Relevant bibliographies by topics / Nonlocal second order operators

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Nonlocal second order operators'

Author: Grafiati
Published: 4 June 2021
Last updated: 2 February 2022

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Journal articles on the topic "Nonlocal second order operators"

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Amster, P., and P. De Nápoli. "A nonlinear second order problem with a nonlocal boundary condition." Abstract and Applied Analysis 2006 (2006): 1–11. http://dx.doi.org/10.1155/aaa/2006/38532.

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We study a nonlinear problem of pendulum-type for ap-Laplacian with nonlinear periodic-type boundary conditions. Using an extension of Mawhin's continuation theorem for nonlinear operators, we prove the existence of a solution under a Landesman-Lazer type condition. Moreover, using the method of upper and lower solutions, we generalize a celebrated result by Castro for the classical pendulum equation.
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Euler, M., N. Euler, and M. C. Nucci. "On nonlocal symmetries generated by recursion operators: Second-order evolution equations." Discrete & Continuous Dynamical Systems - A 37, no. 8 (2017): 4239–47. http://dx.doi.org/10.3934/dcds.2017181.

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Baranets'kyy, Ya O. "Similitude operators generated by nonlocal problems for second-order elliptic equations." Ukrainian Mathematical Journal 44, no. 9 (September 1992): 1072–79. http://dx.doi.org/10.1007/bf01058366.

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Li, Meili, and Chunhai Kou. "Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions." Discrete Dynamics in Nature and Society 2009 (2009): 1–11. http://dx.doi.org/10.1155/2009/641368.

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The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem.
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Kandemir, Mustafa. "SOLVABILITY OF BOUNDARY VALUE PROBLEMS WITH TRANSMISSION CONDITIONS FOR DISCONTINUOUS ELLIPTIC DIFFERENTIAL OPERATOR EQUATIONS." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 1 (March 30, 2016): 5842–57. http://dx.doi.org/10.24297/jam.v12i1.609.

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We consider nonlocal boundary value problems which includes discontinuous coefficients elliptic differential operator equations of the second order and nonlocal boundary conditions together with boundary-transmission conditions. We prove coerciveness and Fredholmness for these nonlocal boundary value problems.
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MUSLIM, M., AVADHESH KUMAR, and RAVI P. AGARWAL. "Exact and trajectory controllability of second order nonlinear differential equations with deviated argument." Creative Mathematics and Informatics 26, no. 2 (2017): 181–91. http://dx.doi.org/10.37193/cmi.2017.02.07.

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In this manuscript, we consider a control system governed by a second order nonlinear differential equations with deviated argument in a Hilbert space X. We used the strongly continuous cosine family of bounded linear operators and fixed point method to study the exact and trajectory controllability. Also, we study the exact controllability of the nonlocal control problem. Finally, we give an example to illustrate the application of these results.
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SHAW, JIIN-CHANG, and MING-HSIEN TU. "NONLOCAL EXTENDED CONFORMAL ALGEBRAS ASSOCIATED WITH MULTICONSTRAINT KP HIERARCHY AND THEIR FREE FIELD REALIZATIONS." International Journal of Modern Physics A 13, no. 16 (June 30, 1998): 2723–37. http://dx.doi.org/10.1142/s0217751x98001384.

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We study the conformal properties of the multiconstraint KP hierarchy and its non-standard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extensions of Wn algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian structure of the nonstandard multiconstraint KP hierarchy can be simplified by factorizing its Lax operator to multiplication form. We then diagonalize this simplified Poisson matrix and obtain the free field realizations of its associated nonlocal algebras.
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Anthoni, S. Marshal, J. H. Kim, and J. P. Dauer. "Existence of mild solutions of second-order neutral functional differential inclusions with nonlocal conditions in Banach spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 22 (2004): 1133–49. http://dx.doi.org/10.1155/s0161171204310410.

