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Готові списки джерел за темами / BV solutions

Добірка наукової літератури з теми "BV solutions"

Автор: Grafiati

Опубліковано: 17 серпня 2022

Оновлено: 18 вересня 2022

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Дисертації
Книги
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Статті в журналах з теми "BV solutions":

1

Krejčí, Pavel, and Vincenzo Recupero. "$\rm BV$ solutions of rate independent differential inclusions." Mathematica Bohemica 139, no. 4 (2014): 607–19. http://dx.doi.org/10.21136/mb.2014.144138.

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2

YOUNG, ROBIN. "NONUNIQUENESS OF BV SOLUTIONS OF QUASILINEAR HYPERBOLIC SYSTEMS." Journal of Hyperbolic Differential Equations 09, no. 04 (December 2012): 555–70. http://dx.doi.org/10.1142/s021989161250018x.

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We construct examples of one-dimensional quasilinear hyperbolic systems for which the constant state and Riemann problem are unstable under O(1) perturbations in the space BV. We generate a system and solution consisting of three compressions which focus at the same point, resulting in a nonlinear interaction from which no waves emerge. Since this solution is time-reversible, this leads to nontrivial solutions of the system with constant initial data. These solutions are classical in the sense that they do not contain shocks and are discontinuous only at the origin. We then find some elementary necessary conditions for a system in conservative form to exhibit this type of behavior.

3

Ancona, Fabio, Laura Caravenna, and Andrea Marson. "On the structure of BV entropy solutions for hyperbolic systems of balance laws with general flux function." Journal of Hyperbolic Differential Equations 16, no. 02 (June 2019): 333–78. http://dx.doi.org/10.1142/s0219891619500139.

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The paper describes the qualitative structure of BV entropy solutions of a general strictly hyperbolic system of balance laws with characteristic field either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an accurate description of the local and global wave-front structure of a BV solution generated by a fractional step scheme combined with a wave-front tracking algorithm. This extends the corresponding results in [S. Bianchini and L. Yu, Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension, Comm. Partial Differential Equations 39(2) (2014) 244–273] for strictly hyperbolic system of conservation laws.

4

NOLAN, B. C. "WEAK SOLUTIONS FOR WEAK SINGULARITIES." International Journal of Modern Physics A 17, no. 20 (August 10, 2002): 2769. http://dx.doi.org/10.1142/s0217751x02011965.

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We revisit the problem of the development of singularities in the gravitational collapse of an inhomogeneous dust sphere. As shown by Yodzis et al1, naked singularities may occur at finite radius where shells of dust cross one another. These singularities are gravitationally weak 2, and it has been claimed that at these singularities, the metric may be written in continuous form 2, with locally L∞ connection coefficients 3. We correct these claims, and show how the field equations may be reformulated as a first order, quasi-linear, non-conservative, non-strictly hyperbolic system. We discuss existence and uniqueness of generalized solutions of this system using bounded functions of bounded variation (BV) 4, where the product of a BV function and the derivative of another BV function may be interpreted as a locally finite measure. The solutions obtained provide a dynamical extension to the future of the singularity.

5

Bianchini, Stefano. "BV Solutions of the Semidiscrete Upwind Scheme." Archive for Rational Mechanics and Analysis 167, no. 1 (March 2003): 1–81. http://dx.doi.org/10.1007/s00205-002-0237-2.

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6

Knees, Dorothee. "Convergence analysis of time-discretisation schemes for rate-independent systems." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 65. http://dx.doi.org/10.1051/cocv/2018048.

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It is well known that rate-independent systems involving nonconvex energy functionals in general do not allow for time-continuous solutions even if the given data are smooth. In the last years, several solution concepts were proposed that include discontinuities in the notion of solution, among them the class of global energetic solutions and the class of BV-solutions. In general, these solution concepts are not equivalent and numerical schemes are needed that reliably approximate that type of solutions one is interested in. In this paper, we analyse the convergence of solutions of three time-discretisation schemes, namely an approach based on local minimisation, a relaxed version of it and an alternate minimisation scheme. For all three cases, we show that under suitable conditions on the discretisation parameters discrete solutions converge to limit functions that belong to the class of BV-solutions. The proofs rely on a reparametrisation argument. We illustrate the different schemes with a toy example.

7

Anzellotti, G. "BV solutions of quasilinear PDEs in divergence form." Communications in Partial Differential Equations 12, no. 1 (January 1987): 77–122. http://dx.doi.org/10.1080/03605308708820485.

