336 research outputs found
Analysis of anisotropic nonlocal operators and jump processes
No full textChaker J. Analysis of anisotropic nonlocal operators and jump processes. Bielefeld: Universität Bielefeld; 2017
Regularity of solutions to anisotropic nonlocal equations
No full textChaker J. Regularity of solutions to anisotropic nonlocal equations. Mathematische Zeitschrift. 2020;296:1135–1155.We study harmonic functions associated to systems of stochastic differential equations of the form dXi t = Ai1( Xt-)dZ1 t + center dot center dot center dot + Aid (Xt-)dZd t, i. {1,..., d}, where Z j t are independent one-dimensional symmetric stable processes of order aj. (0, 2), j. {1,..., d}. In this article we prove Holder regularity of bounded harmonic functions with respect to solutions to such systems
Regularity estimates for fractional orthotropic p-Laplacians of mixed order
No full textChaker J, Ki M. Regularity estimates for fractional orthotropic p-Laplacians of mixed order. Advances in Nonlinear Analysis . 2022;11(1):1307-1331.We study robust regularity estimates for a class of nonlinear integro-differential operators with anisotropic and singular kernels. In this paper, we prove a Sobolev-type inequality, a weak Harnack inequality, and a local Holder estimate
Entropy dissipation estimates for the Boltzmann equation without cut-off
No full textChaker J, Silvestre L. Entropy dissipation estimates for the Boltzmann equation without cut-off . Kinetic and Related Models. 2023.We prove the the entropy production of the Boltzmann equation, in the non cutoff regime, is bounded from below by a weighted Lp norm of the solution. The estimate holds for a wide range of potentials including soft po-tentials as well as very soft potentials. We discuss applications of this estimate for weak solutions of the Boltzmann equation. In particular, we obtain that weak solutions must be belong to the space L1([0, T], Lpq(Rd)) for some precise exponents p and q
Repetitive current control of two-level and interleaved three-phase PWM utility connected converters
No full textThis thesis is mainly concerned with investigations into digital repetitive current controlof two-level and interleaved utility connected PWM converters. The research ismotivated by the relatively poor performance of classical (PI) controllers when theutility voltage harmonic distortion is high. This is due to the low gain, and poordisturbance rejection of the PI controller at the utility harmonic frequencies. Repetitivefeedback controllers have the ability to track or reject periodic disturbances, such asutility harmonics, as they naturally have high gains at the utility voltage harmonicfrequencies, assuming that these frequencies do not change.Repetitive controllers (RC) are known for being sensitive to variations in systemparameters and disturbance frequency, which in practice renders them either ineffectiveor unstable. Another challenge arises from the memory requirements of RC in case ofthe absence of even harmonics, which can make its practical implementation difficultand expensive. In addition, another problem that has not been investigated extensivelyin the literature is that the effectiveness of RC is severely limited by the limitedbandwidth of the plant (the utility connected converter and its filter). Theoreticalanalysis and simulation results presented in this thesis show that RC could noteffectively reject disturbances at frequencies above the closed loop system bandwidth.The design of the converter's output filter bandwidth and the values of its componentsneed to be selected carefully, to enable RC to be used effectively.The research in this thesis focuses on investigating the practical implementation andperformance limits of two types of repetitive controllers (conventional and oddharmonics),used for current control of two-level utility connected converter with LCLoutput filter. The odd-harmonic repetitive controller halves the memory requirementand offers higher gains only at odd harmonic frequencies of interest. The overall controlscheme consists of the traditional classical tracking controller with a dual loop feedbacksystem and RC. The results indicate that the repetitive controller improves the steadystate error and the total harmonic distortion of the output current, provided that theplant's bandwidth is sufficiently large.Finally, a repetitive controller for an interleaved utility connected converter has beendesigned and investigated in this study. The interleaved converter system has higherbandwidth than the two-level converter, which improves the effectiveness of RC. Itprovides good disturbance rejection compared to classical controllers which results inlow output current THD. The RC was demonstrated to be robust despite uncertainty inutility impedance, while achieving a fast almost zero error convergence. The proposedRC has been experimentally implemented using a DSP and the results indicate that thequality of output current complies with international standards on harmonic limits andmatches simulation results obtained from the Matlab/Simulink model of the system
Local regularity for nonlocal equations with variable exponents
No full textChaker J, Ki M. Local regularity for nonlocal equations with variable exponents. Mathematische Nachrichten . 2023;296(9):27 Seiten.In this paper, we study local regularity properties of minimizers of nonlocal variational functionals with variable exponents and weak solutions to the corresponding Euler-Lagrange equations. We show that weak solutions are locally bounded when the variable exponent p is only assumed to be continuous and bounded. Furthermore, we prove that bounded weak solutions are locally Holder continuous under some additional assumptions on p. On the one hand, the class of admissible exponents is assumed to satisfy a log-Holder-type condition inside the domain, which is essential even in the case of local equations. On the other hand, since we are concerned with nonlocal problems, we need an additional assumption on p outside the domain
Harnack inequality for nonlocal problems with non-standard growth
No full textChaker J, Ki M, Weidner M. Harnack inequality for nonlocal problems with non-standard growth. Mathematische Annalen . 2022;386:533–550 .We prove a full Harnack inequality for local minimizers, as well as weak solutions to nonlocal problems with non-standard growth. The main auxiliary results are local boundedness and a weak Harnack inequality for functions in a corresponding De Giorgi class. This paper builds upon a recent work on regularity estimates for such nonlocal problems by the same authors
-Laplacian of mixed order
No full textChaker J, Ki M, Weidner M. The concentration-compactness principle for the nonlocal anisotropic p-Laplacian of mixed order. Nonlinear Analysis : Theory, Methods & Applications . 2023;232: 113254.In this paper, we study the existence of minimizers of the Sobolev quotient for a class of nonlocal operators with an orthotropic structure having different exponents of integrability and different orders of differentiability. Our method is based on the concentration-compactness principle which we extend to this class of operators. One consequence of our main result is the existence of a nontrivial nonnegative solution to the corresponding critical problem.& COPY; 2023 Elsevier Ltd. All rights reserved
Dr. Jamil Jalibi: The Fragrence of Personal Relation and Research
No full textDr Jamil Jalibi (1929-2019) is a well-known writer, literary historian and critic. There are over thirty books on these genres, to his credit. He wrote a matchless History of Urdu Literature and edited a legendary literary magazine, Naya Daur, for many years. In this article, the author has remembered him, through his personal reflections. Unpublished letters of Dr Jamil Jalibi, addressed to the author, have also been produced here. These letters not only express his sentiments towards his addressee but also reflect his own personality through the words of affection and literature. Questions raised by the author are also answered by the literary genius. Issues requiring explanations have been expounded on, in the endnotes
Nonlocal operators with singular anisotropic kernels
No full textChaker J, Kaßmann M. Nonlocal operators with singular anisotropic kernels. Communications in Partial Differential Equations . 2019;45(1):1-31.We study nonlocal operators acting on functions in the Euclidean space. The operators under consideration generate anisotropic jump processes, e.g., a jump process that behaves like a stable process in each direction but with a different index of stability. Its generator is the sum of one-dimensional fractional Laplace operators with different orders of differentiability. We study such operators in the general framework of bounded measurable coefficients. We prove a weak Harnack inequality and Holder regularity results for solutions to corresponding integro-differential equations
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