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We study the existence of mild solutions of the nonlinear second-order neutral functional differential and integrodifferential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of bounded linear operators and a fixed point theorem for condensing maps due to Martelli.
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Mokin, A. Yu. "Spectral properties of a nonlocal second-order difference operator." Differential Equations 50, no. 7 (July 2014): 938–46. http://dx.doi.org/10.1134/s001226611407009x.

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Todorov, Todor D. "Nonlocal problem for a general second-order elliptic operator." Computers & Mathematics with Applications 69, no. 5 (March 2015): 411–22. http://dx.doi.org/10.1016/j.camwa.2014.12.014.

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Dissertations / Theses on the topic "Nonlocal second order operators"

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Us, Oleksiy. "On the qualitative theory of second order elliptic operators." Thesis, University of Bristol, 2001. http://hdl.handle.net/1983/da98356b-08c1-4377-a57b-3abd0b62ed5a.

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Brabazon, Keeran J. "Multigrid methods for nonlinear second order partial differential operators." Thesis, University of Leeds, 2014. http://etheses.whiterose.ac.uk/8481/.

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This thesis is concerned with the efficient numerical solution of nonlinear partial differential equations (PDEs) of elliptic and parabolic type. Such PDEs arise frequently in models used to describe many physical phenomena, from the diffusion of a toxin in soil to the flow of viscous fluids. The main focus of this research is to better understand the implementation and performance of nonlinear multigrid methods for the solution of elliptic and parabolic PDEs, following their discretisation. For the most part finite element discretisations are considered, but other techniques are also discussed. Following discretisation of a PDE the two most frequently used nonlinear multigrid methods are Newton-Multigrid and the Full Approximation Scheme (FAS). These are both very efficient algorithms, and have the advantage that when they are applied to practical problems, their execution times scale linearly with the size of the problem being solved. Even though this has yet to be proved in theory for most problems, these methods have been widely adopted in practice in order to solve highly complex nonlinear (systems of) PDEs. Many research groups use either Newton-MG or FAS without much consideration as to which should be preferred, since both algorithms perform satisfactorily. In this thesis we address the question as to which method is likely to be more computationally efficient in practice. As part of this investigation the implementation of the algorithms is considered in a framework which allows the direct comparison of the computational effort of the two iterations. As well as this, the convergence properties of the methods are considered, applied to a variety of model problems. Extensive results are presented in the comparison, which are explained by available theory whenever possible. The strength and range of results presented allows us to confidently conclude that for a practical problem, discretised using a finite element discretisation, an improved efficiency and stability of a Newton-MG iteration, compared to an FAS iteration, is likely to be observed. The relative advantage of a Newton-MG method is likely to be larger the more complex the problem being solved becomes.
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Noble, Raymond Keith. "Some problems associated with linear differential operators." Thesis, Cardiff University, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238160.

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Mason, Colin Stuart. "Boundary perturbations and ultracontractivity of singular second order elliptic operators." Thesis, King's College London (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.395943.

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Yang, Xue. "Neumann problems for second order elliptic operators with singular coefficients." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html.

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In this thesis, we prove the existence and uniqueness of the solution to a Neumann boundary problem for an elliptic differential operator with singular coefficients, and reveal the relationship between the solution to the partial differential equation (PDE in abbreviation) and the solution to a kind of backward stochastic differential equations (BSDE in abbreviation).This study is motivated by the research on the Dirichlet problem for an elliptic operator (\cite{Z}). But it turns out that different methods are needed to deal with the reflecting diffusion on a bounded domain. For example, the integral with respect to the boundary local time, which is a nondecreasing process associated with the reflecting diffusion, needs to be estimated. This leads us to a detailed study of the reflecting diffusion. As a result, two-sided estimates on the heat kernels are established. We introduce a new type of backward differential equations with infinity horizon and prove the existence and uniqueness of both L2 and L1 solutions of the BSDEs. In this thesis, we use the BSDE to solve the semilinear Neumann boundary problem. However, this research on the BSDEs has its independent interest. Under certain conditions on both the "singular" coefficient of the elliptic operator and the "semilinear coefficient" in the deterministic differential equation, we find an explicit probabilistic solution to the Neumann problem, which supplies a L2 solution of a BSDE with infinite horizon. We also show that, less restrictive conditions on the coefficients are needed if the solution to the Neumann boundary problem only provides a L1 solution to the BSDE.
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Shimoda, Taishi. "Hypoellipticity of second order differential operators with sign-changing principal symbols /." Sendai : Tohoku Univ, 2000. http://www.loc.gov/catdir/toc/fy0713/2007329003.html.