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8

Bressan, Alberto, and Wen Shen. "Small BV Solutions of Hyperbolic Noncooperative Differential Games." SIAM Journal on Control and Optimization 43, no. 1 (January 2004): 194–215. http://dx.doi.org/10.1137/s0363012903425581.

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9

Lerner, Nicolas, and Ferruccio Colombini. "Uniqueness of continuous solutions for BV vector fields." Duke Mathematical Journal 111, no. 2 (February 2002): 357–84. http://dx.doi.org/10.1215/s0012-7094-01-11126-5.

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10

Minh, Mach Nguyet. "BV solutions constructed using the epsilon-neighborhood method." ESAIM: Control, Optimisation and Calculus of Variations 22, no. 1 (January 2016): 188–207. http://dx.doi.org/10.1051/cocv/2015001.

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Більше джерел

Дисертації з теми "BV solutions":

1

Faria, Josiane Cristina de Oliveira. "Estabilidade fraca de soluções lagrangeanas de equações semigeostroficas." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307165.

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Orientadores: Helena Judith Nussenzveig Lopes, Milton da Costa Lopes Filho
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-10T07:01:21Z (GMT). No. of bitstreams: 1 Faria_JosianeCristinadeOliveira_D.pdf: 915381 bytes, checksum: 33fbbc86d823554534cbe546850e707d (MD5) Previous issue date: 2008
Resumo: As equações semigeostrocas, introduzidas por Hoskins e Bretherton em 1972 em [20], sao um conjunto de equacoes que modelam fluxos atmosfericos/ oceanicos de larga escala. Elas possuem uma formulação em variaveis duais que se presta ao tratamento analítico. Alguns autores estudaram esta formulação, veja, por exemplo, [3], [14], [22], [12], [21],em particular obtendo existencia de solucões fracas em espaços de medidas. Contudo, ha dificuldades em converter soluções fracas da formulação dual em soluções fracas na formulação original, e portanto de interpretar fisicamente as soluções obtidas. Em [11], Culled e Feldman provaram a existencia de soluções Lagrangeanas para o sistema semigeostrofico em coordenadas fisicas com vorticidade potencial em Lp, p > 1. No presente trabalho estendemos os resultados de Cullen e Feldman para o caso limite p = 1 e estudamos o comportamento de sequencias de soluções Lagrangeanas correspondentes a uma sequencia de vorticidades potenciais iniciais convergindo fortemente em L1. Provamos que tais soluções Lagrangeanas convergem em L1 loc. Exibimos um contra-exemplo que sugere que nosso resultado não pode ser estendido para o espaço das medidas de Radon
Abstract: The semigeostrophic equations, which were introduced by Hoskins and Bretherton in 1972 in [20], are a set of equations that model large-escale atmospheric/ocean ows. They have a formulation in dual variables which can be analytically treated. Some authors studied these equations in dual variables, see for instance [3], [14], [22], [12], [21], particularly it is obtained existence of weak solutions in the space of Radon measures. In [11], Cullen and Feldman proved existence of Lagrangian solutions for the semigeostrophic system in physical variables with initial potential vorticity in Lp, p > 1. In the present work we extend Cullen and Feldman's result to the limit case p = 1 and we study the behavior of sequences of Lagrangian solutions corresponding to a sequence of initial potential vorticities converging strongly in L1. We prove that these Lagrangian solutions converge in L1 loc. However, there is difficulties in to turn weak solutions in dual formulations into solutions in original formulation, and therefore there is dificulties in to interpret the obtained solutions physically. We show by means of a counterexample that our result cannot be extended to the space of Radon measures
Doutorado
Matematica - Analise
Doutor em Matemática

2

Guelmame, Billel. "Sur une régularisation hamiltonienne et la régularité des solutions entropiques de certaines équations hyperboliques non linéaires." Thesis, Université Côte d'Azur, 2020. https://tel.archives-ouvertes.fr/tel-03177654.

