imposed. This structure is important in many statistical applications, including image-based regression in which a set of images are used to locate image regions predictive of a response variable such as human behavior. Such large datasets are increasingly common. In our study, we employ the split Bregman method and the fast Fourier transform, which jointly have a high data-level parallelism that is distinct in a two-dimensional setting. Our multi-GPU parallelization achieves remarkably improved speed. Specifically, we obtained as much as 433 times improved speed over that of the reference CPU implementation. We demonstrate the speed and scalability of the algorithm using several datasets, including 8100 samples of 512 × 512 images. Compared to the single GPU counterpart, our method also showed improved computing speed as well as high scalability. We describe the various elements of our study as well as our experience with the subtleties in selecting an existing algorithm for parallelization. It is critical that memory bandwidth be carefully considered for multi-GPU algorithms. Supplementary material for this article is available online. [ABSTRACT FROM PUBLISHER]

As full waveform inversion (FWI) requires large computation time, a variety of techniques have been suggested to reduce the computational burden. In this study, we use wavenumber-space-time domain modelling, which directly generatescommonmid-point (CMP) gathers, to implement theFWIalgorithm. The modelling technique, which is suitable for laterally invariant velocity models, synthesises CMP gathers efficiently by using limited wavenumber components, and therefore allows reduced computation time for FWI. To consider the accuracy as well as the efficiency of FWI, the Gauss- Newton method using the approximate Hessian matrix is chosen in this study. Rather than using all of the wavenumber components, our FWI algorithm can be accelerated by using only a few components. The wavenumber components can be chosen through an analysis of the residual wavefields. To validate the usefulness of our method,we first use a one-dimensional (1D) velocity model. From the 1D model example, we note that our FWI algorithm can be successful if given a reliable initial velocity model and sufficient data with a long offset distance. Even though our algorithm is valid for only horizontally layered velocity models, we apply our algorithm to a two-dimensional (2D) velocity model with lateral velocity variations. Through the 2D velocity example, we confirm that our FWI can be used to estimate subsurface structures with dipping interfaces if the dips are moderate and the structures can thus be considered to be locally flat. [ABSTRACT FROM AUTHOR]

This paper proposes new bounds on the prices of European-style swaptions for affine and quadratic interest rate models. These bounds are computable whenever the joint characteristic function of the state variables is known. In particular, our lower bound involves the computation of a one-dimensional Fourier transform independently of the swap length. In addition, we control the error of our method by providing a new upper bound on swaption price that is applicable to all considered models. We test our bounds on different affine models and on a quadratic Gaussian model. We also apply our procedure to the multiple curve framework. The bounds are found to be accurate and computationally efficient. [ABSTRACT FROM PUBLISHER]

We study the asymptotic behavior of the solutions related to a singularly perturbed q-difference-differential problem in the complex domain. The analytic solution can be splitted according to the nature of the equation and its geometry so that both, Gevrey andGevrey asymptotic phenomena are observed and can be distinguished, relating the analytic and the formal solution. The proof leans on a two level novel version of Ramis–Sibuya theorem under Gevrey and q-Gevrey orders. [ABSTRACT FROM PUBLISHER]

The present article is concerned with the investigation of disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures, in the presence of the combined effects of Hall currents and magnetic field. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi theories of type-II and type-III. Laplace and Fourier transform techniques are applied to solve the problem. The analytical expressions of displacements, stress components, temperature change, and current density components are obtained in the transformed domain. A numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of Hall current and two temperatures on resulting quantities. Some special cases are also deduced from the present investigation. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce the concept of the-product which is a very useful tool to obtain theanalytic Fourier–Feynman transform. We then use this concept to obtain various integration formulas involving the-product, the convolution product and the first variation. [ABSTRACT FROM AUTHOR]

In this article, we consider some characterizations for the stationary distribution of Ornstein–Uhlenbeck process with a two-state Markov switching. We show that if the drift coefficients α(1), α(2) are negative real numbers and diffusion coefficients σ(1), σ(2) are not equal to zero, then the stationary distributions of OU process with a two-state Markov switching have the density functions and the explicit Fourier transform of stationary density functions are obtained under some special cases. Furthermore, under some stronger assumptions for transition rate of the Markov chain, the Fourier transform of the density functions of stationary distribution can be approximated by where , πj is the invariant measure of Markov chain. Besides, some explicit expressions for the stationary distribution are presented and a numerical figure is used to illustrate our result. [ABSTRACT FROM AUTHOR]

In this paper, a series of new high-order numerical approximations toα-th Caputo derivatives (0<α<2) is derived based on a compound of shift operators and high-order approximations to Riemann–Liouville derivatives. The convergence order is independent of the derivative orderα, rather than the previous error estimates. Several numerical examples including the Caputo-type advection–diffusion equation are displayed, which support the derived numerical schemes. [ABSTRACT FROM PUBLISHER]

