Academic literature on the topic 'Riemannův problém'

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Journal articles on the topic "Riemannův problém"

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Zeitsch, Peter. "On the Riemann Function." Mathematics 6, no. 12 (2018): 316. http://dx.doi.org/10.3390/math6120316.

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Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E.T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to S L ( 2 , R ) . Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever.
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Zhixin, L., and B. A. Kats. "Riemann boundary-value problem on Cassini spirals." Issues of Analysis 28, no. 1 (2021): 101–10. http://dx.doi.org/10.15393/j3.art.2021.9770.

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Han, Xinli, and Lijun Pan. "The Perturbed Riemann Problem with Delta Shock for a Hyperbolic System." Advances in Mathematical Physics 2018 (September 5, 2018): 1–11. http://dx.doi.org/10.1155/2018/4925957.

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In this paper, we study the perturbed Riemann problem with delta shock for a hyperbolic system. The problem is different from the previous perturbed Riemann problems which have no delta shock. The solutions to the problem are obtained constructively. From the solutions, we see that a delta shock in the corresponding Riemann solution may turn into a shock and a contact discontinuity under a perturbation of the Riemann initial data. This shows the instability and the internal mechanism of a delta shock. Furthermore, we find that the Riemann solution of the hyperbolic system is instable under this perturbation, which is also quite different from the previous perturbed Riemann problems.
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Durmagambetov, Asset. "Reduction of modern problems of mathematics to the classical Riemann-Poincare-Hilbert problem." European Journal of Pure and Applied Mathematics 11, no. 4 (2018): 1143–76. http://dx.doi.org/10.29020/nybg.ejpam.v11i4.3328.

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Using the example of a complicated problem such as the Cauchy problem for the Navier--Stokes equation, we show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of solutions for this case. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation, which we consider as a velocity component in the Navier--Stokes equation. The same scheme of reduction of Riemann integral equations for the zeta function to the Poincar\'e--Riemann--Hilbert boundary-value problem allows us to construct effective estimates that describe the behaviour of the zeros of the zeta function very well.
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Kurganov, Alexander, and Eitan Tadmor. "Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers." Numerical Methods for Partial Differential Equations 18, no. 5 (2002): 584–608. http://dx.doi.org/10.1002/num.10025.

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Chen, Yang, and Alexander R. Its. "A Riemann–Hilbert approach to the Akhiezer polynomials." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1867 (2007): 973–1003. http://dx.doi.org/10.1098/rsta.2007.2058.

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In this paper, we study those polynomials, orthogonal with respect to a particular weight, over the union of disjoint intervals, first introduced by N. I. Akhiezer, via a reformulation as a matrix factorization or Riemann–Hilbert problem. This approach complements the method proposed in a previous paper, which involves the construction of a certain meromorphic function on a hyperelliptic Riemann surface. The method described here is based on the general Riemann–Hilbert scheme of the theory of integrable systems and will enable us to derive, in a very straightforward way, the relevant system of Fuchsian differential equations for the polynomials and the associated system of the Schlesinger deformation equations for certain quantities involving the corresponding recurrence coefficients. Both of these equations were obtained earlier by A. Magnus. In our approach, however, we are able to go beyond Magnus' results by actually solving the equations in terms of the Riemanni Θ -functions. We also show that the related Hankel determinant can be interpreted as the relevant τ -function.
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Bolottn, L. B. "THE SECOND BOUNDARY VALUE PROBLEM OF RIEMANN'S TYPE FOR BIANALYTICAL FUNCTIONS WITH DISCONTINUOUS COEFFICIENTS." Mathematical Modelling and Analysis 9, no. 3 (2004): 193–200. http://dx.doi.org/10.3846/13926292.2004.9637252.

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The paper is devoted to the investigation of one of the basic boundary value problems of Riemann's type for bianalytical functions with discontinuous coefficients. In the course of work there was made out a constructive method for solution of the problem in a unit circle. There was also found out that the solution of the problem under consideration consists in consequent solutions of two Riemann's boundary value problems for analytical functions in a unit circle. Besides, the example is constructed.
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Vyugin, Il'ya V. "Riemann-Hilbert problem for scalar Fuchsian equations and related problems." Russian Mathematical Surveys 66, no. 1 (2011): 35–62. http://dx.doi.org/10.1070/rm2011v066n01abeh004727.

