Relevant bibliographies by topics / Adjointness

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

Academic literature on the topic 'Adjointness'

Author: Grafiati
Published: 4 June 2025
Last updated: 15 July 2025

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Journal articles on the topic "Adjointness"

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Hidaka, Takeru, and Fumio Hiroshima. "Self-adjointness of the semi-relativistic Pauli–Fierz Hamiltonian." Reviews in Mathematical Physics 27, no. 07 (2015): 1550015. http://dx.doi.org/10.1142/s0129055x15500154.

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The spinless semi-relativistic Pauli–Fierz Hamiltonian [Formula: see text] in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, Hf the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli–Fierz model with a fixed total momentum P ∈ ℝd: [Formula: see text] is also proven for arbitrary P.
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Mulry, Philip S. "Adjointness in recursion." Annals of Pure and Applied Logic 32 (1986): 281–89. http://dx.doi.org/10.1016/0168-0072(86)90056-4.

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Menni, M., and C. Smith. "Modes of Adjointness." Journal of Philosophical Logic 43, no. 2-3 (2013): 365–91. http://dx.doi.org/10.1007/s10992-012-9266-y.

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KOLB, MARTIN. "ON THE STRONG UNIQUENESS OF SOME FINITE DIMENSIONAL DIRICHLET OPERATORS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 02 (2008): 279–93. http://dx.doi.org/10.1142/s0219025708003117.

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We prove essential self-adjointness of a class of Dirichlet operators in ℝn using the hyperbolic equation approach. This method allows one to prove essential self-adjointness under minimal conditions on the logarithmic derivative of the density and a condition of Muckenhoupt type on the density itself.
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Wu, Xiaohong, Junjie Huang, and Eerdun Buhe. "On Symplectic Self-Adjointness of Hamiltonian Operator Matrices." Symmetry 15, no. 12 (2023): 2163. http://dx.doi.org/10.3390/sym15122163.

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The symmetry of the spectrum and the completeness of the eigenfunction system of the Hamiltonian operator matrix have important applications in the symplectic Fourier expansion method in elasticity. However, the symplectic self-adjointness of Hamiltonian operator matrices is important to the characterization of the symmetry of the point spectrum. Therefore, in this paper, the symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied by using the spectral method of unbounded block operator matrices, and some sufficient conditions of the symplectic self-adjointness of infinite dimensional Hamiltonian operators are obtained. In addition, the necessary and sufficient conditions are also investigated for some special infinite dimensional Hamiltonian operators.
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Sandovici, Adrian. "Self-adjointness and skew-adjointness criteria involving powers of linear relations." Journal of Mathematical Analysis and Applications 470, no. 1 (2019): 186–200. http://dx.doi.org/10.1016/j.jmaa.2018.09.063.

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Wang, Aiping, Jerry Ridenhour, and Anton Zettl. "Construction of regular and singular Green's functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 1 (2012): 171–98. http://dx.doi.org/10.1017/s0308210510001630.

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The Green function of singular limit-circle problems is constructed directly for the problem, not as a limit of sequences of regular Green's functions. This construction is used to obtain adjointness and self-adjointness conditions which are entirely analogous to the regular case. As an application, a new and explicit formula for the Green function of the classical Legendre problem is found.
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Morsi, Nehad N. "Propositional calculus under adjointness." Fuzzy Sets and Systems 132, no. 1 (2002): 91–106. http://dx.doi.org/10.1016/s0165-0114(02)00108-2.

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Betti, Renato. "Adjointness in descent theory." Journal of Pure and Applied Algebra 116, no. 1-3 (1997): 41–47. http://dx.doi.org/10.1016/s0022-4049(96)00161-2.

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Ricci, Paolo Emilio. "ADJOINTNESS FOR SHEFFER POLYNOMIALS." Jnanabha 50, no. 01 (2020): 57–64. http://dx.doi.org/10.58250/jnanabha.2020.50107.

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In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them have been studied. In this article new sets of Sheffer polynomials are introduced defining a sort of adjointness property. As an application, we show the adjoint set of Actuarial polynomials and derive their main characteristics.
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Dissertations / Theses on the topic "Adjointness"

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Nita, A. "Essential Self-Adjointness of the Symplectic Dirac Operators." Thesis, University of Colorado at Boulder, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10108819.

