Relevant bibliographies by topics / Sturm-Liouville type

Academic literature on the topic 'Sturm-Liouville type'

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Published: 6 September 2023

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Journal articles on the topic "Sturm-Liouville type"

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Goktas, Sertac. "A New Type of Sturm-Liouville Equation in the Non-Newtonian Calculus." Journal of Function Spaces 2021 (October 31, 2021): 1–8. http://dx.doi.org/10.1155/2021/5203939.

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In mathematical physics (such as the one-dimensional time-independent Schrödinger equation), Sturm-Liouville problems occur very frequently. We construct, with a different perspective, a Sturm-Liouville problem in multiplicative calculus by some algebraic structures. Then, some asymptotic estimates for eigenfunctions of the multiplicative Sturm-Liouville problem are obtained by some techniques. Finally, some basic spectral properties of this multiplicative problem are examined in detail.
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Cernea, Aurelian. "Variational inclusions for a Sturm-Liouville type differential inclusion." Mathematica Bohemica 135, no. 2 (2010): 171–78. http://dx.doi.org/10.21136/mb.2010.140694.

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Bas, Erdal, Ramazan Ozarslan, and Dumitru Baleanu. "Sturm-Liouville difference equations having Bessel and hydrogen atom potential type." Open Physics 16, no. 1 (December 26, 2018): 801–9. http://dx.doi.org/10.1515/phys-2018-0100.

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Abstract In this work, we bring a different approach for Sturm-Liouville problems having Bessel and hydrogen atom type and we provide a basis for direct and inverse problems. From this point of view, we find representations of solutions and asymptotic expansions for eigenfunctions. Furthermore, some numerical estimations are given to illustrate the necessity of the Sturm-Liouville difference equations with the potential function for the convenience to the spectral theory. The behavior of eigenfunctions for the Sturm-Liouville problem having Bessel and hydrogen atom potential type is analyzed and compared to each other. And then, comparisons are showed by tables and figures.
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Li, Shuang, Jinming Cai, and Kun Li. "Matrix Representations for a Class of Eigenparameter Dependent Sturm–Liouville Problems with Discontinuity." Axioms 12, no. 5 (May 15, 2023): 479. http://dx.doi.org/10.3390/axioms12050479.

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Matrix representations for a class of Sturm–Liouville problems with eigenparameters contained in the boundary and interface conditions were studied. Given any matrix eigenvalue problem of a certain type and an eigenparameter-dependent condition, a class of Sturm–Liouville problems with this specified condition was constructed. It has been proven that each Sturm–Liouville problem is equivalent to the given matrix eigenvalue problem.
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Buterin, Sergey, and G. Freiling. "Inverse spectral-scattering problem for the Sturm-Liouville operator on a noncompact star-type graph." Tamkang Journal of Mathematics 44, no. 3 (September 30, 2013): 327–49. http://dx.doi.org/10.5556/j.tkjm.44.2013.1422.

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We study the Sturm-Liouville operator on a noncompact star-type graph consisting of a finite number of compact and noncompact edges under standard matching conditions in the internal vertex. We introduce and investigate the so-called spectral-scat\-tering data, which generalize the classical spectral data for the Sturm-Liouville operator on the half-line and the scattering data on the line. Developing the idea of the method of spectral mappings we prove that the specification of the spectral-scattering data uniquely determines the Sturm-Liouville operator on the graph.
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Karahan, D., and K. R. Mamedov. "ON A q-BOUNDARY VALUE PROBLEM WITH DISCONTINUITY CONDITIONS." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 13, no. 4 (2021): 5–12. http://dx.doi.org/10.14529/mmph210401.

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In this paper, we studied q-analogue of Sturm–Liouville boundary value problem on a finite interval having a discontinuity in an interior point. We proved that the q-Sturm–Liouville problem is self-adjoint in a modified Hilbert space. We investigated spectral properties of the eigenvalues and the eigenfunctions of q-Sturm–Liouville boundary value problem. We shown that eigenfunctions of q-Sturm–Liouville boundary value problem are in the form of a complete system. Finally, we proved a sampling theorem for integral transforms whose kernels are basic functions and the integral is of Jackson’s type.
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Rynne, Bryan P. "The asymptotic distribution of the eigenvalues of right definite multiparameter Sturm-Liouville systems." Proceedings of the Edinburgh Mathematical Society 36, no. 1 (February 1993): 35–47. http://dx.doi.org/10.1017/s0013091500005873.

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This paper studies the asymptotic distribution of the multiparameter eigenvalues of a right definite multiparameter Sturm–Liouville eigenvalue problem. A uniform asymptotic analysis of the oscillation number of solutions of a single Sturm–Liouville type equation with potential depending on a general parameter is given; these results are then applied to the system of multiparameter Sturm–Liouville equations to give the asymptotic eigenvalue distribution for the system as a function of a “multi-index” oscillation number.
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Porter, D., and D. S. G. Stirling. "Integral operators of Sturm-Liouville type." Integral Equations and Operator Theory 38, no. 1 (March 2000): 51–65. http://dx.doi.org/10.1007/bf01192301.