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Minkevich, A. V. "Towards the theory of regular accelerating Universe in Riemann-Cartan space-time." International Journal of Modern Physics A 31, no. 02n03 (2016): 1641011. http://dx.doi.org/10.1142/s0217751x16410116.

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The problems of modern cosmology and attempts of its solution are considered. The applying of gravitation theory in the Riemann-Cartan space-time as the most natural generalization of Einstein gravitation theory in order to solve the principal cosmological problems is discussed. The gravitation theory in the Riemann-Cartan space-time leading to the solution of the problem of cosmological singularity and dark energy problem is analyzed.
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Fatykhov, A. Kh, and P. L. Shabalin. "Solvability homogeneous Riemann-Hilbert boundary value problem with several points of turbulence." Issues of Analysis 25 (September 2018): 31–39. http://dx.doi.org/10.15393/j3.art.2018.5530.

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Dissertations / Theses on the topic "Riemannův problém"

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Semmler, Gunter. "Nonlinear Riemann-Hilbert Problems." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola&quot, 2009. http://nbn-resolving.de/urn:nbn:de:swb:105-7341443.

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Riemann-Hilbert-Probleme sind Randwertaufgaben für im Einheitskreis $\mathbb D$ holomorphe Funktionen $w$, deren Randwerte $w(t)$ auf gewissen Kurven $M_t$ liegen sollen. Ein Teil der Untersuchungen ist dem Fall explizit gegebener Kurven gewidmet. Dabei werden bekannte Resultate über glatte Kurven auf stetige Restriktionskurven erweitert, und die Existenz von Lösungen in gewissen Hardy-Räumen gezeigt. Die Eindeutigkeitsfrage führt auf ein Gegenbeispiel, das zugleich eine Vermutung aus einer Dissertation von Belch widerlegt. Der andere Teil der Untersuchungen ist dem klassischen Fall geschlossener Restriktionskurven gewidmet. Hier steht statt der Abschwächung von Glattheitsvoraussetzungen die Formulierung geeigneter Nebenbedingungen im Mittelpunkt. Die Abhängigkeit der Lösung von Zusatzbedingungen erweist sich als Verallgemeinerung des Verhaltens von Blaschkeprodukten. Für drei Interpolationpunkte kann charakterisiert werden, wann durch sie eine Lösung mit Windungszahl 1 verläuft, durch $k$ Interpolationspunkte wird die Existenz einer Lösung mit Windungszahl $k-1$ gezeigt.
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Dewaal, Nicholas. "The Importance of the Riemann-Hilbert Problem to Solve a Class of Optimal Control Problems." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1759.pdf.

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Fernández, Sánchez Percy. "El problema de Riemann Hilbert : sobre superficies de Riemann no compactas." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96150.

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En el ICM (Intemational Congress of Mathematicians) de 1900, Hilbert presenta 23 problemas que establecieron el curso de gran parte de las investigaciones matemáticas del siglo XX. El 21° problema es la existencia de ecuaciones diferenciales lineales, con un grupo de monodromía y singularidades prescritas. Este artículo trata este problema sobre superficies de Riemann no compactas.
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Gu, Xiang. "Hamiltonian structures and Riemann-Hilbert problems of integrable systems." Scholar Commons, 2018. https://scholarcommons.usf.edu/etd/7677.

