For d≥2,D≥1, let Pd,D denote the set of all degree d polynomials in D dimensions with real coefficients without linear terms. We prove that for any Calderón-Zygmund kernel, K, the maximally modulated ...and maximally truncated discrete singular integral operator,supP∈Pd,D,N|∑0<|m|≤Nf(x−m)K(m)e2πiP(m)|, is bounded on ℓp(ZD), for each 1<p<∞. Our proof introduces a stopping time based off of equidistribution theory of polynomial orbits to relate the analysis to its continuous analogue, introduced and studied by Stein-Wainger:supP∈Pd,D|∫RDf(x−t)K(t)e2πiP(t)dt|.
First harmonic analysis (FHA) is arguably the most widely used analytical technique for wireless power transfer (WPT) circuits due to its simplicity. Although FHA can provide closed-form solutions, ...the existence of rectifier diode forward voltage drop and higher order harmonics, especially the second and third harmonics at variable duty cycle operation, can significantly deteriorate its accuracy. This paper presents an accurate and efficient method called enhanced multiple harmonic analysis (eMHA) for the optimal design and optimal control of WPT systems. The eMHA method considers the nature of nonlinear rectification networks under nonsinusoidal current and reexamines the concept of the equivalent load. As a result, the rectified WPT system is transformed into a series of linear systems with complex load impedances. The steady-state electric quantities can be then explicitly calculated. This enables eMHA to seamlessly work with numerical optimization algorithms to facilitate the automated design and optimization of WPT systems. An example of optimal design and optimal control of a 10 W WPT system is demonstrated. The results obtained by eMHA and FHA are also compared. A prototype of the designed circuit was constructed. The accuracy and effectiveness of eMHA are verified by experimental measurements. This paper is accompanied by a MATLAB-based analytical tool with a graphical user interface demonstrating the effects of circuit variables on electrical quantities and waveforms.
When intense light interacts with an atomic gas, recollision between an ionizing electron and its parent ion creates high-order harmonics of the fundamental laser frequency. This sub-cycle effect ...generates coherent soft X-rays and attosecond pulses, and provides a means to image molecular orbitals. Recently, high harmonics have been generated from bulk crystals, but what mechanism dominates the emission remains uncertain. To resolve this issue, we adapt measurement methods from gas-phase research to solid zinc oxide driven by mid-infrared laser fields of 0.25 volts per ångström. We find that when we alter the generation process with a second-harmonic beam, the modified harmonic spectrum bears the signature of a generalized recollision between an electron and its associated hole. In addition, we find that solid-state high harmonics are perturbed by fields so weak that they are present in conventional electronic circuits, thus opening a route to integrate electronics with attosecond and high-harmonic technology. Future experiments will permit the band structure of a solid to be tomographically reconstructed.
Condition monitoring plays an important role in improving reliability of power electronic converters including their dc-link capacitors because it contributes to predicting converter failures. This ...paper presents an analysis of a six-pulse diode rectifier used in the front-end of a three-phase PWM inverter intended for current-sensor-less condition monitoring of a dc-link capacitor. The analysis reveals the ripple current flowing out of a front-end six-pulse diode rectifier having ac line and dc inductors, which allows condition monitoring of both the capacitance and equivalent-series resistance (ESR) of the capacitor without using current sensors. Theoretical analysis reveals that the capacitor current is calculated by the three-phase ac source voltage, ac line inductor, dc inductor, and output power of the inverter. Experimental results obtained from a 200-V laboratory system confirmed that both the ESR and capacitance changes were observed without any current sensors.
Explicit Salem sets in Rn Fraser, Robert; Hambrook, Kyle
Advances in mathematics (New York. 1965),
03/2023, Letnik:
416
Journal Article
Recenzirano
We construct the first explicit (i.e., non-random) examples of Salem sets in Rn of arbitrary prescribed Hausdorff dimension. This completely resolves a problem proposed by Kahane more than 50 years ...ago. The construction is based on a form of Diophantine approximation in number fields.
This study proposed a novel approach for generating crushable agglomerates with realistic particle shapes in discrete element modeling (DEM). The morphologies of sand particles were obtained by X-ray ...micro-computed tomography scanning and image processing. Based on the particle surface reconstructed by spherical harmonic analysis, the crushable agglomerates with realistic particle shapes can be generated in DEM simulations. The results of single particle crushing tests showed that particle shapes significantly influence the fracture patterns and crushing strengths of sand particles. Furthermore, two one-dimensional compression tests were conducted to investigate the particle shape effect on micro- and macro-mechanical behaviors of crushable sands.
Communication infrastructure (CI) in microgrids (MGs) allows for the application of different control architectures for the secondary control (SC) layer. The use of new SC architectures involving CI ...is motivated by the need to increase MG resilience and handle the intermittent nature of distributed generation units. The structure of SC is classified into three main categories, including centralized SC (CSC) with a CI, distributed SC (DISC) generally with a low-data-rate CI, and decentralized SC (DESC) with communication-free infrastructure. To meet the MGs' operational constraints and optimize performance, control and communication must be utilized simultaneously in different control layers. In this survey, we review and classify all types of SC policies from CI-based methods to communication-free policies, including CSC, averaging-based DISC, consensus-based DISC methods, containment pinning consensus, event-triggered DISC, washout-filter-based DESC, and state-estimation-based DESC. Each structure is scrutinized from the viewpoint of the relevant literature. Challenges such as clock drifts, cyber-security threats, and the advantage of event-triggered approaches are presented. Fully decentralized approaches based on state-estimation and observation methods are also addressed. Although these approaches eliminate the need of any CI for the voltage and frequency restoration, during black start process or other functionalities related to the tertiary layer, a CI is required. Power hardware-in-the-loop experimental tests are carried out to compare the merits and applicability of different SC structures.
In various sections of the classical Fourier Analysis, the problem of the convergence of the integrals
as
and
under various assumptions on the functions f and g are considered. In this paper, we ...study some analogues of such problems for weight integrals of the form
for functions f and g from some weighted functional classes that are connected with Fourier-Bessel harmonic analysis.
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