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Teka, Kubrom Hisho. "The obstacle problem for second order elliptic operators in nondivergence form." Diss., Kansas State University, 2012. http://hdl.handle.net/2097/14035.

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Doctor of Philosophy
Department of Mathematics
Ivan Blank
We study the obstacle problem with an elliptic operator in nondivergence form with principal coefficients in VMO. We develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results, in turn, allow us to begin the study of the regularity of the free boundary, and we show existence of blowup limits, a basic measure stability result, and a measure-theoretic version of the Caffarelli alternative proven in Caffarelli's 1977 paper ``The regularity of free boundaries in higher dimensions." Finally, we show that blowup limits are in general not unique at free boundary points.
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Kim, Nanhee. "Carleman estimates for the general second order operators and applications to inverse problems." Diss., Wichita State University, 2010. http://hdl.handle.net/10057/3652.

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We derive Carleman estimates with two large parameters for a general partial di erential operator of second order under explicit su cient global conditions of pseudo-convexity on the weight function. We use these estimates to derive the most natural Carleman type estimates for the anisotropic system of elasticity with residual stress. Also, we give applications to uniqueness and stability of the continuation, observability, and identi cation of the residual stress from boundary measurements.
Thesis (Ph.D.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics
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Debroux, Noémie. "Mathematical modelling of image processing problems : theoretical studies and applications to joint registration and segmentation." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR02/document.

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Dans cette thèse, nous nous proposons d'étudier et de traiter conjointement plusieurs problèmes phares en traitement d'images incluant le recalage d'images qui vise à apparier deux images via une transformation, la segmentation d'images dont le but est de délimiter les contours des objets présents au sein d'une image, et la décomposition d'images intimement liée au débruitage, partitionnant une image en une version plus régulière de celle-ci et sa partie complémentaire oscillante appelée texture, par des approches variationnelles locales et non locales. Les relations étroites existant entre ces différents problèmes motivent l'introduction de modèles conjoints dans lesquels chaque tâche aide les autres, surmontant ainsi certaines difficultés inhérentes au problème isolé. Le premier modèle proposé aborde la problématique de recalage d'images guidé par des résultats intermédiaires de segmentation préservant la topologie, dans un cadre variationnel. Un second modèle de segmentation et de recalage conjoint est introduit, étudié théoriquement et numériquement puis mis à l'épreuve à travers plusieurs simulations numériques. Le dernier modèle présenté tente de répondre à un besoin précis du CEREMA (Centre d'Études et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement) à savoir la détection automatique de fissures sur des images d'enrobés bitumineux. De part la complexité des images à traiter, une méthode conjointe de décomposition et de segmentation de structures fines est mise en place, puis justifiée théoriquement et numériquement, et enfin validée sur les images fournies
In this thesis, we study and jointly address several important image processing problems including registration that aims at aligning images through a deformation, image segmentation whose goal consists in finding the edges delineating the objects inside an image, and image decomposition closely related to image denoising, and attempting to partition an image into a smoother version of it named cartoon and its complementary oscillatory part called texture, with both local and nonlocal variational approaches. The first proposed model addresses the topology-preserving segmentation-guided registration problem in a variational framework. A second joint segmentation and registration model is introduced, theoretically and numerically studied, then tested on various numerical simulations. The last model presented in this work tries to answer a more specific need expressed by the CEREMA (Centre of analysis and expertise on risks, environment, mobility and planning), namely automatic crack recovery detection on bituminous surface images. Due to the image complexity, a joint fine structure decomposition and segmentation model is proposed to deal with this problem. It is then theoretically and numerically justified and validated on the provided images
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Calvo, D., and Bert-Wolfgang Schulze. "Edge symbolic structures of second generation." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2994/.

