Relevant bibliographies by topics / First-order differential operators

Academic literature on the topic 'First-order differential operators'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "First-order differential operators"

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Ismailov, Z. I., and P. Ipek Al. "BOUNDEDLY SOLVABLE NEUTRAL TYPE DELAY DIFFERENTIAL OPERATORS OF THE FIRST ORDER." Eurasian Mathematical Journal 10, no. 3 (2019): 20–27. http://dx.doi.org/10.32523/2077-9879-2019-10-3-20-27.

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Ueno, Kazushige. "On pseudoelliptic systems of first order differential equations." Nagoya Mathematical Journal 108 (December 1987): 15–51. http://dx.doi.org/10.1017/s0027763000002634.

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In the study of elliptic differential operators of second order, we found that the automorphism pseudogroups are of finite type ([4]). However this fact takes a complete change in elliptic differential operators of first order.So as to make the objects which can be dealt with clear, we introduce the concept of pseudoellipticity of first order differential operators (Definition 1.1), which is naturally satisfied by first order elliptic differential operators.
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Ipek Al, P., and Z. I. Ismailov. "First Order Selfadjoint Differential Operators with Involution." Lobachevskii Journal of Mathematics 42, no. 3 (March 2021): 496–501. http://dx.doi.org/10.1134/s1995080221030045.

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Gatse, Servais Cyr. "Some Properties of First Order Differential Operators." Advances in Pure Mathematics 09, no. 11 (2019): 934–43. http://dx.doi.org/10.4236/apm.2019.911046.

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Ismailov, Z. I., B. O. Guler, and P. Ipek. "Solvability of first order functional differential operators." Journal of Mathematical Chemistry 53, no. 9 (July 28, 2015): 2065–77. http://dx.doi.org/10.1007/s10910-015-0534-2.

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Ismailov, Zameddin I. "Multipoint normal differential operators of first order." Opuscula Mathematica 29, no. 4 (2009): 399. http://dx.doi.org/10.7494/opmath.2009.29.4.399.

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Pembe; ISMAILOV, İPEK. "SELFADJOINT SINGULAR DIFFERENTIAL OPERATORS FOR FIRST ORDER." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 67, no. 2 (2018): 156–64. http://dx.doi.org/10.1501/commua1_0000000870.

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Chernyshov, M. K. "Invertibility of first-order linear differential operators." Mathematical Notes 64, no. 5 (November 1998): 688–93. http://dx.doi.org/10.1007/bf02316297.

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ÖZTÜRK MERT, Rukiye, Bülent YILMAZ, and Zameddin I. Ismailov. "Multipoint selfadjoint quasi-differential operators for first order." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 68, no. 1 (April 11, 2018): 964–72. http://dx.doi.org/10.31801/cfsuasmas.501414.

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İpek, Pembe, and Zameddin İsmailov. "Boundedly solvable degenerate differential operators for first order." Universal Journal of Mathematics and Applications 1, no. 1 (March 15, 2018): 68–73. http://dx.doi.org/10.32323/ujma.387330.

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Dissertations / Theses on the topic "First-order differential operators"

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Bär, Christian, and Werner Ballmann. "Boundary value problems for elliptic differential operators of first order." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6002/.

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We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.
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Strogies, Nikolai. "Optimization of nonsmooth first order hyperbolic systems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17633.