We consider the problem of estimating a regression function when a covariate is measured with error. Using the local polynomial estimator of Delaigle et al. [(2009), ‘A Design-adaptive Local Polynomial Estimator for the Errors-in-variables Problem’,Journal of the American Statistical Association, 104, 348–359] as a benchmark, we propose an alternative way of solving the problem without transforming the kernel function. The asymptotic properties of the alternative estimator are rigorously studied. A detailed implementing algorithm and a computationally efficient bandwidth selection procedure are also provided. The proposed estimator is compared with the existing local polynomial estimator via extensive simulations and an application to the motorcycle crash data. The results show that the new estimator can be less biased than the existing estimator and is numerically more stable. [ABSTRACT FROM PUBLISHER]

In this article, we consider European option pricing for time-changed Brownian models using Laplace transform. We obtain a general formula for the option price as the integral of a real-valued function involving the Laplace transform of the random time change. Unlike the usual Fourier transform technique, our method does not suffer from difficulties specific to complex integration, such as the evaluation of multiple-valued functions, and allows for a model-independent analysis of the truncation error. In the numerical analysis part, we compare option prices in variance gamma (VG), normal inverse Gaussian (NIG), and generalized hyperbolic (GH) models obtained by Laplace transform with those obtained by the Fourier transform method introduced by Carr and Madan in 1999. The results show that our method converges faster than the Fourier approach when the Laplace transforms of the subordinators decay exponentially, for examples like NIG and GH models. [ABSTRACT FROM PUBLISHER]

The aim of the present work is to introduce solution of special dual integral equations by the orthogonal polynomials. We consider a system of dual integral equations with trigonometric kernels which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions and convert them to Cauchy-type singular integral equations. We use the Chebyshev orthogonal polynomials to construct approximate solution for Cauchy-type singular integral equations which will solve the main dual integral equations. Numerical results demonstrate effectiveness of this method. [ABSTRACT FROM AUTHOR]

In phase unwrapping, the locations and densities of the residues are indicative of the severity of the unwrapping problem. Gdeisat et al. proposed an algorithm to increase the number of residues in a wrapped phase map to improve the results of phase unwrapping. The method proposed, though, is extremely time-consuming involving the computation of a Fourier transform along with the selection and shift of its spectral components. Moreover, there is no theoretical analysis on the reasons why the frequency shift should be able to increase the number of residues. In an attempt to address these problems, we propose a simple algorithm to increase the number of residues in a wrapped phase map. The algorithm uses a simple multiply operation in spatial domain to realize the frequency shift exploiting the frequency shift property of Fourier transform. We also discuss the relationship between the number of residues and frequency shift. Experimental results have demonstrated that the proposed method can speed up by more than 50% of the calculation time. [ABSTRACT FROM PUBLISHER]

It is well known that the magnitude of transformer inrush current depends on several factors such as transformer construction and the angle of the applied voltage at the time of energization. In this paper, a novel approach is proposed to compute inrush current in both of time and frequency domains taking into consideration the significance of formulas derived based on magnetic circuit of five-limb transformer. Electric circuit nonlinear mathematical equations are applied to solve inrush problem based on iteration via MATLAB code. The comparison of the Harmonic domain simulation results obtained from Hartley transform with that of Fourier transform proves the capability of Hartley transform to accurately assess inrush current requiring less number of computations. [ABSTRACT FROM PUBLISHER]

New index transforms, involving the squares of Bessel functions of the first kind as the kernel, are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces. Inversion theorems are proved. As an interesting application, a solution to the initial value problem for the third-order partial differential equation, involving the Laplacian, is obtained. [ABSTRACT FROM AUTHOR]

Accurate and real-time measurement of the power system signals’ phasor is an open challenge in future smart grids. This article analyzes the performance of three recently proposed phasor estimators and compares them with the proposed estimator algorithm. The article proposes an improved recursive wavelet transform for real-time estimation of phasor and frequency in smart power systems. The proposed algorithm performance is compared with the commonly used full-cycle discrete Fourier transform (DFT), the improved discrete Fourier transform, and the wavelet transform based methods. It is shown that improved recursive wavelet transform possesses an improvement over a wide range of decaying DC components, harmonic distortions, frequency deviations, and sampling frequency. These characteristics of the improved recursive wavelet transform make it a good candidate for real-time applications in any smart power system. [ABSTRACT FROM AUTHOR]

In this paper we examine necessary and sufficient conditions on the sequences of norm of the derivatives of functions insuch that their spectrum (the support of their Fourier transform) is contained in a given compact set in. [ABSTRACT FROM PUBLISHER]

