Science topics: AnalysisHarmonic Analysis
Science topic
Harmonic Analysis - Science topic
Ths group is devoted to Harmonic Analysis (Fourier Analysis, Time Frequency A., Gabor Analysis...)
Publications related to Harmonic Analysis (10,000)
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We consider the Laplacian with drift in Rn$\mathbb {R}^n$ defined by Δν=∑i=1n(∂2∂xi2+2νi∂∂xi)$\Delta _\nu = \sum _{i=1}^n(\frac{\partial ^2}{\partial x_i^2} + 2 \nu _i\frac{\partial }{\partial {x_i}})$ where ν=(ν1,…,νn)∈Rn∖{0}$\nu =(\nu _1,\ldots ,\nu _n)\in \mathbb {R}^n\setminus \lbrace 0\rbrace$. This operator is self‐adjoint with respect to the...
This study focuses on the internal tides (ITs) off the Amazon shelf in the tropical Atlantic. It is based on 2 km horizontally gridded observations along the swaths of SWOT (Surface Water and Ocean Topography) track 20 during the calibration/validation phase (Cal/Val, 1 d orbit) from late March to early July 2023. We evaluate the amplitude of M2, N...
For each 1 ≤ i ≤ n , let k i ≥ 1 and let Δ i be a set of vertices of a non-degenerate simplex of k i + 1 points in $${\mathbb R}^{{k_{i}}+1}$$ R k i + 1 . If $$A \subseteq [0,1]^{k_{1}+1} \times \cdots \times [0,1]^{{k_{n}}+1}$$ A ⊆ [ 0 , 1 ] k 1 + 1 × ⋯ × [ 0 , 1 ] k n + 1 is a Lebesgue measurable set of measure at least δ , we show that there exi...
Among six-phase motors, those featuring symmetrical winding arrangements with a single neutral point (S6N1) offer enhanced fault tolerance. However, a single neutral point lowers the dc-link utilization in the linear pulsewidth modulation (PWM) range. Most previous multiphase overmodulation (OVM) methods address this limitation by injecting just no...
As a promising technology, grid-forming (GFM) converters can provide voltage and frequency support in grid-connected mode, and power local loads in islanded mode. Multiple GFM converters connected to the same point of common coupling (PCC) should not only ensure harmonic current sharing, but also reduce the PCC voltage harmonics. Most of the existi...
The application of electric fields induces changes in the symmetry of crystals, which can be observed spectroscopically as variations in the even harmonic generation. In this study, we report the ultrafast modulation of GaAs crystal symmetry using strong terahertz field. The modulation is recorded by the vibration of even harmonic intensity which d...
The optimization of DC-DC converters is crucial for enhancing their performance and efficiency in various applications. This study focuses on the sensitivity analysis of DC-DC converters to parametric variations, which plays a key role in designing robust and efficient systems. The methodology involves developing a simulation model that describes t...
The representation of the affine group is a crucial topic in harmonic analysis. In this paper, we use the wavelet transform to investigate the intertwining operator. This, approach helps compare different unitary representations of the affine group.
The prediction of tidal fields is crucial in coastal and marine hydrodynamic analyses, particularly in complex tidal environments, as it plays an essential role in disaster warning and fisheries management. However, monitoring the entire tidal field is impractical, and harmonic analysis and numerical simulation methods continue to face challenges i...
We introduce a new technique for the fields of harmonic analysis and PDE, simultaneous saturation. Simultaneous saturation is a framework for controlling the size of a set where each element of the set is large. In this paper we apply this framework to multilinear restriction type estimates. Here the elements of the set are $Tf(p)$ where $T$ is an...
Background
High‐resolution brain imaging is crucial in clinical diagnosis and neuroscience, with ultra‐high field strength MRI systems (≥7T$ \ge 7\ {\mathrm{T}}$) offering significant advantages for imaging neuronal microstructures. However, achieving magnetic field homogeneity is challenging due to engineering faults during the installation of sup...
Mechanical shaking enables efficient harvesting of olives, especially in hilly regions where automated farming is not feasible. This study delves into branch and olive detachment modeling to enhance the efficiency of a hand-held branch shaker. Shaking time, forces, accelerations, olive detachment forces and harvesting efficiency were experimentally...