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Wir betrachten Optimalsteuerungsprobleme, die von partiellen Differentialgleichungen beziehungsweise Variationsungleichungen mit Differentialoperatoren erster Ordnung abhängen. Wir führen die Reformulierung eines Tagebauplanungsproblems, das auf stetigen Funktionen beruht, ein. Das Resultat ist ein Optimalsteuerungsproblem für Viskositätslösungen einer Eikonalgleichung. Die Existenz von Lösungen dieses und bestimmter Hilfsprobleme, die von semilinearen PDG‘s mit künstlicher Viskosität abhängen, wird bewiesen, Stationaritätsbedingungen hergeleitet und ein schwaches Konsistenzresultat für stationäre Punkte präsentiert. Des Weiteren betrachten wir Optimalsteuerungsprobleme, die von stationären Variationsungleichungen erster Art mit linearen Differentialoperatoren erster Ordnung abhängen. Wir diskutieren Lösbarkeit und Stationaritätskonzepte für diese Probleme. Für letzteres vergleichen wir Ergebnisse, die entweder durch die Anwendung von Penalisierungs- und Regularisierungsansätzen direkt auf Ebene von Differentialoperatoren erster Ordnung oder als Grenzwertprozess von Stationaritätssystemen für viskositätsregularisierte Optimalsteuerungsprobleme unter passenden Annahmen erhalten werden. Um die Konsistenz von ursprünglichem und regularisierten Problemen zu sichern, wird ein bekanntes Ergebnis für Lösungen von VU’s mit degeneriertem Differentialoperator erweitert. In beiden Fällen ist die erhaltene Stationarität schwächer als W-stationarität. Die theoretischen Ergebnisse werden anhand numerischer Beispiele verifiziert. Wir erweitern diese Ergebnisse auf Optimalsteuerungsprobleme bezüglich zeitabhängiger VU’s mit Differentialoperatoren erster Ordnung. Hierfür wird die Existenz von Lösungen bewiesen und erneut ein Stationaritätssystem mit Hilfe verschwindender Viskositäten unter bestimmten Beschränktheitsannahmen hergeleitet. Die erhaltenen Ergebnisse werden anhand von numerischen Beispielen verifiziert.
We consider problems of optimal control subject to partial differential equations and variational inequality problems with first order differential operators. We introduce a reformulation of an open pit mine planning problem that is based on continuous functions. The resulting formulation is a problem of optimal control subject to viscosity solutions of a partial differential equation of Eikonal Type. The existence of solutions to this problem and auxiliary problems of optimal control subject to regularized, semilinear PDE’s with artificial viscosity is proven. For the latter a first order optimality condition is established and a mild consistency result for the stationary points is proven. Further we study certain problems of optimal control subject to time-independent variational inequalities of the first kind with linear first order differential operators. We discuss solvability and stationarity concepts for such problems. In the latter case, we compare the results obtained by either utilizing penalization-regularization strategies directly on the first order level or considering the limit of systems for viscosity-regularized problems under suitable assumptions. To guarantee the consistency of the original and viscosity-regularized problems of optimal control, we extend known results for solutions to variational inequalities with degenerated differential operators. In both cases, the resulting stationarity concepts are weaker than W-stationarity. We validate the theoretical findings by numerical experiments for several examples. Finally, we extend the results from the time-independent to the case of problems of optimal control subject to VI’s with linear first order differential operators that are time-dependent. After establishing the existence of solutions to the problem of optimal control, a stationarity system is derived by a vanishing viscosity approach under certain boundedness assumptions and the theoretical findings are validated by numerical experiments.
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Khavanin, Mohammad. "The Method of Mixed Monotony and First Order Delay Differential Equations." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96643.

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In this paper I extend the method of mixed monotony, to construct monotone sequences that converge to the unique solution of an initial value delay differential equation.
En este artículo se prueba una generalización del método de monotonía mixta, para construir sucesiones monótonas que convergen a la solución única de una ecuación diferencial de retraso con valor inicial.
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Morris, Andrew Jordan. "Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds." Phd thesis, 2010. http://hdl.handle.net/1885/8864.

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The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood--Paley--Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the origin. When we apply harmonic analysis to obtain estimates, the local theory only requires that we do so up to a finite scale. This allows us to consider manifolds with exponential volume growth in situations where the global theory requires polynomial volume growth. A holomorphic functional calculus is constructed for operators on a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. We prove that this functional calculus is bounded if and only if certain local quadratic estimates hold. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that the functional calculus is bounded. This theory allows us to define local Hardy spaces of differential forms that are adapted to a class of first-order differential operators on a complete Riemannian manifold with at most exponential volume growth. The local geometric Riesz transform associated with the Hodge--Dirac operator is bounded on these spaces provided that a certain condition on the exponential growth of the manifold is satisfied. A characterisation of these spaces in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ. Finally, we introduce a class of first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincar\'{e} inequality holds. A local quadratic estimate is established for certain perturbations of these operators. As an application, we solve the Kato square root problem for divergence form operators on complete Riemannian manifolds with Ricci curvature bounded below that are embedded in Euclidean space with a uniformly bounded second fundamental form. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.
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Books on the topic "First-order differential operators"

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Hounie, Jorge. Local solvability of first order linear operators with Lipschitz coefficients. Recife, Brasil: Universidade Federal de Pernambuco, Centro de Ciências Exatas e da Natureza, Departamento de Matemática, 1990.