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We begin this dissertation by presenting a brief introduction to the theory of solitons and integrability (plus some classical methods applied in this field) in Chapter 1, mainly using the Korteweg-de Vries equation as a typical model. At the end of this Chapter a mathematical framework of notations and terminologies is established for the whole dissertation. In Chapter 2, we first introduce two specific matrix spectral problems (with 3 potentials) associated with matrix Lie algebras $\mbox{sl}(2;\mathbb{R})$ and $\mbox{so}(3;\mathbb{R})$, respectively; and then we engender two soliton hierarchies. The computation and analysis of their Hamiltonian structures based on the trace identity affirms that the obtained hierarchies are Liouville integrable. This chapter shows the entire process of how a soliton hierarchy is engendered by starting from a proper matrix spectral problem. In Chapter 3, at first we elucidate the Gauge equivalence among three types $u$-linear Hamiltonian operators, and construct then the corresponding B\"acklund transformations among them explicitly. Next we derive the if-and-only-if conditions under which the linear coupling of the discussed u-linear operators and matrix differential operators with constant coefficients is still Hamiltonian. Very amazingly, the derived conditions show that the resulting Hamiltonian operators is truncated only up to the 3rd differential order. Finally, a few relevant examples of integrable hierarchies are illustrated. In Chapter, 4 we first present a generalized modified Korteweg-de Vries hierarchy. Then for one of the equations in this hierarchy, we build the associated Riemann-Hilbert problems with some equivalent spectral problems. Next, computation of soliton solutions is performed by reducing the Riemann-Hilbert problems to those with identity jump matrix, i.e., those correspond to reflectionless inverse scattering problems. Finally a special reduction of the original matrix spectral problem will be briefly discussed.
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Desideri, Laura. "Problème de Plateau, équations fuchsiennes et problème de Riemann-Hilbert." Phd thesis, Université Paris-Diderot - Paris VII, 2009. http://tel.archives-ouvertes.fr/tel-00452508.

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Ce mémoire est consacré à la résolution du problème de Plateau à bord polygonal dans l'espace euclidien et dans l'espace de Minkowski de dimension trois. Il s'appuie sur la méthode de résolution proposée par René Garnier dans le cas euclidien dans un article publié en 1928 et qui a été oublié depuis, voire ignoré à l'époque. Plus géométrique et constructive que la méthode variationnelle, l'approche de Garnier est cependant parfois très compliquée, voire obscure et incomplète. On retranscrit sa démonstration dans un formalisme moderne, tout en proposant de nouvelles preuves plus simples, et en en complétant certaines lacunes. Ce travail repose principalement sur l'utilisation plus systématique des systèmes fuchsiens et la mise en évidence du lien entre la réalité de ces systèmes et leur monodromie. Ceci nous permet d'étendre le résultat de Garnier dans l'espace de Minkowski. La méthode de Garnier repose sur le fait que, par la représentation de Weierstrass spinorielle des surfaces minimales, on peut associer une équation fuchsienne réelle du second ordre définie sur la sphère de Riemann à tout disque minimal à bord polygonal. La monodromie de cette équation est déterminée par les directions orientées des côtés du bord. Pour résoudre le problème de Plateau, on est donc amené à résoudre un problème de Riemann-Hilbert. On procède ensuite en deux étapes : on construit d'abord, par déformations isomonodromiques, la famille de tous les disques minimaux dont le bord est un polygone de directions orientées données. Puis on montre, en étudiant les longueurs des côtés des bords polygonaux, qu'on obtient ainsi tout polygone comme bord d'un disque minimal.
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TINTAYA, PERCY ALEXANDER CACERES. "RIEMANN HILBERT PROBLEMS IN RANDOM MATRIX THEORY." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=26432@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Estudamos as noções básicas da Teoria das Matrizes Aleatórias e em particular discutimos o Emsemble Unitário Gaussiano. A continuação descrevemos o gaz de Dyson em equilíbrio e fora do equilíbrio que permite interpretar a informação estatística dos autovalores das matrizes aleatórias. Além desso mostramos descrições alternativas dessa informação estatística. Em seguida discutimos aspectos diferentes dos polinômios ortogonais. Uma dessas caracterizações é dada pelos problemas de Riemann-Hilbert. As técnicas dos problemas de Riemann-Hilbert são uma ferramenta eficaz e potente na Teoria das Matrizes Aleatórias a qual discutimos com mais cuidado. Finalmente usamos o método de máxima gradiente na análise assintótico dos polinômios ortogonais.<br>We review the basic notions of the Random Matrix Theory and in particular the Gaussian Unitary Ensemble. In what follows we describe the Dyson gas in equilibrium and nonequilibrium that allows one to interpret the statistical information of the eigenvalues of random matrices. Furthermore we show alternative descriptions of this statistical information. In the following we discuss different aspects of orthogonal polynomials. One of these caracterizations is given by a Riemann Hilbert problem. Riemann Hilbert problem techniques are an efficient and powerfull tool for Random Matrix Theory which we discuss in more detail. In the final part we use the steepest descent method in the asymptotic analysis of orthogonal polynomials.
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Belch, Rudiger. "Extremal interpolation and nonlinear Riemann-Hilbert problems." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624100.