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JOHNSON, RUSSELL, and LUCA ZAMPOGNI. "SOME REMARKS CONCERNING REFLECTIONLESS STURM–LIOUVILLE POTENTIALS." Stochastics and Dynamics 08, no. 03 (September 2008): 413–49. http://dx.doi.org/10.1142/s0219493708002391.

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We consider the class of reflectionless Sturm–Liouville potentials and the subclass consisting of "Sato–Segal–Wilson" potentials. We construct illustrative examples lying in these classes, in particular we adapt the constructions of Craig and Levitan to the Sturm–Liouville case. We also discuss an inverse problem of Kotani type in the context of Sato–Segal–Wilson potentials.
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Buterin, Sergey. "An inverse spectral problem for Sturm-Liouville-type integro-differential operators with robin boundary conditions." Tamkang Journal of Mathematics 50, no. 3 (September 2, 2019): 207–21. http://dx.doi.org/10.5556/j.tkjm.50.2019.3347.

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The perturbation of the Sturm--Liouville differential operator on a finite interval with Robin boundary conditions by a convolution operator is considered. The inverse problem of recovering the convolution term along with one boundary condition from the spectrum is studied, provided that the Sturm--Liouville potential as well as the other boundary condition are known a priori. The uniqueness of solution for this inverse problem is established along with necessary and sufficient conditions for its solvability. The proof is constructive and gives an algorithm for solving the inverse problem.
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Dissertations / Theses on the topic "Sturm-Liouville type"

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Alici, Haydar. "A General Pseudospectral Formulation Of A Class Of Sturm-liouville Systems." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612435/index.pdf.

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In this thesis, a general pseudospectral formulation for a class of Sturm-Liouville eigenvalue problems is consructed. It is shown that almost all, regular or singular, Sturm-Liouville eigenvalue problems in the Schrö
dinger form may be transformed into a more tractable form. This tractable form will be called here a weighted equation of hypergeometric type with a perturbation (WEHTP) since the non-weighted and unperturbed part of it is known as the equation of hypergeometric type (EHT). It is well known that the EHT has polynomial solutions which form a basis for the Hilbert space of square integrable functions. Pseudospectral methods based on this natural expansion basis are constructed to approximate the eigenvalues of WEHTP, and hence the energy eigenvalues of the Schrö
dinger equation. Exemplary computations are performed to support the convergence numerically.
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Navarro, Sepúlveda Gustavo Estéban. "Singular Limits in Liouville Type Equations With Exponential Neumann Data." Tesis, Universidad de Chile, 2010. http://www.repositorio.uchile.cl/handle/2250/103684.

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En este trabajo de memoria se demostró un teorema de existencia para la ecuación de Liouville con condición de borde no lineal: El primer paso en esta demostración consiste en la aproximación del problema original usando un ansatz de la solución que explota en m puntos cuando el parámetro épsilon tiende a cero, más un término de corrección, sobre el cual se obtienen un conjunto de ecuaciones que van a caracterizar la solución del problema principal. En el capítulo 4 se analizó el operador lineal asociado a estas ecuaciones y se encontró un resultado de solubilidad al modificar la ecuación con términos aditivos de coeficientes cj, j = 1, . . . , m. A continuación se estableció la existencia de una solución al problema no lineal con la modificación aditiva y se estudió su comportamiento en función de los puntos singulares. Se demostró que la solución del problema principal, dada por el hecho de encontrar un conjunto de puntos tales que cj = 0, ∀ j, puede ser reducida al análisis de los puntos críticos de una función φm. En el capítulo final se mostró que existen al menos dos de estos puntos críticos y en consecuencia al menos dos soluciones del problema principal que explotan en m puntos.
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Marcel, Patrick. "Nouvelle série de supralgébres de Lie généralisant l'algébre de Virasoro et opérateurs différentiels de type Sturm-Liouville." Aix-Marseille 1, 1999. http://www.theses.fr/1999AIX11005.