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<p> The main problem we consider in this thesis is the essential self-adjointness of the symplectic Dirac operators D and D constructed by Katharina Habermann in the mid 1990s. Her constructions run parallel to those of the well-known Riemannian Dirac operators, and show that in the symplectic setting many of the same properties hold. For example, the symplectic Dirac operators are also unbounded and symmetric, as in the Riemannian case, with one important difference: the bundle of symplectic spinors is now infinite-dimensional, and in fact a Hilbert bundle. This infinite dimensionality makes the classical proofs of essential self-adjointness fail at a crucial step, namely in local coordinates the coefficients are now seen to be unbounded operators on L2(Rn). A new approach is needed, and that is the content of these notes. We use the decomposition of the spinor bundle into countably many finite-dimensional subbundles, the eigenbundles of the harmonic oscillator, along with the simple behavior of D and D with respect to this decomposition, to construct an inductive argument for their essential self-adjointness. This requires the use of ancillary operators, constructed out of the symplectic Dirac operators, whose behavior with respect to the decomposition is transparent. By an analysis of their kernels we manage to deduce the main result one eigensection at a time.</p>
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Cabral, Rodrigo Augusto Higo Mafra. "O teorema espectral e a propriedade de \"self-adjointness\" para alguns operadores de Schrödinger." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-07032015-154510/.

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Neste texto são demonstrados, a partir do ponto de vista da teoria dos espaços de Hilbert e da teoria das C*-álgebras, teoremas relacionados a operadores auto-adjuntos em espaços de Hilbert, entre os quais estão o Teorema Espectral, o teorema de Kato-Rellich e a desigualdade de Kato. Também são dadas aplicações destes teoremas a alguns operadores de Schrödinger provenientes da Física-Matemática.<br>In this text we prove, within the Hilbert spaces theory and C*-algebras points of view, some theorems which are related to self-adjoint operators acting on Hilbert spaces, among which are the Spectral Theorem, the Kato-Rellich theorem and Kato\'s inequality. Also, some applications to Schrödinger operators coming from the Mathematical-Physics context are given.
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Wünsch, Andreas [Verfasser], and Marcel [Akademischer Betreuer] Griesemer. "Self-adjointness and domain of a class of generalized Nelson models / Andreas Wünsch ; Betreuer: Marcel Griesemer." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2017. http://d-nb.info/1147759480/34.

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Mortad, Mohammed Hichem. "Normal products of self-adjoint operators and self-adjointness of the perturbed wave operator on L²(Rn)." Thesis, University of Edinburgh, 2003. http://hdl.handle.net/1842/15434.

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This thesis contains five chapters. The first two are devoted to the background which consists of integration, Fourier analysis, distributions and linear operators in Hilbert spaces. The third chapter is a generalization of a work done by Albrecht-Spain in 2000. We give a shorter proof of the main theorem they proved for bounded operators and we generalize it to unbounded operators. We give a counterexample that shows that the result fails to be true for another class of operators. We also say why it does not hold. In chapters four and five, the idea is the same, that is to find classes of unbounded, real-valued V<i>s </i>for which  + <i>V</i> is self-adjoint on <i>D</i>(), where  is the wave operator. Throughout these two chapters we will see how different the Laplacian and the wave operator can be.
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Nikolaishvili, George. "Investigation of the Equations Modelling Chemical Waves Using Lie Group Analysis." Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-3996.

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A system of nonlinear di fferential equations, namely, the Belousov-Zhabotinskii reaction model has been investigated for nonlinear self-adjointness using the recent work of Professor N.H.Ibragimov. It is shown that the model is not nonlinearly self-adjoint. The symmetries of the system and nonlinear conservation laws are calculated. The modi fied system, which is nonlinearly self-adjoint, is also analysed. Its symmetries and conservation laws are presented.
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Oelker, Martin [Verfasser], and Dirk-André [Akademischer Betreuer] Deckert. "On domain, self-adjointness, and spectrum of Dirac operators for two interacting particles / Martin Oelker ; Betreuer: Dirk-André Deckert." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2019. http://d-nb.info/1190563703/34.

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Prüfert, Uwe. "Solving optimal PDE control problems : optimality conditions, algorithms and model reduction." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2016. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-204639.

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This thesis deals with the optimal control of PDEs. After a brief introduction in the theory of elliptic and parabolic PDEs, we introduce a software that solves systems of PDEs by the finite elements method. In the second chapter we derive optimality conditions in terms of function spaces, i.e. a systems of PDEs coupled by some pointwise relations. Now we present algorithms to solve the optimality systems numerically and present some numerical test cases. A further chapter deals with the so called lack of adjointness, an issue of gradient methods applied on parabolic optimal control problems. However, since optimal control problems lead to large numerical schemes, model reduction becomes popular. We analyze the proper orthogonal decomposition method and apply it to our model problems. Finally, we apply all considered techniques to a real world problem.
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Hsu, Yueh-Sheng. "On the random Schrödinger operators in the continuous setting." Electronic Thesis or Diss., Université Paris sciences et lettres, 2024. http://www.theses.fr/2024UPSLD009.

