Relevant bibliographies by topics / Nonlocal operators

Academic literature on the topic 'Nonlocal operators'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Nonlocal operators"

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DU, QIANG, MAX GUNZBURGER, R. B. LEHOUCQ, and KUN ZHOU. "A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS." Mathematical Models and Methods in Applied Sciences 23, no. 03 (January 14, 2013): 493–540. http://dx.doi.org/10.1142/s0218202512500546.

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A vector calculus for nonlocal operators is developed, including the definition of nonlocal divergence, gradient, and curl operators and the derivation of the corresponding adjoint operators. Nonlocal analogs of several theorems and identities of the vector calculus for differential operators are also presented. Relationships between the nonlocal operators and their differential counterparts are established, first in a distributional sense and then in a weak sense by considering weighted integrals of the nonlocal adjoint operators. The operators of the nonlocal calculus are used to define volume-constrained problems that are analogous to elliptic boundary-value problems for differential operators; this is demonstrated via some examples. Another application discussed is the posing of abstract nonlocal balance laws and deriving the corresponding nonlocal field equations; this is demonstrated for heat conduction and the peridynamics model for continuum mechanics.
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Chen, Yufu, and Hongqing Zhang. "NONLOCAL SYMMETRIES AND NONLOCAL RECURSION OPERATORS." Acta Mathematica Scientia 21, no. 1 (January 2001): 103–8. http://dx.doi.org/10.1016/s0252-9602(17)30582-9.

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Lee, Hwi, and Qiang Du. "Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 1 (January 2020): 105–28. http://dx.doi.org/10.1051/m2an/2019053.

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Nonlocal gradient operators are prototypical nonlocal differential operators that are very important in the studies of nonlocal models. One of the simplest variational settings for such studies is the nonlocal Dirichlet energies wherein the energy densities are quadratic in the nonlocal gradients. There have been earlier studies to illuminate the link between the coercivity of the Dirichlet energies and the interaction strengths of radially symmetric kernels that constitute nonlocal gradient operators in the form of integral operators. In this work we adopt a different perspective and focus on nonlocal gradient operators with a non-spherical interaction neighborhood. We show that the truncation of the spherical interaction neighborhood to a half sphere helps making nonlocal gradient operators well-defined and the associated nonlocal Dirichlet energies coercive. These become possible, unlike the case with full spherical neighborhoods, without any extra assumption on the strengths of the kernels near the origin. We then present some applications of the nonlocal gradient operators with non-spherical interaction neighborhoods. These include nonlocal linear models in mechanics such as nonlocal isotropic linear elasticity and nonlocal Stokes equations, and a nonlocal extension of the Helmholtz decomposition.
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Lee, Duckhwan, and Herschel Rabitz. "Scaling of nonlocal operators." Physical Review A 32, no. 2 (August 1, 1985): 877–82. http://dx.doi.org/10.1103/physreva.32.877.

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Lizama, Carlos, Marina Murillo-Arcila, and Alfred Peris. "Nonlocal operators are chaotic." Chaos: An Interdisciplinary Journal of Nonlinear Science 30, no. 10 (October 2020): 103126. http://dx.doi.org/10.1063/5.0018408.

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Lou, Yifei, Xiaoqun Zhang, Stanley Osher, and Andrea Bertozzi. "Image Recovery via Nonlocal Operators." Journal of Scientific Computing 42, no. 2 (August 27, 2009): 185–97. http://dx.doi.org/10.1007/s10915-009-9320-2.

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DI CECIO, G., and G. PAFFUTI. "SOME PROPERTIES OF RENORMALONS IN GAUGE THEORIES." International Journal of Modern Physics A 10, no. 10 (April 20, 1995): 1449–63. http://dx.doi.org/10.1142/s0217751x95000693.