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Dans cette thèse, nous étudions certaines régularisations conservatives et non dispersives pour des lois de conservation. Ces régularisations sont obtenues en s’inspirant de celle du système de Saint-Venant introduite par Clamond et Dutykh. Nous étudions également la régularité, dans des espaces BV généralisés, des solutions entropiques de certaines équations hyperboliques non linéaires. Dans la première partie, nous obtenons et étudions une régularisation appropriée de l’équation de Burgers inviscide, ainsi que sa généralisation aux lois de conservation scalaires. Nous prouvons que cette généralisation est localement bien posée pour les solutions régulières. Nous montrons aussi l’existence globale des solutions qui satisfont une inégalité d’Oleinik pour des flux uniformément convexes. Lorsque le paramètre de régularisation ``l’’ tend vers zéro, nous prouvons que ces solutions convergent, pour une sous-suite, vers les solutions de la loi de conservation scalaire originale, au moins pour un petit intervalle de temps.Nous généralisons également les équations Saint-Venant régularisées afin d’obtenir une régularisation du système d’Euler barotrope, ainsi qu’une régularisation du système de Saint-Venant avec fond variable. Nous montrons que ces deux systèmes sont bien posés localement dans Hs, avec s≥2. Dans la deuxième partie, nous démontrons un effet régularisant, sur les conditions initiales, des lois de conservation scalaires pour un flux lipschitzien strictement convexe, ainsi que pour des équations scalaires avec un terme source linéaire. Dans certains cas, nous donnons une borne de l’effet régularisant. Enfin, nous prouvons l’existence globale des solutions entropiques d’une classe de système triangulaire ayant une équation de transport dans BV^s x L^∞ où s > 1/3
In this thesis, we study some non-dispersive conservative regularisations for the scalar conservation laws and also for the barotropic Euler system. Those regularisations are obtained inspired by a regularised Saint-Venant system introduced by Clamond and Dutykh in 2017. We also study the regularity, in generalised BV spaces, of the entropy solutions of some nonlinear hyperbolic equations. In the first part, we obtain and study a suitable regularisation of the inviscid Burgers equation, as well as its generalisation to scalar conservation laws. We prove that this regularisation is locally well-posedness for smooth solutions. We also prove the global existence of solutions that satisfy a one-sided Oleinik inequality for uniformly convex fluxes. When the regularising parameter ``l’’ goes to zero, we prove that the solutions converge, up to a subsequence, to the solutions of the original scalar conservation law, at least for a short time. We also generalise the regularised Saint-Venant equations to obtain a regularisation of the barotropic Euler system, and the Saint-Venant system with uneven bottom. We prove that both systems are locally well-posed in Hs, with s ≥ 2. In the second part, we prove a regularising effect, on the initial data, of scalar conservation laws with Lipschitz strictly convex flux, and of scalar equations with a linear source term. For some cases, we give a limit of the regularising effect.Finally, we prove the global existence of entropy solutions of a class of triangular systems involving a transport equation in BV^s x L^∞ where s > 1/3

3

Al, Zohbi Maryam. "Contributions to the existence, uniqueness, and contraction of the solutions to some evolutionary partial differential equations." Thesis, Compiègne, 2021. http://www.theses.fr/2021COMP2646.

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Dans cette thèse, nous nous sommes principalement intéressés à l’étude théorique et numérique de quelques équations qui décrivent la dynamique des densités des dislocations. Les dislocations sont des défauts microscopiques qui se déplacent dans les matériaux sous l’effet des contraintes extérieures. Dans un premier travail, nous démontrons un résultat d’existence globale en temps des solutions discontinues pour un système hyperbolique diagonal qui n’est pas nécessairement strictement hyperbolique, dans un espace unidimensionnel. Ainsi dans un deuxième travail, nous élargissons notre portée en démontrant un résultat similaire pour un système d’équations de type eikonal non-linéaire qui est en fait une généralisation du système hyperbolique déjà étudié. En effet, nous prouvons aussi l’existence et l’unicité d’une solution continue pour le système eikonal. Ensuite, nous nous sommes intéressés à l’analyse numérique de ce système en proposant un schéma aux différences finies, par lequel nous montrons la convergence vers le problème continu et nous consolidons nos résultats avec quelques simulations numériques. Dans une autre direction, nous nous sommes intéressés à la théorie de contraction différentielle pour les équations d’évolutions. Après avoir introduit une nouvelle distance, nous construisons une nouvelle famille des solutions contractantes positives pour l’équation d’évolution p-Laplace
In this thesis, we are mainly interested in the theoretical and numerical study of certain equations that describe the dynamics of dislocation densities. Dislocations are microscopic defects in materials, which move under the effect of an external stress. As a first work, we prove a global in time existence result of a discontinuous solution to a diagonal hyperbolic system, which is not necessarily strictly hyperbolic, in one space dimension. Then in another work, we broaden our scope by proving a similar result to a non-linear eikonal system, which is in fact a generalization of the hyperbolic system studied first. We also prove the existence and uniqueness of a continuous solution to the eikonal system. After that, we study this system numerically in a third work through proposing a finite difference scheme approximating it, of which we prove the convergence to the continuous problem, strengthening our outcomes with some numerical simulations. On a different direction, we were enthused by the theory of differential contraction to evolutionary equations. By introducing a new distance, we create a new family of contracting positive solutions to the evolutionary p-Laplacian equation

4

Aujol, Jean-François. "Contribution à l'analyse de textures en traitement d'images par méthodes variationnelles et équations aux dérivées partielles." Phd thesis, Université de Nice Sophia-Antipolis, 2004. http://tel.archives-ouvertes.fr/tel-00006303.