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Cette thèse porte sur les opérateurs de Schrödinger aléatoires dans un cadre continu, en particulier ceux avec un potentiel de bruit blanc gaussien. La définition de ces opérateurs différentiels est généralement non triviale et nécessite la renormalisation dans les dimensions d ≥ 2. Nous présentons d’abord un cadre général pour traduire le problème de construction de l’opérateur en EDP stochastiques. Cette approche nous permet de définir l’opérateur en question, d’établir son auto-adjonction et d’étudier son spectre.Par la suite, nous passons à l’étude de l’Hamiltonien d’Anderson continu dans deux configurations spatiales distinctes :d’abord dans une boîte bornée de longueur latérale L avec une condition de bord de Dirichlet nulle pour les dimensionsd ≤ 3, et ensuite dans l’espace Euclidien Rd, pour d ∈ {2, 3}. Dans le premier cas, l’opérateur admet des valeurs propres λn,L, pour lesquelles nous identifions l’asymptotique presque sûre lorsque L → ∞. Cet asymptotique est conforme aux résultats antérieurs dans la littérature pour les dimensions 1 et 2, tandis que notre résultat en dimension 3 est nouveau. Dans le second cas, nous proposons une nouvelle technique de construction en utilisant la théorie des solutions de l’équation parabolique associée, ce qui permet de prouver l’auto-adjonction et de montrer que le spectre est presque sûrement égal à R. Cette approche confirme le résultat récemment établi en dimension 2 dans la littérature, cependant notre construction semble plus élémentaire ; pour la dimension 3, notre résultat est nouveau.Enfin, nous présentons un projet en cours qui aborde le cas où un champ magnétique uniforme est appliqué au système : cela conduit à l’étude de l’Hamiltonien de Landau perturbé par le potentiel de bruit blanc. Notre objectif est de définir l’opérateur dans l’espace R² sans recourir à une théorie de renormalisation sophistiquée. Cependant, la non-bornitude du bruit blanc sur R²pose des défis techniques supplémentaires. Pour surmonter cela, l’utilisation du théorème de Faris-Lavine est discutée<br>This thesis studies the random Schrödinger operators in continuous setting, particularly those with Gaussian white noise potential. The definition of such differential operators is generally non-trivial and necessitates renormalization in dimensions d ≥ 2. We first present a general framework to translate the problem of operator construction into stochastic PDEs. This approach enables us to define the operator at stake and establishes its self-adjointness, as well as to investigate its spectrum.Subsequently, we proceed to study the continuous Anderson Hamiltonian under two distinct spatial settings: first on a bounded box with side length L with zero Dirichlet boundary condition for dimensions d ≤ 3, and second on the full Euclidean space Rd, for d ∈ {2, 3}. In the former case, the operator admits eigenvalues λn,L, for which we identify the almost sure asymptotic as L → ∞. This asymptotic aligns with previous findings in the literature for dimension 1 and 2, while our result in dimension 3 is new. In the latter case, we propose a new construction technique employing the solution theory to the associated parabolic equation which allows to prove self-adjointness and show that the spectrum equals to R almost surely. This approach reconfirms the recently established result in dimension 2, but our construction seems to be more elementary; for dimension 3, our result is new.Lastly, we present an ongoing project addressing the case where a uniform magnetic field is applied to the system : this leads to the study of Landau Hamiltonian perturbed by the white noise potential. Our objective is to define the operator on full space R² without resorting to sophisticated renormalization theory. However, the unboundedness of white noise on R² poses additional technical challenges. To overcome this, the usage of Faris-Lavine theorem is discussed
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Prüfert, Uwe. "Solving optimal PDE control problems : optimality conditions, algorithms and model reduction." Doctoral thesis, 2015. https://tubaf.qucosa.de/id/qucosa%3A23035.

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This thesis deals with the optimal control of PDEs. After a brief introduction in the theory of elliptic and parabolic PDEs, we introduce a software that solves systems of PDEs by the finite elements method. In the second chapter we derive optimality conditions in terms of function spaces, i.e. a systems of PDEs coupled by some pointwise relations. Now we present algorithms to solve the optimality systems numerically and present some numerical test cases. A further chapter deals with the so called lack of adjointness, an issue of gradient methods applied on parabolic optimal control problems. However, since optimal control problems lead to large numerical schemes, model reduction becomes popular. We analyze the proper orthogonal decomposition method and apply it to our model problems. Finally, we apply all considered techniques to a real world problem.:Introduction The state equation Optimal control and optimality conditions Algorithms The \"lack of adjointness\" Numerical examples Efficient solution of PDEs and KKT- systems A real world application Functional analytical basics Codes of the examples
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Books on the topic "Adjointness"

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Gray, J. W. Formal Category Theory: Adjointness For 2-Categories. Springer London, Limited, 2006.