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We find the explicit operatorial form of renormalon type singularities in Abelian gauge theory. Local operators of dimension six take care of the first UV renormalon; nonlocal operators are needed for IR singularities. In the effective Lagrangian constructed with these operators nonlocal imaginary parts appearing in the usual perturbative expansion at large orders are canceled.
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Xu, Xin-Jian, and Chuan-Fu Yang. "Inverse nodal problem for nonlocal differential operators." Tamkang Journal of Mathematics 50, no. 3 (September 2, 2019): 337–47. http://dx.doi.org/10.5556/j.tkjm.50.2019.3361.

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Inverse nodal problem consists in constructing operators from the given zeros of their eigenfunctions. The problem of differential operators with nonlocal boundary condition appears, e.g., in scattering theory, diffusion processes and the other applicable fields. In this paper, we consider a class of differential operators with nonlocal boundary condition, and show that the potential function can be determined by nodal data.
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Ishikawa, Tomomi. "Perturbative matching of continuum and lattice quasi-distributions." EPJ Web of Conferences 175 (2018): 06028. http://dx.doi.org/10.1051/epjconf/201817506028.

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Matching of the quasi parton distribution functions between continuum and lattice is addressed using lattice perturbation theory specifically withWilson-type fermions. The matching is done for nonlocal quark bilinear operators with a straightWilson line in a spatial direction. We also investigate operator mixing in the renormalization and possible O(a) operators for the nonlocal operators based on a symmetry argument on lattice.
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Shakhmurov, Veli B. "Degenerate Differential Operators with Parameters." Abstract and Applied Analysis 2007 (2007): 1–27. http://dx.doi.org/10.1155/2007/51410.

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The nonlocal boundary value problems for regular degenerate differential-operator equations with the parameter are studied. The principal parts of the appropriate generated differential operators are non-self-adjoint. Several conditions for the maximal regularity uniformly with respect to the parameter and the Fredholmness in Banach-valuedLp−spaces of these problems are given. In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.
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Dissertations / Theses on the topic "Nonlocal operators"

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Dzhugan, Aleksandr <1994&gt. "Advanced properties of some nonlocal operators." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amsdottorato.unibo.it/10002/3/PhD%20Thesis%20Dzhugan.pdf.

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In this thesis, we deal with problems, related to nonlocal operators. In particular, we introduce a suitable notion of integral operators acting on functions with minimal requirements at infinity. We also present results of stability under the appropriate notion of convergence and compatibility results between polynomials of different orders. The theory is developed not only in the pointwise sense, but also in viscosity setting. Moreover, we discover the main properties of extremal type operators, with some applications. Then using the notion of viscosity solutions and Ishii-Lions technique, we give a different proof of the regularity of the solutions to equations involving fully nonlinear nonlocal operators. In the last part of the thesis we deal with domain variation solutions and with notions of a viscosity solution to two phase free boundary problem. We are looking at minima of energy functionals, the latter involving p(x)-Laplace operator or a non-negative matrix. Apart from the Riemannian case, we also consider the related Bernoulli functional in noncommutative framework. Finally, we formulate the suitable definition of a viscosity solution in Carnot groups.
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Schulze, Tim [Verfasser]. "Nonlocal operators with symmetric kernels / Tim Schulze." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1206592125/34.

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Bucur, C. D. "SOME NONLOCAL OPERATORS AND EFFECTS DUE TO NONLOCALITY." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/2434/488032.

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In this thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and some other types of fractional derivatives. We make an extensive introduction to the fractional Laplacian and to some related contemporary research themes. We add to this some original material: the potential theory of this operator and a proof of Schauder estimates with the potential theory approach, the study of a fractional elliptic problem in $mathbb{R}^n$ with convex nonlinearities and critical growth, and a stickiness property of $s$-minimal surfaces as $s$ gets small. Also, focusing our attention on some particular traits of the fractional Laplacian, we prove that other fractional operators have a similar behavior: Caputo stationary functions satisfy a particular density property in the space of smooth functions; an extension operator can be build for Marchaud-stationary functions.
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BUCUR, CLAUDIA DALIA. "Some nonlocal operators and effects due to nonlocality." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/10281/277792.