This study introduces a novel space-time fractional diffusion equation with the capacity to model a diverse spectrum of diffusion processes. The equation incorporates Caputo-type time derivatives with an arbitrary order \(\beta\) and introduces a spatial-fractional operator known as the fractional Bessel operator. The fundamental solution of this e...
Background/Objectives: While previous study results have suggested an elevated risk of type 2 diabetes with potato consumption, limited and inconsistent results are available on the association of potato consumption with the risk of cardiovascular disease (CVD) and hypertension (HTN). We assessed the associations of (i) total potato consumption wit...
New Caledonia, in the southwestern tropical Pacific, has recently been identified as a hot spot for energetic semidiurnal internal tides. In a companion paper, the life cycle of coherent internal tides, characterized by fixed amplitude and phase, was investigated in the regions through harmonic analysis of a year-long, hourly time series from numer...
Internal tides are known to contain a substantial component that cannot be explained by (deterministic) harmonic analysis, and the remaining nonharmonic component is considered to be caused by random oceanic variability. For nonharmonic internal tides originating from distributed sources, the superposition of many waves with different degrees of ra...
We describe a method for constraining Laplacian and Dirac spectra of two dimensional compact orientable hyperbolic spin manifolds and orbifolds. The key ingredient is an infinite family of identities satisfied by the spectra. These spectral identities follow from the consistency between 1) the spectral decomposition of functions on the spin bundle...
A substantial fraction of internal tides cannot be explained by (deterministic) harmonic analysis. The remaining nonharmonic part is considered to be caused by random oceanic variability, which modulates wave amplitudes and phases. The statistical aspects of this stochastic process have not been analysed in detail, although statistical models for s...
We present a systematic study of the spin-resolved Josephson diode effect (JDE) in strongly spin-polarized ferromagnets (sFM) coupled to singlet superconductors (SC) via ferromagnetic insulating interfaces (FI). All metallic parts are described in the framework of the quasiclassical Usadel Green's function theory applicable to diffusive systems. Th...
The study of the Earth’s ionosphere is a topic that has increased in relevance over the past few decades. The ability to predict the ionosphere’s behavior, as well as to mitigate the effects of its rapid changes, is a matter of primary importance in satellite communications, positioning, and navigation applications at present. Ionosphere perturbati...
Purpose: This study aims to improve the design to prevent vibration and improve railway performance by examining the behaviour of the railway track supported by a concrete sleeper. Design/Methodology/Approach: The simulation for dynamic stresses has been carried out using Finite element modelling and analysis for the track-sleeper system's dynamic...
This paper investigates the effects of particle morphology (PM) and particle size distribution (PSD) on the micro-macro mechanical behaviours of granular soils through a novel X-ray micro-computed tomography (μCT)-based discrete element method (DEM) technique. This technique contains the grain-scale property extraction by the X-ray μCT, DEM paramet...
Time-modulated metasurface can serve as a spoofing cloak partially covering on a static real target, thereby generating false targets in the High-Resolution Range Profile (HRRP) and making the real target undetectable. This paper proposes an Electronic Counter-CounterMeasures (ECCM) detection method to nullify the spoofing capabilities of time-modu...
Available online This study employs harmonic analysis to investigate the relationship between Petkim stock prices and the USD/TL exchange rate. The harmonic analysis is a robust analytical method in modern time series analysis, particularly suitable for data exhibiting stationary characteristics without any apparent trend. This approach emphasizes...
Rationally constructed materials have enabled access to optical capabilities beyond nature’s limitations, thanks to advances made in both theory and experiment. These synthetic composites allow subwavelength confinement of electromagnetic energy and facilitate unparalleled control over different aspects of electromagnetic waves (polarization, ampli...
Electric vehicles (EVs) are poised to take center stage in daily transportation, gradually replacing vehicles solely reliant on combustion engines. Therefore, it is essential to address power quality issues associated with their integration into smart cities. Interleaved DC‐to‐DC boost converters are utilized to fulfill the objectives of voltage re...
We consider when there is absolute or unconditional convergence of series of various types of stochastic processes. These processes include differences of averages in ergodic theory and harmonic analysis, like the classical Cesaro average in ergodic theory and Lebesgue derivatives in harmonic analysis.