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Cette these se compose principalement de deux articles. Article i : une nouvelle serie de superalgebres de lie generalisant l'algebre de neveu-schwarz nous considerons des generalisations de l'algebre de virasoro introduites par v. Ovsienko et c. Roger. Il s'agit d'extensions de l'algebre des champs de vecteurs sur le cercle par le module des densites tensorielles et de leur extension centrale. Nous classifions les superanalogues de ces algebres de lie. Le resultat est le suivant : pour chacune de ces algebres (a une exception pres) il existe une superalgebre de lie associee. Ces superalgebres generalisent l'algebre de neveu-schwarz. Article ii : generalisations de l'algebre de virasoro et operateurs matriciels de type sturm-liouville. Nous associons a chaque algebre mentionnee ci-dessus (a une exception pres) un espace d'operateurs differentiels matriciels. Nous montrons que l'action naturelle de chaque algebre sur l'espace d'operateurs associe coincide avec l'action coadjointe de chacune de ces algebres, generalisant ainsi la propriete de kirillov-segal reliant l'algebre de virasoro aux operateurs de sturm-liouville. Les operateurs de l'article ii s'obtiennent en utilisant l'action coadjointe des superalgebres donnees dans l'article i. Ceci montre l'universalite d'un resultat donne par a. Kirillov dans lequel les operateurs de sturm-liouville sont obtenus grace a l'action coadjointe de la superalgebre de neveu-schwarz. Ces articles sont completes par des chapitres techniques demontrant les principaux resultats.
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Mtiri, Foued. "Études des solutions de quelques équations aux dérivées partielles non linéaires via l'indice de Morse." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0150/document.

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Cette thèse porte principalement sur l'étude des solutions de certaines équations aux dérivées partielles elliptiques via l'indice de Morse, y compris des solutions stables, i.e. quand l'indice de Morse est égal à zéro. Elle comporte deux parties indépendantes.Dans la première partie, sous des hypothèses sur-linéaires et sous-critiques sur f, on établit d'abord une estimation explicite de la norme L [infini] des solutions de -Δu = f(u) avec u = 0 sur le bord, via leurs indices de Morse. On propose une approche plus transparente et plus souple que le travail de Yang [1998], ce qui nous permet de traiter des non linéarités très proches de la croissance critique. Les résultats obtenus nous ont motivé de travailler sur des équations polyharmoniques (-Δ)ku = f(x; u) avec notamment k = 2 et 3. Avec des hypothèses semblables à Yang [1998] sur f et des conditions au bord convenables, on obtient pour la première fois des estimations explicites de solution des équations polyhamoniques, via l'indice de Morse. Dans la seconde partie, on considère un système de Lane-Emden-Δu = ρ(x)vp; -Δv = ρ(x)u θ ; u; v > 0; dans RN; avec 1 < p< θ et un poids radial ρ strictement positif. Nous montrons la non-existence de solution stable en petites dimensions N. Nos résultats améliorent les travaux précédents de Cowan & Fazly [2012]; Fazly [2012]; Hu [2015], et fournissent notamment des résultats du type Liouville pour solution stable, en petites dimensions N, valables pour tout 1 < ρ min(4 3 ; θ)
The main concern of this thesis deals with the study of solutions of several elliptic partial differential equations via the Morse index, including the stable solutions, i.e. when the Morse index is zero. The thesis has two independent parts. In the first part, under suplinear and subcritical assumptions on f, we establish firstly some explicit estimation for the L1 norms of solutions to -Δu = f(u) avec u = 0 on the boundary, via its Morse index. We propose an approach more transparent and easier than the work of Yang [1998], which allow us to treat some nonlinearities very close to the critical growth. These results motivated us to consider the polyharmonic equations (-Δ)ku = f(x; u) with especially k = 2 and 3. With the hypothesis on f similar to Yang [1998] and appropriate boundary conditions, we obtain for the _rst time some explicit estimations of solution via its Morse index, for the polyharmonic equations.In the second part, we consider a Lane-Emden system -Δu = ρ(x)vp; -Δv = ρ(x)u_; u; v > 0; in RN; with 1 < p< θ and a radial positive weight ρ. We prove the non-existence of stable solution in small dimension case. Our results improve the previous works Cowan & Fazly [2012]; Fazly [2012]; Hu [2015], especially we prove some general Liouville type results for stable solutions in small dimension which hold true for any 1 < ρ min(4 3 ; θ)
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LIN, JI-TIAN, and 林吉田. "On the eigenvalues of the sturm-liouville type differential equations." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/58164804038595731403.

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Bhat, Srivatsa K. "On the isospectrals of Rayleigh and Timoshenko beams and a new version of Bresse-Timoshenko equations." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/5399.

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Book chapters on the topic "Sturm-Liouville type"

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Bandle, Catherine. "Extremal Problems for Eigenvalues of the Sturm-Liouville Type." In General Inequalities 5, 319–36. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7192-1_26.

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Weidmann, Joachim. "Appendix to section 6: Semi-boundedness of Sturm-Liouville type operators." In Spectral Theory of Ordinary Differential Operators, 104–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077970.

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Abramovich, Shoshana. "Bounds of Jensen’s Type Inequality and Eigenvalues of Sturm–Liouville System." In Springer Optimization and Its Applications, 1–11. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3498-6_1.