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In this thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and to some other types of fractional derivatives (the Caputo and the Marchaud derivatives). We make an extensive introduction to the fractional Laplacian, we present some related contemporary research results and we add some original material. Indeed, we study the potential theory of this operator, introduce a new proof of Schauder estimates using the potential theory approach, we study a fractional elliptic problem in Rn with convex nonlinearities and critical growth and we present a stickiness property of nonlocal minimal surfaces for small values of the fractional parameter. Also, we point out that the (nonlocal) character of the fractional Laplacian gives rise to some surprising nonlocal effects. We prove that other fractional operators have a similar behavior: in particular, Caputo-stationary functions are dense in the space of smooth functions; moreover, we introduce an extension operator for Marchaud-stationary functions.
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Voigt, Paul [Verfasser], and Moritz [Akademischer Betreuer] KaßMann. "Nonlocal operators on domains / Paul Voigt ; Betreuer: Moritz Kaßmann." Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/1139117726/34.

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Felsinger, Matthieu [Verfasser]. "Parabolic equations associated with symmetric nonlocal operators / Matthieu Felsinger." Bielefeld : Universitätsbibliothek Bielefeld, 2013. http://d-nb.info/1042557322/34.

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FRASSU, SILVIA. "Dirichlet problems for several nonlocal operators via variational and topological methods." Doctoral thesis, Università degli Studi di Cagliari, 2021. http://hdl.handle.net/11584/309589.

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The main topic of the thesis is the study of elliptic differential equations with fractional order driven by nonlocal operators, as the fractional p-Laplacian, the fractional Laplacian for p=2, the general nonlocal operator and its anisotropic version. Recently, great attention has been focused on the study of fractional and nonlocal operators of elliptic type, both for pure mathematical research and in view of concrete real-world applications. This type of operators arises in a quite natural way in many different contexts, such as, among others, game theory, image processing, optimization, phase transition, anomalous diffusion, crystal dislocation, water waves, population dynamics and geophysical fluid dynamics. The main reason is that nonlocal operators are the infinitesimal generators of Lévy-type stochastic processes. Such processes extend the concept of Brownian motion, where the infinitesimal generator is the Laplace operator, and may contain jump discontinuities. Our aim is to show existence and multiplicity results for nonlinear elliptic Dirichlet problems, driven by a nonlocal operator, by applying variational and topological methods. Such methods usually exploit the special form of the nonlinearities entering the problem, for instance its symmetries, and offer complementary information. They are powerful tools to show the existence of multiple solutions and establish qualitative results on these solutions, for instance information regarding their location. The topological and variational approach provides not just existence of a solution, usually several solutions, but allow to achieve relevant knowledge about the behavior and properties of the solutions, which is extremely useful because generally the problems cannot be effectively solved, so the precise expression of the solutions is unknown. As a specific example of property of a solution that we look for is the sign of the solution, for example to be able to determine whether it is positive, or negative, or nodal (i.e., sign changing).
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Abatangelo, N. "Large Solutions for Fractional Laplacian Operators." Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/320258.

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The thesis studies linear and semilinear Dirichlet problems driven by different fractional Laplacians. The boundary data can be smooth functions or also Radon measures. The goal is to classify the solutions which have a singularity on the boundary of the prescribed domain. We first remark the existence of a large class of harmonic functions with a boundary blow-up and we characterize them in terms of a new notion of degenerate boundary trace. Via some integration by parts formula, we then provide a weak theory of Stampacchia's sort to extend the linear theory to a setting including these functions: we study the classical questions of existence, uniqueness, continuous dependence on the data, regularity and asymptotic behaviour at the boundary. Afterwards we develop the theory of semilinear problems, by adapting and generalizing some sub- and supersolution methods. This allows us to build the fractional counterpart of large solutions in the elliptic PDE theory of nonlinear equations, giving sufficient conditions for the existence. The thesis is concluded with the definition and the study of a notion of nonlocal directional curvatures.
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Foghem, Gounoue Guy Fabrice [Verfasser]. "$L^2$-Theory for nonlocal operators on domains / Guy Fabrice Foghem Gounoue." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1219215139/34.