We use quantum harmonic analysis and representation theory to provide a new proof of Xia's theorem: "Toeplitz operators are norm dense in the Toeplitz algebra over the Bergman space of the unit ball."
In a hemostatic ultrasonic scalpel, high-frequency ultrasonic vibrations generate localized heat, leading to simultaneous cutting and coagulation of the area in contact with the tissue. Optimizing the design parameters results in more precise cutting and better tissue coagulation. This research involves optimization of the design and evaluation of...
Carleson and sparse collections of sets play a central role in dyadic harmonic analysis. We employ methods from optimization theory to study such collections. First, we present a strongly polynomial algorithm to compute the Carleson constant of a collection of sets, improving on the recent approximation algorithm of Rey. Our algorithm is based on s...
One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's problem: determining the optimal regularity of the initial condition $f$ of the Schr\"odinger equation given by \begin{equation*} \begin{cases} i\frac{\partial u}{\partial t} -\Delta_{\mathbb{R}^n} u=0\:,\:\:\: (x,t) \in \mathbb{R}^n \times \mathbb{R}\:, \newline u...
The simple spring structure, with detachable electrical contacts, is a very suitable solution for many applications, such as electromechanical relays and connectors. However, they are prone to exhibit instantaneous interruption faults under mechanical vibration environments. In this paper, the governing equations of the modal analysis of a beam wit...
We present a comprehensive framework for studying and leveraging morphological symmetries in robotic systems. These are intrinsic properties of the robot’s morphology, frequently observed in animal biology and robotics, which stem from the replication of kinematic structures and the symmetrical distribution of mass. We illustrate how these symmetri...
A novel method for the direction of arrival (DOA) estimation of coherent signals under a space–time–coding metasurface (STCM) is proposed in this paper. Noticeably, the STCM can replace multi-channel arrays with a single channel, which can be utilized to modulate incident electromagnetic waves and generate harmonics. However, coherent signals are o...
This article pays homage to the life and work of Hans Georg Feichtinger. It focusses on his major mathematical achievements and important professional aspects.
The reform of Ukraine’s competition law is an important step towards integration into the European economic space, contributing to the development of transparent and fair market relations. A key direction of this reform is the improvement of merger control and the harmonization of national norms with EU legislation, particularly Regulation No. 139/...
Potato, a vital food and cash crop, necessitates precise identification and area estimation for effective planting planning, market regulation, and yield forecasting. However, extracting large-scale crop areas using satellite remote sensing is fraught with challenges, such as low spatial resolution, cloud interference, and revisit cycle limitations...
The Halo Conjecture presents one of the outstanding open problems in the theory of differentiation of integrals. In this paper we discuss the Halo Conjecture and its connections with topics of current interest in harmonic analysis.
High-frequency sea level observations from long-term tide gauges are indispensable for a wide array of scientific inquires, including storm surges, ocean tides, and tsunamis. The University of Hawaii Sea Level Center (UHSLC) stands as a pivotal sea level database, offering meticulously curated, hourly sea level records across the global ocean throu...
In this study, we present an improved linear quadratic closed-loop rotor vibration controller that uses a steady-state Kalman filter and an augmented integral controller to improve the traditional T-matrix–based rotor vibration controller. The proposed linearized vibration controller features closed-loop stability more rigorously than the conventio...
Gyrotron driven by the axis-encircling electron beam is a pathway for generating frequency-tunable terahertz radiation on multiple harmonics. In this article, a large-orbit gyrotron (LOG) is designed, manufactured, and experimentally investigated. A magnetic cusp gun (MCG), demonstrating high robustness over a broad range of magnetic fields, has be...
In this article, an approach is presented to ensure that a rooftop solar power plant performs efficiently in the face of partial shading. A two-stage, five-level H-Bridge hardware structure has been implemented to achieve lower switching losses compared to conventional two-level inverters. This design reduces heat generation and enhances the effici...
Sinusoidal modeling (SM) has been studied for speech modeling, which aims at representing and flexibly resynthesizing the speech waveform by the frequency and complex amplitude of several components. However, SM methods model the speech frame by frame, which inevitably leads to a loss of information between individual frames. In addition, SM method...