With the goal of predicting progressive pavement distress (damage and rutting) under millions of cycles of moving vehicular loading, an efficient analysis framework is developed by combining the ideas of Fourier transform, finite element discretisation and time-scale separation. Using the simple observation of time-scale separation between evolution of pavement damage/rutting, temperature variation and traffic load variation, the analysis under millions of cycles is reduced to a few hundred analyses of stress and strain evolution under a single cycle of moving load. A new method called Fourier-finite element (FFE) method is proposed for each independent stress analysis. Essentially, Fourier analysis is used to eliminate the time dimension as well as the spatial dimension in the direction of traffic, reducing the problem to a set of two-dimensional problems, which are in turn solved using the finite element method (FEM). The FFE method is more efficient than direct three-dimensional (3D) FEM by orders of magnitude, but captures the 3D effects in an accurate manner. The FFE stress analysis technique is combined with time-scale separation-based ideas to develop a pavement performance modelling framework. A 20-year pavement simulation is presented to illustrate the efficiency of the proposed framework. [ABSTRACT FROM PUBLISHER]

Spaces of Boehmians having-growth () are constructed and studied. For, the Fourier transform is defined and properties are established. An inversion formula and an uncertainty principle are given for Boehmians. [ABSTRACT FROM PUBLISHER]

In this paper, we establishlocal uncertainty principle for the Fourier transform; and we deduceversion of Heisenberg–Pauli–Weyl uncertainty principle. We use also thelocal uncertainty principle, the partial Fourier integrals and the techniques of Donoho–Stark, we present two uncertainty principles of concentration type in thetheory, when. Some numerical applications are given. [ABSTRACT FROM AUTHOR]

Periodic wavelet frames have gained considerable popularity in recent years, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. In this article, we introduce the concept of periodic wavelet frame on local fields of positive characteristic and show that under weaker conditions the periodization of any wavelet frame constructed by the unitary extension principle with dilation factor 𝔭−1is a periodic wavelet frame on local fields. Moreover, based on the mixed extension principle and Fourier-based techniques of the wavelet frames, we present an explicit method for a pair of dual periodic wavelet frames on local fields of positive characteristic. [ABSTRACT FROM PUBLISHER]

Two methods of solving the inverse heat conduction problem with employment of the discrete Fournier transform are presented in this article. The first one operates similarly to the SVD algorithm and consists in reducing the number of components of the discrete Fournier transform which are taken into account to determine the solution to the inverse problem. The second method is related to the regularization of the solution to the inverse problem in the discrete Fournier transform domain. Those methods were illustrated by numerical examples. In the first example, an influence of the boundary conditions disturbance by a random error on the solution to the inverse problem (its stability) was examined. In the second example, the temperature distribution on the inner boundary of the multiply connected domain was determined. Results of calculations made in both ways brought very good outcomes and confirm the usefulness of applying the discrete Fournier transform to solving inverse problems. [ABSTRACT FROM AUTHOR]

In this study, we consider the frictional sliding contact problem between a functionally graded magnetoelectroelastic (MEE) layer resting on a perfectly insulated rigid half plane and a perfectly conducting rigid flat punch with frictional heat generation. The punch is subjected to magnetoelectromechanical loads. The graded layer is modeled as a nonhomogeneous medium with a transversely isotropic stress–strain law and an exponential variation of the magnetoelectrothermoelastic properties along the thickness direction. Neglecting inertia effects and assuming a constant friction coefficient, the solution is obtained within the framework of steady-state plane magnetoelectrothermoelasticity under plane strain conditions. The heat equation is first solved using Fourier transform to yield the temperature field in the layer which is then substituted in the MEE governing equations. These equations are solved analytically using the same transform leading to three coupled Cauchy-type singular integral equations in which the main unknowns are the normal contact stress, the electric displacement, and the magnetic induction. These equations are then solved numerically to obtain the distributions of the normal contact stress, electric displacement, and magnetic induction at the surface of the graded medium. The main objective of this paper is to study the effect of the nonhomogeneity parameter; the friction coefficient; and the elastic, electric, and magnetic coefficients on the surface contact pressure, electric displacement, and magnetic induction distributions for the case of flat punch profile. [ABSTRACT FROM PUBLISHER]

New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces. Inversion theorems are proved. As an interesting application, a solution of the initial value problem for the second-order partial differential equation, involving the Laplacian, is obtained. It is noted that the corresponding operators with the imaginary part of the modified Bessel function of the first kind lead to the familiar Kontorovich–Lebedev transform and its inverse. [ABSTRACT FROM AUTHOR]

In this paper, for real para-vector-valued signals, we obtain stronger uncertainty principles in terms of covariance and absolute covariance based on Fourier transform in both directional and the spatial cases. We provide certain conditions that give rise to the equal relation between the two uncertainty principles. Examples are presented to verify the results. [ABSTRACT FROM AUTHOR]

New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the Kontorovich–Lebedev and Fourier cosine transforms are established. Inversion theorems are proved. As an application, a solution of the initial value problem for the fourth order partial differential equation, involving the Laplacian is presented. [ABSTRACT FROM AUTHOR]

For the Fourier transformof a general (non-trivial) self-similar measure μ on the real line, we prove a large deviation estimate [ABSTRACT FROM PUBLISHER]

In this paper, Cauchy wavelet transform of ultra-distributions in tube domains is defined and its various properties are studied using the theory of Cauchy integrals and Poisson integrals of ultra-distributions. [ABSTRACT FROM PUBLISHER]