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Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

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Marrakesh Workshop on Geometric Analysis of Several Complex Variables and Related Topics (2010 Marrakech, Morocco). Geometric analysis of several complex variables and related topics: Marrakesh Workshop on Geometric Analysis of Several Complex Variables and Related Topics, May 10-14, 2010, Marrakesh, Morocco. Edited by Barkatou Y. 1967-. Providence, R.I: American Mathematical Society, 2011.

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Gesztesy, Fritz, Barry Simon, H. Holden, and Gerald Teschl. Spectral analysis, differential equations, and mathematical physics: A festschrift in honor of Fritz Gesztesy's 60th birthday. Providence, Rhode Island: American Mathematical Society, 2013.

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Litvinov, G. L. (Grigoriĭ Lazarevich), 1944- editor of compilation and Sergeev, S. N., 1981- editor of compilation, eds. Tropical and idempotent mathematics and applications: International Workshop on Tropical and Idempotent Mathematics, August 26-31, 2012, Independent University, Moscow, Russia. Providence, Rhode Island: American Mathematical Society, 2014.

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Amenta, Alex, and Pascal Auscher. Elliptic Boundary Value Problems with Fractional Regularity Data: The First Order Approach. American Mathematical Society, 2018.

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Edmunds, David, and Des Evans. Spectral Theory and Differential Operators. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.001.0001.

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This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and makes applications to such questions. After the exposition of the abstract theory in the first four chapters, Sobolev spaces are introduced and their main properties established. The remaining seven chapters are largely concerned with second-order elliptic differential operators and related boundary-value problems. Particular attention is paid to the spectrum of the Schrödinger operator. Its original form contains material of lasting importance that is relatively unaffected by advances in the theory since 1987, when the book was first published. The present edition differs from the old by virtue of the correction of minor errors and improvements of various proofs. In addition, it contains Notes at the ends of most chapters, intended to give the reader some idea of recent developments together with additional references that enable more detailed accounts to be accessed.
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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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Rajeev, S. G. Vector Fields. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0001.

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The velocity of a fluid at each point of space-time is a vector field (or flow). It is best to think of it in terms of the effect of fluid flow on some scalar field. A vector field is thus a first order partial differential operator, called the material derivative in fluid mechanics. The path of a speck of dust carried along (advected) by the fluid is the integral curve of the velocity field. Even simple vector fields can have quite complicated integral curves: a manifestation of chaos. Of special interest are incompressible (with zero divergence) and irrotational (with zero curl) flows. A fixed point of a vector field is a point at which it vanishes. The derivative of a vector field at a fixed point is a matrix (the Jacobi matrix) whose spectrum is independent of the choice of coordinates.
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Book chapters on the topic "First-order differential operators"

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Eliashberg, Y., and N. Mishachev. "First order linear differential operators." In Graduate Studies in Mathematics, 179–87. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/gsm/048/21.

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Levajković, Tijana, and Dora Seleši. "Nonhomogeneous First-order Linear Malliavin Type Differential Equation." In Pseudo-Differential Operators, Generalized Functions and Asymptotics, 353–69. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0585-8_20.

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Lesch, Matthias, and Mark M. Malamud. "The Inverse Spectral Problem for First Order Systems on the Half Line." In Differential Operators and Related Topics, 199–238. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8403-7_16.

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Booss, B., and D. D. Bleecker. "Elliptic Differential Operators of First Order with Boundary Conditions." In Universitext, 199–208. New York, NY: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4684-0627-6_16.

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Kmit, I. "Smoothing Effect and Fredholm Property for First-order Hyperbolic PDEs." In Pseudo-Differential Operators, Generalized Functions and Asymptotics, 219–38. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0585-8_11.

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Lorenzoni, Paolo, and Andrea Savoldi. "First Order Hamiltonian Operators of Differential-Geometric Type in 2D." In Springer Proceedings in Mathematics & Statistics, 371–78. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2636-2_25.