This paper presents the design and optimization of a low-weight helium-free Nb-Ti CCT superconducting magnet (MAGDEM – MAGent DEMonstrator) for the R&D phase of the ISOLDE Superconducting Recoil Separator (ISRS) at CERN (Geneva, Switzerland). The system can be expanded to other accelerator applications demanding compact lightweight superconducting...
This letter presents second-harmonic termination techniques for inductively source-degenerated cascode CMOS low-noise amplifiers (LNAs) with a transformer (TF)-based harmonic network. The proposed harmonic trap circuit terminates the second-order distortion generated in the common-source stage of the cascode structure, thereby improving the lineari...
For dual three-phase permanent magnet synchronous machines (DPMSMs), this article presents three dynamic overmodulation methods for selecting optimal duty cycles with maximum dc-link utilization. Concretely, the voltage references computed by the current controller exceed the modulating constraints when suffering a large reference or sudden load ch...
The estimation of signal distortions caused by sensor movement is a fundamental problem in modern signal processing systems. Standard Doppler analysis estimates signal distortions by assuming that all objects in the system travel at a constant velocity. The increasing speed and complexity of modern systems, however, requires an understanding of how...
A sound field estimation method using moving microphones is proposed. The sound field is modelled with an infinite sequence of spherical harmonic coefficients for each frequency in the discrete Fourier transform domain, and the harmonic coefficients are estimated using Bayesian inference. The proposed method allows for the use of microphones with a...
In a single-phase grid-tie system, the presence of a second harmonic current (SHC) on the DC side reduces the conversion efficiency and lifetime of the DC source. For a system whose front-end is a boost type converter, a digital band-stop filter (BSF) with a center frequency of 120 Hz could be introduced in the voltage sampling loop to suppress the...
There is the third harmonic current in five-phase permanent magnet synchronous motors (PMSMs), thus causing the distortion of stator currents and additional copper loss. Although the existing finite-control-set with virtual voltage vectors (FCS-V3s) can eliminate the harmonic voltage of harmonic subspace, it completely loses the ability to control...
The HVDC transmission system with a line-commutated converter is prone to commutation failure when connected to a weak AC grid and has disadvantages such as a large footprint of AC filters and high noise from the converter transformer. This paper presents a shunt capacitor-commutated converter (SCCC) without AC filters, using a constant extinction...
This study proposes a dual-band rectifier that utilizes a symmetric impedance control network (SICN) for highly efficient wireless power transfer. The proposed rectifier comprises a voltage doubler and an SICN connected to each diode of the voltage doubler. The SICN controls the input impedance seen by each diode at two fundamental frequencies and...
This paper presents an alternative solution for higher frequency power amplifier design. Using a plasticpackaged GaN transistor and high-efficiency design techniques, a power amplifier for the space-to-earth satellite was designed and fabricated. The proposed design approach relies on determining an appropriate design space for the matching network...
This paper proposes an asymmetric phase model predictive current control (MPCC) interleaving method to improve the power density, power factor (PF), and total harmonic distortion (THD) of power factor correction (PFC) converters. The MPCC method does not use a modulator, which makes it difficult to apply the conventional interleave method. Furtherm...
This paper presents the implementation of two-section coaxial stepped impedance resonators (SIRs) solution to control the attenuated band of Tx bandpass filters. This type of resonator has two degrees of freedom, in the transverse and longitudinal dimensions. At a fixed fundamental frequency, this allows the dimensions of the resonators to be modul...
The integration of distributed generation (DG), renewable energy sources (RES), and power electronic converters into distribution systems (DSs) has introduced significant power quality (PQ) challenges, such as voltage fluctuations, harmonic distortions, and transients. These issues can undermine the reliability and stability of power systems, makin...
This paper investigates the vibration behavior of a chimney at the Tripoli-West power plant under wind loads. Finite element models of the chimney are developed to analyze the existing chimney structure, and assess the impact of repositioning the supporting rings typically used in such chimneys. Both free vibration modal analysis and forced vibrati...
Geoid undulation has been determined for Nigeria in order to demonstrate its relationship with topography and the dynamic structure of the Earth’s interior. Spherical harmonic expansion using the Earth Gravitational Model 2008 (EGM2008) referenced to the WGS84 (World Geodetic System 1984) with coefficients extending to degree 2190 and order 2159 wa...