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Анотація:

Cette thèse est un travail en mathématiques appliquées. Elle aborde quelques problèmes en analyse d'images et utilise des outils mathématiques spécifiques.

L'objectif des deux premières parties de cette thèse
est de proposer un modèle pour décomposer une image f en trois composantes : f=u+v+w.
La première composante, u, contient l'information géométrique. On peut la considérer comme une esquisse de l'image originale f.
La seconde composante, v, contient l'information texture.
La troisième composante, w, contient le bruit présent dans l'image originale.
Notre approche repose sur l'utilisation d'espaces mathématiques
adaptés à chaque composante: l'espace BV des fonctions à variations bornées pour u, un espace G proche du dual de BV pour les textures, et un espace de Besov d'exposant négatif E pour le bruit.
Nous effectuons l'étude mathématique complète des différents modèles que nous proposons.
Nous illustrons notre approche par de nombreux exemples, et donnons deux applications concrètes : une première en restauration d'images RSO, et une seconde en compression d'images.

Dans la troisième et dernière partie de cette thèse, nous nous intéressons
spécifiquement à la composante texturée.
Nous proposons un algorithme de classification supervisée pour les images texturées. L'approche utilisée est basée sur l'utilisation de la méthode des contours actifs et d'un terme d'attache aux donnés spécifiques au textures. Ce dernier est construit à partir d'une transformée en paquets d'ondelettes. Nous obtenons ainsi une fonctionnelle, dont le minimum correspond à la classification cherchée. Nous résolvons numériquement ce problème à l'aide d'un système couplé d'EDP que nous plongeons dans un schéma dynamique. Nous illustrons notre démarche par de nombreux exemples numériques. Nous effectuons également l'étude théorique de la fonctionnelle de classification.

5

Papafitsoros, Konstantinos. "Novel higher order regularisation methods for image reconstruction." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/246692.

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In this thesis we study novel higher order total variation-based variational methods for digital image reconstruction. These methods are formulated in the context of Tikhonov regularisation. We focus on regularisation techniques in which the regulariser incorporates second order derivatives or a sophisticated combination of first and second order derivatives. The introduction of higher order derivatives in the regularisation process has been shown to be an advantage over the classical first order case, i.e., total variation regularisation, as classical artifacts such as the staircasing effect are significantly reduced or totally eliminated. Also in image inpainting the introduction of higher order derivatives in the regulariser turns out to be crucial to achieve interpolation across large gaps. First, we introduce, analyse and implement a combined first and second order regularisation method with applications in image denoising, deblurring and inpainting. The method, numerically realised by the split Bregman algorithm, is computationally efficient and capable of giving comparable results with total generalised variation (TGV), a state of the art higher order method. An additional experimental analysis is performed for image inpainting and an online demo is provided on the IPOL website (Image Processing Online). We also compute and study properties of exact solutions of the one dimensional total generalised variation problem with L^{2} data fitting term, for simple piecewise affine data functions, with or without jumps . This gives an insight on how this type of regularisation behaves and unravels the role of the TGV parameters. Finally, we introduce, study and analyse a novel non-local Hessian functional. We prove localisations of the non-local Hessian to the local analogue in several topologies and our analysis results in derivative-free characterisations of higher order Sobolev and BV spaces. An alternative formulation of a non-local Hessian functional is also introduced which is able to produce piecewise affine reconstructions in image denoising, outperforming TGV.

6

Rizik, Vivian. "Analysis of an elasto-visco-plastic model describing dislocation dynamics." Thesis, Compiègne, 2019. http://www.theses.fr/2019COMP2505.