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Hanel, Clemens, Günther Hörmann, Christian Spreitzer, and Roland Steinbauer. "Wave Equations and Symmetric First-order Systems in Case of Low Regularity." In Pseudo-Differential Operators, Generalized Functions and Asymptotics, 283–96. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0585-8_15.

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Marmolejo-Olea, Emilio, and Marius Mitrea. "Harmonic Analysis for General First Order Differential Operators in Lipschitz Domains." In Clifford Algebras, 91–114. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2044-2_6.

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Ismailov, Zameddin I., and Pembe Ipek. "Spectrums of Solvable Pantograph Type Delay Differential Operators for First Order." In Springer Proceedings in Mathematics & Statistics, 299–311. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28443-9_21.

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Vabishchevich, Petr, and Petr Zakharov. "Domain Decomposition Scheme for First-Order Evolution Equations with Nonselfadjoint Operators." In Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications, 279–302. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7172-1_14.

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Conference papers on the topic "First-order differential operators"

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Al, Pembe Ipek, and Zameddin I. Ismailov. "First order maximally dissipative singular differential operators." In THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136124.

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Yılmaz, Fatih, and Meltem Sertbaş. "Singular degenerate normal differential operators for first-order." In THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136138.

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YÜKSEL, U. "FIRST-ORDER DIFFERENTIAL OPERATORS ASSOCIATED TO THE CAUCHY-RIEMANN OPERATOR OF CLIFFORD ANALYSIS." In Proceedings of the 6th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812837332_0034.

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Fărcăşeanu, Maria, Mihai Mihăilescu, and Denisa Stancu-Dumitru. "A maximum principle for a class of first order differential operators." In 8th Congress of Romanian Mathematicians. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789813142862_0007.

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Шкаликов, А. "Spectral properties of ordinary differential operators generated by first order systems." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh1t-2021-10-06.32.

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Ismailov, Zameddin I., and Pembe Ipek. "Boundedly solvable multipoint differential operators of first order on right semi-axis." In ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930464.

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Ismailov, Zameddin I., Elif O. Çevik, Bahadır O. Guler, and Pembe Ipek. "Structure of spectrum of solvable pantograph differential operators for the first order." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893810.

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TROOSHIN, IGOR, and MASAHIRO YAMAMOTO. "HOCHSTADT-LIEBERMAN TYPE THEOREM FOR A NON-SYMMETRIC SYSTEM OF FIRST-ORDER ORDINARY DIFFERENTIAL OPERATORS." In Proceedings of the International Conference on Inverse Problems. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704924_0018.

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Regis, Carlos Danilo Miranda, José Vinicius Miranda Cardoso, Ítalo Pontes Oliveira, and Marcelo Sampaio Alencar. "Performance of the objective video quality metrics with perceptual weighting considering first and second order differential operators." In the 18th Brazilian symposium. New York, New York, USA: ACM Press, 2012. http://dx.doi.org/10.1145/2382636.2382653.

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Caruntu, Dumitru I. "On Transverse Vibrations of Rectangular Plates of Unidirectional Parabolic Thickness Variation." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80903.

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This paper presents an approach for finding the solution of partial differential equation describing the motion of transverse vibrations of rectangular plates of unidirectional convex parabolic varying thickness. The partial differential equation consists of three operators: fourth-order spatial-dependent, second-order spatial-dependent, and second-order time-dependent. Using the method of multiple scales, the partial differential equation has been reduced to two simpler partial differential equations which can be analytically solved and which represent two levels of approximation. The first partial differential equation was a homogeneous equation and consisted of two operators, the fourth-order spatial-dependent and second-order time-dependent. Using the factorization method, so-called zero-order approximation of the exact solution has been found. The second partial differential equation was an inhomogeneous equation. Its solution, so-called first-order approximation of the exact solution has been found. This way the first-order approximations of the natural frequencies and mode shapes are found. Various boundary conditions can be considered. The influence of Poisson’s ratio on the natural frequencies and mode shapes could be further studied using the approximations reported here. This approach can be extended to nonlinear, and/or forced vibrations.
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