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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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Edmunds, D. E., and W. D. Evans. Unbounded Linear Operators. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0003.

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This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.
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Book chapters on the topic "Adjointness"

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Lewin, Mathieu. "Self-adjointness." In Universitext. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-66878-4_2.

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Mortad, Mohammed Hichem. "Self-Adjointness." In Counterexamples in Operator Theory. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97814-3_21.

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Teschl, Gerald. "Self-adjointness and spectrum." In Mathematical Methods in Quantum Mechanics. American Mathematical Society, 2009. http://dx.doi.org/10.1090/gsm/099/03.

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Keller, Matthias, Daniel Lenz, and Radosław K. Wojciechowski. "Markov Uniqueness and Essential Self-Adjointness." In Grundlehren der mathematischen Wissenschaften. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81459-5_4.

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Kassel, Fanny, and Toshiyuki Kobayashi. "Essential Self-adjointness of the Laplacian." In Lecture Notes in Mathematics. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-96-1957-3_6.

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Hislop, P. D., and I. M. Sigal. "Self-Adjointness: Part 1. The Kato Inequality." In Introduction to Spectral Theory. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0741-2_8.

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Güneysu, Batu. "Essential Self-adjointness of Covariant Schrödinger Operators." In Covariant Schrödinger Semigroups on Riemannian Manifolds. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68903-6_12.

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Lewin, Mathieu. "Self-adjointness Criteria: Rellich, Kato and Friedrichs." In Universitext. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-66878-4_3.

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Hislop, P. D., and I. M. Sigal. "Self-Adjointness: Part 2. The Kato-Rellich Theorem." In Introduction to Spectral Theory. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0741-2_13.

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Gandarias, M. L., and M. Rosa. "Nonlinear Self-Adjointness for some Generalized KdV Equations." In Discontinuity and Complexity in Nonlinear Physical Systems. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01411-1_1.

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Conference papers on the topic "Adjointness"

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ESTEBAN, MARIA J., and MICHAEL LOSS. "SELF-ADJOINTNESS VIA PARTIAL HARDY-LIKE INEQUALITIES." In Proceedings of the QMath10 Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812832382_0004.

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Wojtowicz, Ralph L. "Symbolic Dynamics and Unpredictability Defined by Right Adjointness." In COMPUTING ANTICIPATORY SYSTEMS: CASYS'03 - Sixth International Conference. AIP, 2004. http://dx.doi.org/10.1063/1.1787331.

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Tracinà, Rita. "Nonlinear self-adjointness of a class of generalized diffusion equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756408.

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Gandarias, M. L., M. S. Bruzón, and M. Rosa. "Symmetries and nonlinear self-adjointness for a generalized fisher equation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756409.

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Fedorov, Vladimir E., and Marina V. Plekhanova. "Nonlinear self-adjointness method for the Baer – Nunziato equations system." In XV ALL-RUSSIAN SEMINAR “DYNAMICS OF MULTIPHASE MEDIA” (DMM2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5027325.

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Gandarias, M. L., and M. S. Bruzon. "Nonlinear self-adjointness and conservation laws for some third order equations." In 2012 IEEE 4th International Conference on Nonlinear Science and Complexity (NSC). IEEE, 2012. http://dx.doi.org/10.1109/nsc.2012.6304752.

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Silva, Priscila Leal da, and Igor Leite Freire. "On certain shallow water models, scaling invariance and strict self-adjointness." In XXXV CNMAC - Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2015. http://dx.doi.org/10.5540/03.2015.003.01.0022.

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Heather, M. A. "The Anticipatory and Systemic Adjointness of E-Science Computation on the Grid." In COMPUTING ANTICIPATORY SYSTEMS: CASYS 2001 - Fifth International Conference. AIP, 2002. http://dx.doi.org/10.1063/1.1503732.

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Restrepo, Mauricio, Chris Cornelis, and Jonatan Gomez. "Characterization of neighborhood operators for covering based rough sets, using duality and adjointness." In Fourth International Workshop on Knowledge Discovery, Knowledge Management and Decision Support. Atlantis Press, 2013. http://dx.doi.org/10.2991/.2013.12.

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Gandarias, M. L., and M. S. Bruzón. "Nonlinear self-adjointness and conservation laws for a porous medium equation with absorption." In NONLINEAR AND MODERN MATHEMATICAL PHYSICS: Proceedings of the 2nd International Workshop. AIP, 2013. http://dx.doi.org/10.1063/1.4828683.

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