From the tidal constituent harmonic constant spherical coordinate grid, construct a normalized tidal load spherical harmonic coefficient model and a first-degree tidal load spherical harmonic coefficient model by spherical harmonic analysis.
The tidal load spherical harmonic coefficient model format is the same as FES2004 ocean tidal load model in...
Long time series of velocity profiles collected by up-looking acoustic profilers in the westernmost sill of the Strait of Gibraltar show an unexpected pattern in the deepest ∼80 m of the water column, consisting in an appreciable diurnal weakening of the measured horizontal velocity. A harmonic analysis performed on long time series reveals a surpr...
From the global load spherical coordinate grid model time series such as land/sea surface atmosphere, land water and sea level variation, construct the normalized surface load spherical harmonic coefficient (m) model time series by spherical harmonic analysis and calculate the load effect time series (Xcm, Ycm, Zcm, in unit of mm) on Earth's center...
The article presents studies of prefabricated slotting cutters for heavy lathes and rotary machines designed for cutting deep grooves with a width of 32 to 40 mm in parts such as rotating bodies. The research methods used were simulation modeling of the three-dimensional stress-strain state of prefabricated cutter structures, simulation modeling of...
Although artificial intelligence (AI) is often perceived as the field of computer science that experienced the greatest development, without the wide scope of mathematical fields and methods, AI would not be possible. Mathematical areas in AI include standard methods of analysis (continuous or discrete), set theory and various logic’s (propositiona...
In modern power systems, the prevalence of harmonic distortion mandates robust monitoring. Harmonic monitoring faces formidable challenges due to significant uncertainties in measurements, network parameters, and the varying nature of harmonic sources alongside the limited deployment of harmonic meters and inaccessible nodes. A remedy involves the...
The Calderón reproducing formula is the most important in the study of harmonic analysis, which has the same property as the one of approximate identity in many special function spaces. In this note, we use the idea of separation variables and atomic decomposition to extend single parameter to two-parameters and discuss the convergence of Calderón...
We define Bregman variation of semimartingales. We give its pathwise representation, It\^o-type isometry for martingales, and applications to harmonic analysis.
We investigate classical continuous systems characterized by singular velocity distributions, where the corresponding Radon measures are defined over the entire space with infinite mass. These singular distributions are used to model particle velocities in systems where traditional velocity distributions do not apply. As a result, the particle posi...
We study a summability method called almost convergence for bounded measurable functions defined on a locally compact abelian group. We define almost convergence using topologically invariant means and exhibit two different kinds of necessary and sufficient conditions, one is analytic and the other is functional analytic, for a given function to be...
A long standing problem in abstract harmonic analysis concerns the strong Arens irregularity (sAir, for short) of the Fourier algebra $A(G)$ of a locally compact group $G.$ The groups for which $A(G)$ is known to be sAir are all amenable. So far this class includes the abelian groups, the discrete amenable groups, the second countable amenable grou...
This paper is devoted to the growth of high-order Sobolev norms of solutions in time in the context of the Hartree equation in 2- or 3-dimensional spaces. By combining modified energies with appropriate Strichartz estimates, we derive polynomial-time bounds for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{...
This paper delves into the Dunkl-Bessel operator on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^{d+1}_+$$\end{document} and its corresponding harmonic...
The foundation of the turbo-generator comprises a generator, turbine, and associated
equipment situated on the top of the frame foundation, which consists of a bottom raft, top
deck, and columns. The current study examines how the geometrical characteristics of the
frame foundation, such as slab thickness, column dimensions, and length, affect t...
The complexity of improving controllers for Active Magnetic Bearing Systems (AMBs), which are essential parts of fast electronic transport networks such as electric cars, aviation technology, and defense systems is examined in this research work. It evaluates AMBs’ robustness against abrupt harmonic disruptions using wavelet transform methodologies...
The article presents a computational and experimental study of the dynamic characteristics of a spacecraft telescope frame mock-up. The main attention is paid to the methodology of vibrodynamic tests using a three-component laser vibrometer and the creation of a finite element model of the mock-up under study. To analyze the dynamics of the structu...