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Dans cette thèse on s'intéresse à l'analyse théorique et numérique de la dynamique des densités des dislocations, où les dislocations sont des défauts cristallins, apparaissant à l'échelle microscopique dans les alliages métalliques. En particulier, on considère en premier temps l'étude du modèle de Groma-Czikor-Zaiser (GCZ) et en second temps l'étude du modèle de Groma-Balog (GZ). Il s'agit en réalité d'un système d'équations de type paraboliques et de type Hamilton-Jacobi non-linéaires. Au départ, nous démontrons un résultat d'existence et d'unicité d'une solution régulière en utilisant le principe de comparaison et un argument de point fixe pour concernant le modèle GCZ. Ensuite, nous démontrons un résultat d'existence global en temps pour le modèle de GB, en se basant sur les notions des solutions de viscosités discontinues et sur une nouvelle estimation sur la variation totale de la solution, ainsi que sur la propagation à vitesse finie des équations régissantes. Ce résultat est étendu aussi au cas des systèmes d'équations d'Hamilton-Jacobi général. Enfin, nous proposons un schéma numérique semi-explicite permettant la discrétisation du modèle de GB. Nous montons, en s'appuyant sur l'étude théorique, que la solution discrète convergent vers la solution continue, ainsi qu'une estimation d'erreur entre la solution continue et la solution numérique. Des simulations montrant la robustesse du schème numériques sont également présentées
In this thesis, we are interested in the theoretical and numerical analysis o the dynamics of dislocation densities, where dislocations are crystalline defects appearing at the microscopic scale in metallic alloys. Particularly, the study of the Groma-Czikor-Zaiser model (GCZ) and the study of the Groma-Balog model (GB) are considered. The first is actually a system of parabolic type equations, where as, the second is a system of non-linear Hamilton-Jacobi equations. Initially, we demonstrate an existence and uniqueness result of a regular solution using a comparison principle and a fixed point argument for the GCZ model. Next, we establish a time-based global existence result for the GB model, based on notions of discontinuous viscosity solutions and a new estimate of total solution variation, as well as finite velocity propagation of the governed equations. This result is extended also to the cas of general Hamilton-Jacobi equation systems. Finally, we propose a semi-explicit numerical scheme allowing the discretization of the GB model. Based on the theoretical study, we prove that the discrete solution converges toward the continuous solution, as well as an estimate of error between the continuous solution and the numerical solution has been established. Simulations showing the robustness of the numerical scheme are also presented

Книги з теми "BV solutions":

1

Dennis, Faber, Verhoeven Frédéric, and Vermunt Niels. Part III Europe, 12 The Use of a Composition Plan as a Valuation and Distribution Framework. Oxford University Press, 2017. http://dx.doi.org/10.1093/law/9780198755371.003.0012.

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The commencement of chapter 11 proceedings in respect of Lehman Brothers Holdings Inc (LBHI) triggered the downfall of its intricate web of group companies around the world. The Dutch incorporated second-tier subsidiary Lehman Brothers Treasury Co BV (LBT) was declared bankrupt on 8 October 2008 – the largest bankruptcy case in Dutch history and unprecedented in Dutch insolvency practice. Various new features were tested (and approved by the court) in the LBT proceedings which could provide important lessons for future large insolvency cases of issuers of debt securities on the international capital markets. Despite the fact that the Dutch Bankruptcy Code dates back more than a century ago and was not designed for several complex issues which arose in the LBT proceedings, the chapter argues, it did facilitate a tailored made solution for an effective and transparent settlement of the affairs of the main treasury entity of the Lehman Brothers group.

Частини книг з теми "BV solutions":

1

Bianchini, Stefano. "BV Solutions of Semidiscrete Upwind Scheme." In Hyperbolic Problems: Theory, Numerics, Applications, 135–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55711-8_11.

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2

Dafermos, Constantine M. "BV Solutions for Systems of Balance Laws." In Grundlehren der mathematischen Wissenschaften, 585–622. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-49451-6_16.

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3

Bressan, Alberto. "BV Solutions to Hyperbolic Systems by Vanishing Viscosity." In Lecture Notes in Mathematics, 1–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-72187-1_1.

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4

Dafermos, Constantine M. "Construction of BV Solutions by the Vanishing Viscosity Method." In Grundlehren der mathematischen Wissenschaften, 557–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-49451-6_15.

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5

Dafermos, Constantine M. "Construction of BV Solutions by the Vanishing Viscosity Method." In Grundlehren der mathematischen Wissenschaften, 517–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04048-1_15.

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6

Kosiński, Witold. "On the Concept of Weak Solutions in the BV-Space." In Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications, 320–28. Wiesbaden: Vieweg+Teubner Verlag, 1989. http://dx.doi.org/10.1007/978-3-322-87869-4_33.