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Chaker, Jamil [Verfasser], and Moritz [Akademischer Betreuer] KaßMann. "Analysis of anisotropic nonlocal operators and jump processes / Jamil Chaker ; Betreuer: Moritz Kaßmann." Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/1150181672/34.

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Books on the topic "Nonlocal operators"

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Beghin, Luisa, Francesco Mainardi, and Roberto Garrappa, eds. Nonlocal and Fractional Operators. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69236-0.

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Andreu-Vaillo, Fuensanta. Nonlocal diffusion problems. Providence, R.I: American Mathematical Society, 2010.

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Nonlocal diffusion problems. Providence, R.I: American Mathematical Society, 2010.

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Yu, Savin Anton, and Sternin B. I︠U︡, eds. Elliptic theory and noncommutative geometry: Nonlocal elliptic operators. Basel: Birkhäuser, 2008.

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Danielli, Donatella, Arshak Petrosyan, and Camelia Pop, eds. New Developments in the Analysis of Nonlocal Operators. Providence, Rhode Island: American Mathematical Society, 2019. http://dx.doi.org/10.1090/conm/723.

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Rabczuk, Timon, Huilong Ren, and Xiaoying Zhuang. Computational Methods Based on Peridynamics and Nonlocal Operators. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20906-2.

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Mainardi, Francesco, Luisa Beghin, and Roberto Garrappa. Nonlocal and Fractional Operators. Springer International Publishing AG, 2022.

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Mainardi, Francesco, Luisa Beghin, and Roberto Garrappa. Nonlocal and Fractional Operators. Springer International Publishing AG, 2021.

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Ren, Huilong, Timon Rabczuk, and Xiaoying Zhuang. 'Computational Methods Based on Peridynamics and Nonlocal Operators: Theory and Applications. Springer International Publishing AG, 2023.

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Nazaykinskiy, Vladimir E., A. Yu Savin, and B. Yu Sternin. Elliptic Theory and Noncommutative Geometry: Nonlocal Elliptic Operators (Operator Theory: Advances and Applications Book 183). Birkhäuser, 2008.

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Book chapters on the topic "Nonlocal operators"

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Mazón, José M., Julio Daniel Rossi, and J. Julián Toledo. "Nonlocal Operators." In Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets, 45–52. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-06243-9_4.

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Krasil’ shchik, I. S., and P. H. M. Kersten. "Nonlocal theory." In Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations, 99–153. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-017-3196-6_3.

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Nyeo, Su-Long. "Evolution Equations for Nonlocal Hadron Operators." In Contemporary Topics in Medium Energy Physics, 37–50. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-9835-7_4.

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Rossi, Julio D. "The First Eigenvalue for Nonlocal Operators." In Trends in Mathematics, 741–72. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-02104-6_22.

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Rabczuk, Timon, Huilong Ren, and Xiaoying Zhuang. "First-Order Nonlocal Operator Method." In Computational Methods Based on Peridynamics and Nonlocal Operators, 67–97. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20906-2_3.

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Rabczuk, Timon, Huilong Ren, and Xiaoying Zhuang. "Higher Order Nonlocal Operator Method." In Computational Methods Based on Peridynamics and Nonlocal Operators, 123–56. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20906-2_5.

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Caffarelli, Luis A., and Yannick Sire. "On Some Pointwise Inequalities Involving Nonlocal Operators." In Harmonic Analysis, Partial Differential Equations and Applications, 1–18. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52742-0_1.

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Aksoylu, Burak, and Fatih Celiker. "Comparison of Nonlocal Operators Utilizing Perturbation Analysis." In Lecture Notes in Computational Science and Engineering, 589–606. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-39929-4_57.

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Karlovich, Yuri I. "C*-Algebras of Nonlocal Quaternionic Convolution Type Operators." In Clifford Algebras and their Applications in Mathematical Physics, 109–18. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2006-7_13.