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Campana, Camilo. "O problema de Riemann-Hilbert para campos vetoriais complexos." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-25072017-111735/.

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Este trabalho trata de problemas de contorno definidos no plano. O problema central desta tese é chamado Problema de Riemann-Hilbert, o qual pode ser descrito como segue. Seja L um campo vetorial complexo não singular definido em uma vizinhança do fecho de um aberto simplesmente conexo do plano com fronteira suave. O Problema de Riemann-Hilbert para o campo L consiste em obter uma solução para a equação Lu = F(x, y, u) no aberto em estudo, sendo dada uma função F mensurável. Pede-se também que a solução tenha extensão contínua até a fronteira e que satisfaça lá uma condição adicional; trabalha-se aqui no contexto das funções Hölder contínuas. Foram obtidos resultados para o problema acima no caso em que L pertence a uma classe de campos hipocomplexos. O caso clássico conhecido é quando o campo vetorial é o operador de Cauchy-Riemann, ou, mais geralmente, quando é um campo elítico.<br>This work deals with boundary problems in the plane. The central problem in this thesis is the so-called Riemann-Hilbert problem, which may be described as follows. Let L be a non-singular complex vector field defined on a neighborhood of the closure of a simply connected open subset of the plane having smooth boundary. The Riemann-Hilbert problem for the vector field L consists in finding a solution to the equation Lu = F(x, y, u) on the open set under study, where the given function F is measurable. It is also required that the solution have a continuous extension up to the boundary and satisfy an additional condition there. Results were obtained for the above problem when L belongs to a class of hypocomplex vector fields. The well-known classical case is the one in which the vector field under study is the Cauchy-Riemann operator, or more generally when it is an elliptic vector field.
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Hays, Christopher. "Non-Isotopic Symplectic Surfaces in Products of Riemann Surfaces." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2917.

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<html> <head> <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"> </head> Let &Sigma;<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, for each <em>g</em> &ge; 1 and <em>h</em> &ge; 0 we construct an infinite set of infinite families of homotopic but pairwise non-isotopic symplectic surfaces inside the product symplectic manifold &Sigma;<em><sub>g</sub></em> ×&Sigma;<em><sub>h</sub></em>. In particular, we achieve all positive genera from these families, providing first examples of infinite families of homotopic but pairwise non-isotopic symplectic surfaces of even genera inside &Sigma;<em><sub>g</sub></em> ×&Sigma;<em><sub>h</sub></em>.
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Vitti, Ana Paula. "PROBLEMA DE RIEMANN PARA LEIS DE CONSERVAÇÃO ESCALARES." Universidade de São Paulo, 1995. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-24042018-145013/.

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Este trabalho apresenta um estudo sobre a existência, unicidade e comportamento assintótico de soluções para uma lei de conservação escalar da forma ut+ f (u)x = O. Esta solução satisfaz a desigualdade de entropia, e além disso é a única solução com esta propriedade. O problema é estudado via o método das diferenças finitas.<br>In this work we studied the existence, uniqueness and asymptotic behavior of solutions for a single conservation law in the form ut + f (u)x = 0. This solution satisfies the entropy inequality, and furthermore is the unique solution with this propriety. The problem was studied using the finite-difference method.
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Books on the topic "Riemannův problém"

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The Riemann boundary problem on Riemann surfaces. D. Reidel Pub. Co., 1988.

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Rodin, Yu L. The Riemann Boundary Problem on Riemann Surfaces. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2885-5.

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Anosov, D. V. The Riemann-Hilbert problem. Vieweg, 1994.

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Anosov, D. V., and A. A. Bolibruch. The Riemann-Hilbert Problem. Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-322-92909-9.

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Govorov, N. V. Riemann's boundary problem with infinite index. Birkhäuser Verlag, 1994.

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Govorov, N. V. Riemann’s Boundary Problem with Infinite Index. Edited by I. V. Ostrovskii. Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8506-5.