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Operators on a manifold with (geometric) singularities are degenerate in a natural way. They have a principal symbolic structure with contributions from the different strata of the configuration. We study the calculus of such operators on the level of edge symbols of second generation, based on specific quantizations of the corner-degenerate interior symbols, and show that this structure is preserved under compositions.
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Books on the topic "Nonlocal second order operators"

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Shimoda, Taishi. Hypoellipticity of second order differential operators with sign-changing principal symbols. Sendai, Japan: Tohoku University, 2000.

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Fu, Xiaoyu, Qi Lü, and Xu Zhang. Carleman Estimates for Second Order Partial Differential Operators and Applications. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29530-1.

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Pester, Cornelia. A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularities. Berlin: Logos-Verl., 2006.

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Lectures on linear partial differential equations. Providence, R.I: American Mathematical Society, 2011.

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Conference Board of the Mathematical Sciences and National Science Foundation (U.S.), eds. Lectures on the energy critical nonlinear wave equation. Providence, Rhode Island: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, with support from the National Science Foundation, 2015.

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Ellwood, D. (David), 1966- editor of compilation, Rodnianski, Igor, 1972- editor of compilation, Staffilani, Gigliola, 1966- editor of compilation, and Wunsch, Jared, editor of compilation, eds. Evolution equations: Clay Mathematics Institute Summer School, evolution equations, Eidgenössische Technische Hochschule, Zürich, Switzerland, June 23-July 18, 2008. Providence, Rhode Island: American Mathematical Society, 2013.

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1943-, Gossez J. P., and Bonheure Denis, eds. Nonlinear elliptic partial differential equations: Workshop in celebration of Jean-Pierre Gossez's 65th birthday, September 2-4, 2009, Université libre de Bruxelles, Belgium. Providence, R.I: American Mathematical Society, 2011.

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Nahmod, Andrea R. Recent advances in harmonic analysis and partial differential equations: AMS special sessions, March 12-13, 2011, Statesboro, Georgia : the JAMI Conference, March 21-25, 2011, Baltimore, Maryland. Edited by American Mathematical Society and JAMI Conference (2011 : Baltimore, Md.). Providence, Rhode Island: American Mathematical Society, 2012.

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Lopez-Gomez, Julian. Linear Second Order Elliptic Operators. World Scientific Publishing Co Pte Ltd, 2013.

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Edmunds, D. E., and W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators includes the self-adjoint operators, even ones that are not bounded below. The essential self-adjointness of Schrödinger operators whose potentials have strong local singularities are considered, and the quantum-mechanical interpretation of essential self-adjointness is discussed.
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Book chapters on the topic "Nonlocal second order operators"

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Hörmander, Lars. "Second Order Elliptic Operators." In The Analysis of Linear Partial Differential Operators III, 3–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-49938-1_2.

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Marin, Marin, and Andreas Öchsner. "Differential Operators of Second Order." In Essentials of Partial Differential Equations, 17–59. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90647-8_2.

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Schwarz, Fritz. "Decomposition of Second-Order Operators." In Texts & Monographs in Symbolic Computation, 81–90. Vienna: Springer Vienna, 2012. http://dx.doi.org/10.1007/978-3-7091-1286-1_4.

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Feller, William. "ON SECOND ORDER DIFFERENTIAL OPERATORS." In Selected Papers II, 325–40. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16856-2_18.

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Jerison, David, and Antonio Sánchez-Calle. "Subelliptic, second order differential operators." In Lecture Notes in Mathematics, 46–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078245.