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Aksoylu, Burak, Fatih Celiker, and Orsan Kilicer. "Nonlocal Operators with Local Boundary Conditions: An Overview." In Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 1–38. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-22977-5_34-1.

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Conference papers on the topic "Nonlocal operators"

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Korchemsky, Gregory P., Gianluca Oderda, and George Sterman. "Power corrections and nonlocal operators." In The 5th international workshop on deep inelastic scattering and QCD. American Institute of Physics, 1997. http://dx.doi.org/10.1063/1.53732.

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Salembier, Philippe. "Study on nonlocal morphological operators." In 2009 16th IEEE International Conference on Image Processing ICIP 2009. IEEE, 2009. http://dx.doi.org/10.1109/icip.2009.5414374.

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Arriola, E. Ruiz. "Anomalies for nonlocal dirac operators." In The international workshop on hadron physics of low energy QCD. AIP, 2000. http://dx.doi.org/10.1063/1.1303042.

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Glusa, Christian, and Marta D'Elia. "Nonlocal operators with variable coefficients." In Proposed for presentation at the One Nonlocal World, Opening Event held January 22-23, 2021 in Virtual, Virtual, Virtual. US DOE, 2021. http://dx.doi.org/10.2172/1854680.

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Zhu, Wenqiao, Changyu Diao, Min Li, Dongming Lu, and Yu Liu. "Variational Image Matting with Local and Nonlocal Operators." In 2014 International Conference on Virtual Reality and Visualization (ICVRV). IEEE, 2014. http://dx.doi.org/10.1109/icvrv.2014.31.

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Shuo Yang, Jianxun Li, and Zhangyuan Gu. "Nonlocal mathematical morphology and spatially-variant connected operators." In 2015 International Conference on Image and Vision Computing New Zealand (IVCNZ). IEEE, 2015. http://dx.doi.org/10.1109/ivcnz.2015.7761525.

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Lu, Wenqi, and Iain Styles. "Nonlocal Differential Operators Improve Image Reconstruction in Diffuse Optical Tomography." In Clinical and Translational Biophotonics. Washington, D.C.: OSA, 2018. http://dx.doi.org/10.1364/translational.2018.jtu3a.32.

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Lesev, Vadim N., Anna O. Zheldasheva, Oksana I. Bzheumikhova, and Cantemir M. Gukezhev. "On a Nonlocal Model with Operators of Fractional Integro-Differentiation." In 2018 IEEE International Conference "Quality Management, Transport and Information Security, Information Technologies" (IT&QM&IS). IEEE, 2018. http://dx.doi.org/10.1109/itmqis.2018.8525069.

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Ashyralyev, Allaberen, Sema Kaplan, Yasar Sozen, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Positivity of Two-Dimensional Elliptic Differential Operators with Nonlocal Conditions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636803.

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Pan, Huizhu, Wanquan Liu, Baoxiang Huang, Shixiu Zheng, Guojia Hou, and Ruixue Zhao. "A multichannel total variational Retinex model based on nonlocal differential operators." In Ninth International Conference on Graphic and Image Processing, edited by Hui Yu and Junyu Dong. SPIE, 2018. http://dx.doi.org/10.1117/12.2303547.

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Reports on the topic "Nonlocal operators"

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D'Elia, Marta, Mamikon Gulian, Tadele Mengesha, and James Scott. Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition. Office of Scientific and Technical Information (OSTI), December 2021. http://dx.doi.org/10.2172/1855046.

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Fan, Yiming. Nonlocal Operator Learning with Uncertainty Quantification. Office of Scientific and Technical Information (OSTI), August 2021. http://dx.doi.org/10.2172/1813660.

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D'Elia, Marta, Michael L. Parks, Guofei Pang, and George Karniadakis. nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications. Office of Scientific and Technical Information (OSTI), April 2020. http://dx.doi.org/10.2172/1614899.

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