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Dutt, Pravir. A Riemann solver based on a global existence proof for the Riemann problem. ICASE, 1986.

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Menikoff, Ralph. Riemann problem for fluid flow of real materials. Los Alamos National Laboratory, 1988.

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Chowla, S. The Riemann hypothesis and Hilbert's tenth problem. Gordon and Breach, 1987.

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Shuli, Yang, and Zhang Tong 1932-, eds. The two-dimensional Riemann problem in gas dynamics. Longman, 1998.

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Book chapters on the topic "Riemannův problém"

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Maurin, Krzysztof. "The Problem of Poincaré and the Cousin Problems." In The Riemann Legacy. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8939-0_51.

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Roe, Philip L. "Riemann Problem." In Encyclopedia of Applied and Computational Mathematics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_357.

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Sasoh, Akihiro. "Riemann Problem." In Compressible Fluid Dynamics and Shock Waves. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-0504-1_9.

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Caminha Muniz Neto, Antonio. "Riemann’s Integral." In Problem Books in Mathematics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53871-6_10.

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Zheng, Yuxi. "Riemann Problems." In Systems of Conservation Laws. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0141-0_3.

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Tatsien, Li, and Wang Libin. "Generalized Riemann Problem." In Global Propagation of Regular Nonlinear Hyperbolic Waves. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/b78335_7.

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Castro-Orgaz, Oscar, and Willi H. Hager. "The Riemann Problem." In Shallow Water Hydraulics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13073-2_8.

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Faddeev, Ludwig D., and Leon A. Takhtajan. "The Riemann Problem." In Hamiltonian Methods in the Theory of Solitons. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-540-69969-9_3.

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Rosini, Massimiliano Daniele. "The Riemann Problem." In Understanding Complex Systems. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00155-5_4.

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LeFloch, Philippe G. "The Riemann Problem." In Hyperbolic Systems of Conservation Laws. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8150-0_2.

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Conference papers on the topic "Riemannův problém"

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Bukiet, Bruce. "Solving curved detonation Riemann problems." In The tenth American Physical Society topical conference on shock compression of condensed matter. AIP, 1998. http://dx.doi.org/10.1063/1.55687.

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Novokshenov, V. Yu, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "The Riemann-Hilbert problem and special functions." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043854.

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Biswas, Raj Kumar, and Siddhartha Sen. "Numerical Method for Solving Fractional Optimal Control Problems." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87008.

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A numerical technique for the solution of a class of fractional optimal control problems has been proposed in this paper. The technique can used for problems defined both in terms of Riemann-Liouville and Caputo fractional derivatives. In this technique a Reflection Operator is used to convert the right Riemann-Liouville derivative into an equivalent left Riemann-Liouville derivative, and then the two point boundary value problem is solved numerically. The proposed method is straightforward and it uses an available numerical technique to solve fractional differential equations resulting from the formulation. Examples considered here show that the numerical results obtained using this and other techniques agree very well.
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Khimshiashvili, G. "Loop spaces and Riemann-Hilbert problems." In Geometry and Topology of Manifolds. Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc76-0-19.

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Mokry, M. "Flow past airfoils as a Riemann-Hilbert problem." In Theroretical Fluid Mechanics Conference. American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-2161.

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Giorgadze, G. K. "Solvability condition of the Riemann-Hilbert monodromy problem." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_0012.

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Mach, Patryk. "Instabilities of the Riemann problem in relativistic hydrodynamics." In TOWARDS NEW PARADIGMS: PROCEEDING OF THE SPANISH RELATIVITY MEETING 2011. AIP, 2012. http://dx.doi.org/10.1063/1.4734459.

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MORENO, ANA FOULQUIÉ. "RIEMANN-HILBERT PROBLEM FOR A GENERALIZED NIKISHIN SYSTEM." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770752_0035.

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Dmitrieva, I. "Vector boundary Riemann problems in soliton theory." In 2010 International Conference on Mathematical Methods in Electromagnetic Theory (MMET). IEEE, 2010. http://dx.doi.org/10.1109/mmet.2010.5611433.

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Wegert, Elias. "Nonlinear Riemann-Hilbert problems – history and perspectives." In Third CMFT Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812833044_0042.

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