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Aleroev, Temirkhan, and Hedi Aleroeva. "Problems of Sturm–Liouville type for differential equations with fractional derivatives." In Fractional Differential Equations, edited by Anatoly Kochubei and Yuri Luchko, 21–46. Berlin, Boston: De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571660-002.

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Vladimirov, A. A., and I. A. Sheipak. "On Spectral Periodicity for the Sturm–Liouville Problem: Cantor Type Weight, Neumann and Third Type Boundary Conditions." In Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation, 509–16. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0648-0_32.

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Muratbekov, Mussakan B., Madi M. Muratbekov, and Asijat N. Dadaeva. "A Sturm-Liouville Operator with a Negative Parameter and Its Applications to the Study of Differential Properties of Solutions for a Class of Hyperbolic Type Equations." In Springer Proceedings in Mathematics & Statistics, 258–66. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67053-9_24.

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"13. A primer on equations of Sturm–Liouville type." In Differential Equations, 201–20. Berlin, Boston: De Gruyter, 2019. http://dx.doi.org/10.1515/9783110652864-013.

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"8. The Calculation of Eigenvalues for Sturm-Liouville Type Systems." In An Introduction to Invariant Imbedding, 133–46. Society for Industrial and Applied Mathematics, 1992. http://dx.doi.org/10.1137/1.9781611971279.ch8.

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Yang, Chen Ning. "Generalization of Sturm-Liouville Theory to a System of Ordinary Differential Equations with Dirac Type Spectrum." In Selected Papers of Chen Ning Yang II, 106–17. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814449021_0015.

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Conference papers on the topic "Sturm-Liouville type"

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Şen, Erdoğan, Azad Bayramov, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "On a Discontinuous Sturm—Liouville Type Problem with Retarded Argument." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637824.

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Shokouhmand, Hossein, Seyed Reza Mahmoudi, and Kaveh Habibi. "Analytical Solution of Hyperbolic Heat Conduction Equation for a Finite Slab With Arbitrary Boundaries, Initial Condition, and Stationary Heat Source." In ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62058.

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This paper presents an analytical solution of the hyperbolic heat conduction equation for a finite slab that sides are subjected to arbitrary heat source, boundary, and initial conditions. In the mathematical model used in this study, the heating on both sides treated as an apparent heat source while sides of the slab assumed to be insulated. Distribution of the apparent heat source for a problem with arbitrary heating on two boundaries is solved. The solution obtained by separation of variable method using appropriate Fourier series. Being a Sturm-Liouville problem in x-direction, suitable orthogonal functions can be allocated to hyperbolic heat conduction equation depending on the type of boundary conditions. Despite ease of proposed method, very few works has been done to solve hyperbolic heat conduction problems using this method by authors. The main feature of the method is straightforward formulation. In the analysis of heat conduction involving extremely short times, the parabolic heat conduction equation breaks down. By increasing the applications of the fast heat sources such as laser pulse for annealing of semiconductors and high heat flux applications, the need for adequate model of heat conduction has arisen. The hyperbolic heat conduction equation eliminates the paradox of an infinite speed of propagation of thermal disturbances which contradicts with Einstein’s theory of relativity. Moreover, it describes the highly transient temperature distribution in a finite medium more accurately.
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Krikkis, Rizos N., Stratis V. Sotirchos, and Panagiotis Razelos. "Bifurcation Analysis for Horizontal Longitudinal Fins Under Multi-Boiling Conditions." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33632.

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A numerical bifurcation analysis is carried out in order to determine the solution structure of a fin subject to multi-boiling heat transfer mode. The thermal analysis can no longer performed independently of the working fluid since the heat transfer coefficient is temperature dependent and includes the nucleate, the transition and the film boiling regime where the boiling curve is obtained experimentally for a specific fluid. The heat transfer process is modeled using one-dimensional heat conduction with or without heat transfer from the fin tip. Furthermore, five fin profiles are considered: the constant thickness, the trapezoidal, the triangular, the convex parabolic and the parabolic. The multiplicity structure is obtained in order to determine the different types of bifurcation diagrams, which describe the dependence of a state variable of the system (for instance the fin temperature or the heat dissipation) on a design (CCP) or operation parameter (base TD). Specifically the effects of the base TD, of CCP and of the Biot number are analyzed and presented in several diagrams since it is important to know the behavioral features of the heat rejection mechamism such as the number of the possible steady states and the influence of a change in one or more operating variables to these states. Stability analysis is carried out using the “resonance integral” technique and the Sturm-liouville eigen system analysis.
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Muratbekov, Mussakan B., and Madi M. Muratbekov. "Spectral properties of the Sturm-Liouville operator with a parameter that changes sign and their usage to the study of the spectrum of differential operators of mathematical physics belonging to different types." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5049078.

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