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Păltănea, Radu. "Estimates with Second Order Moduli." In Approximation Theory Using Positive Linear Operators, 15–68. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2058-9_2.

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Edmunds, David E., and W. Desmond Evans. "Realisations of Second-Order Linear Elliptic Operators." In Springer Monographs in Mathematics, 159–202. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02125-2_7.

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Luna-Elizarrarás, M. Elena, Michael Shapiro, Daniele C. Struppa, and Adrian Vajiac. "Second Order Complex and Hyperbolic Differential Operators." In Frontiers in Mathematics, 193–99. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24868-4_10.

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Figueroa Sestelo, Rubén, Rodrigo López Pouso, and Jorge Rodríguez López. "Positive Solutions for Second and Higher Order Problems." In Degree Theory for Discontinuous Operators, 135–79. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81604-9_6.

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Figueroa Sestelo, Rubén, Rodrigo López Pouso, and Jorge Rodríguez López. "Second Order Problems and Lower and Upper Solutions." In Degree Theory for Discontinuous Operators, 83–133. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81604-9_5.

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Conference papers on the topic "Nonlocal second order operators"

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Ashyralyev, Allaberen, Ozgur Yildirim, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Second Order of Accuracy Stable Difference Schemes for Hyperbolic Problems Subject to Nonlocal Conditions with Self-Adjoint Operator." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636801.

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Felsberg, Michael. "On second order operators and quadratic operators." In 2008 19th International Conference on Pattern Recognition (ICPR). IEEE, 2008. http://dx.doi.org/10.1109/icpr.2008.4761685.

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Kurtz, Michael J., Guenther Eichhorn, Alberto Accomazzi, Carolyn S. Grant, and Stephen S. Murray. "Second order bibliometric operators in the Astrophysics Data System." In Astronomical Telescopes and Instrumentation. SPIE, 2002. http://dx.doi.org/10.1117/12.460438.

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Mukhtarov, Oktay, Hayati Olgar, and Fahreddin Muhtarov. "Positiveness of second order differential operators with interior singularity." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959658.

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Di Bartolo, L., C. Dors, and W. J. Mansur. "New FD Operators to Solve Second Order Elastic Wave Equation." In 75th EAGE Conference and Exhibition incorporating SPE EUROPEC 2013. Netherlands: EAGE Publications BV, 2013. http://dx.doi.org/10.3997/2214-4609.20130672.

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Arora, Urvashi, and N. Sukavanam. "Approximate controllability of a second order delayed semilinear stochastic system with nonlocal conditions." In 2015 International Conference on Signal Processing, Computing and Control (ISPCC). IEEE, 2015. http://dx.doi.org/10.1109/ispcc.2015.7375031.

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Horing, N. J. M., S. Y. Liu, and H. L. Cui. "Second Order Nonlinear Dielectric Response of a Dynamic, Nonlocal Plasma Subject to Terahertz Radiation." In 2006 Sixth IEEE Conference on Nanotechnology. IEEE, 2006. http://dx.doi.org/10.1109/nano.2006.247576.

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Senik, Nikita N. "On homogenization for periodic elliptic second order differential operators in a strip." In Days on Diffraction 2012 (DD). IEEE, 2012. http://dx.doi.org/10.1109/dd.2012.6402782.

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LANDIM, CLAUDIO. "VARIATIONAL FORMULAE FOR THE CAPACITY INDUCED BY SECOND-ORDER ELLIPTIC DIFFERENTIAL OPERATORS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0153.

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BANGEREZAKO, G., and M. N. HOUNKONNOU. "THE TRANSFORMATION OF POLYNOMIAL EIGENFUNCTIONS OF LINEAR SECOND-ORDER Q-DIFFERENCE OPERATORS: A SPECIAL CASE OF Q-JACOBI POLYNOMIALS." In Proceedings of the Second International Workshop. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777560_0018.

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