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7

Nakayasu, Atsushi, and Piotr Rybka. "Energy Solutions to One-Dimensional Singular Parabolic Problems with $${ BV}$$ Data are Viscosity Solutions." In Springer Proceedings in Mathematics & Statistics, 195–213. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66764-5_9.

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8

Wright, S. F., and S. K. Zeto. "Effects of pH and Al3+ activity on survival of Rhizobium leguminosarum bv. trifolii in a simple solution and on nodulation of red clover in acid soils." In Plant-Soil Interactions at Low pH, 603–9. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3438-5_68.

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9

"BV. Three-dimensional axial symmetry." In Analytical Solutions of Geohydrological Problems, 353–421. Elsevier, 1999. http://dx.doi.org/10.1016/s0167-5648(99)80011-2.

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10

Colombo, Rinaldo M. "BV Solutions to Hyperbolic Conservation Laws." In Series in Contemporary Applied Mathematics, 87–159. WSPC/HEP, 2019. http://dx.doi.org/10.1142/9789813276185_0002.

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Тези доповідей конференцій з теми "BV solutions":

1

Schindler, Sebastian. "Comparison of Design by Analysis Methods." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-94028.

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The paper discusses the advantages and disadvantages of the two well known Design by Analysis methods for unfired pressure vessels: the stress categorisation method (as given e.g. in the 2004 ASME B&BV Code Section VIII Division 2 [1], and EN 13445-3 Annex C [2]) and the new Direct Route (using elastic-plastic finite-element analysis) as given in EN 13445-3 Annex B [2]. A comparison of results is given for examples of various degree of difficulty to show the principal ideas and the applicability of the two approaches: a dished end with a nozzle in the knuckle region, a cylindrical shell to flat end connection and a rather complex header of an air cooler with rectangular cross section. As shown by the considered examples, the Direct Route method gives unique solutions (which is not always the case for stress categorisation) and can be advantageous in some cases, but requires a more time consuming analysis. The questionable design limits given by the 3f-criterion of the stress categorisation method can be avoided by usage of the progressive plastic deformation design check of the Direct Route if the required number of action cycles is low.

2

Haywood, Alan, Andrew Ricks, Bruno Bouckaert, and Julian Hofman. "Dynamic Hull Vane – A Solution for active Pitch Motion Reduction and Resistance Reduction of ships." In SNAME International Conference on Fast Sea Transportation. SNAME, 2021. http://dx.doi.org/10.5957/fast-2021-002.

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The Dynamic Hull Vane® is an actively controlled version of the Hull Vane®, a patented energy-saving and seakeeping device which consists of a submerged wing mounted on the aft ship. The Hull Vane is positioned in the upward flow aft of the ship, to develop forward thrust and reduce the stern wave. Naiad Dynamics US Inc, is a supplier of ride control systems and has worked with Hull Vane BV to develop the Dynamic Hull Vane®. By enabling the Hull Vane® to rotate, it can produce variable lift forces which when suitably controlled can reduce the pitching motions of a vessel in a seaway. This paper describes some of the research carried out on the AMECRC series 13, a generic fast displacement hull.

3

Moon, Jei-Kwon, Eil-Hee Lee, Chong-Hun Jung, and Byung-Chul Lee. "Separation of Technetium in Nitric Acid Solution With an Extractant Impregnated Resin." In 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/icone14-89797.

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An extractant impregnated resin (EIR) was prepared by impregnation of Aliquat 336 into Amberlite XAD-4 for separation of technetium from rhodium in nitric acid solution. The prepared EIR showed high preference for rhenium (chemical analogue of technetium) over rhodium. The adsorption isotherms for rhenium were described well by Langmuir equation in both the single and multi-component systems. Maximum adsorption capacities obtained by modelling the isotherms of rhenium were 2.01 meq g−1 and 1.97 meq g−1 for the single and the multi-component systems, respectively. Column tests were also performed to confirm the separation efficiency of rhenium using a jacketed glass column (φ11 × L 150). The EIR column showed successful separation of rhenium with the breakthrough volume of about 122 BV for the breakthrough concentration of 0.08. Also the breakthrough data were modelled successfully by assuming a homogeneous diffusion model in the particle phase. The diffusivities obtained from the modelling were in the order of 10−7 cm2 min−1 for a rhenium. The rhenium adsorbed on the bed could be eluted with a high purity by using a nitric acid solution.