Syftet med denna uppsats är att utreda vad förutsättningarna för återbetalning vid misstagsbetalning är. Med andra ord vill jag utreda under vilka förhållanden en rätt till återbetalning föreligger och under vilka förhållanden en sådan misstagsbetalning skall vara bestående.

Displacement Green's function is the building block for some semi-analytical methods like Boundary Element Method (BEM), Distributed Point Source Method (DPCM), etc. In this thesis, the displacement Green`s function in anisotropic media due to a time harmonic point force is studied. Unlike the isotropic media, the Green's function in anisotropic media does not have a closed form solution. The dynamic Green's function for an anisotropic medium can be written as a summation of singular and non-singular or regular parts. The singular part, being similar to the result of static Green's function, is in the form of an integral over an oblique circular path in 3D. This integral can be evaluated either by a numerical integration technique or can be converted to a summation of algebraic terms via the calculus of residue. The other part, which is the regular part, is in the form of an integral over the surface of a unit sphere. This integral needs to be evaluated numerically and its evaluation is considerably more time consuming than the singular part. Obtaining dynamic Green's function and its spatial derivatives involves calculation of these two types of integrals. The spatial derivatives of Green's function are important in calculating quantities like stress and stain tensors. The contribution of this thesis can be divided into two parts. In the first part, different integration techniques including Gauss Quadrature, Simpson's, Chebyshev, and Lebedev integration techniques are tried out and compared for evaluation of dynamic Green’s function. In addition the solution from the residue theorem is included for the singular part. The accuracy and performance of numerical implementation is studied in detail via different numerical examples. Convergence plots are used to analyze the numerical error for both Green's function and its derivatives. The second part of contribution of this thesis relates to the mathematical derivations. As mentioned above, the regular part of dynamic Green's function, being an integral over the surface of a unit sphere, is responsible for the majority of computational time. From symmetry properties, this integration domain can be reduced to a hemisphere, but no more simplification seems to be possible for a general anisotropic medium. In this thesis, the integration domain for regular part is further reduced to a quarter of a sphere for the particular case of transversely isotropic material. This reduction proposed for the first time in this thesis nearly halves the number of integration points for the evaluation of regular part of dynamic Green's function. It significantly reduces the computational time.

La restauration de la République conduite par Octavien vit renaître l’activité législative, « florissante » selon les mots d’Ovide (Met., 2.141) « sous la conduite du très juste » Auguste (Met., 5.833). L’association entre Auguste et son oeuvre législative fut telle que parmi les honneurs funèbres, il fut proposé que le nom de chacune des lois figure sur des écriteaux du cortège funéraire. La lex accompagnait Auguste au tombeau. Ses successeurs abandonnèrent progressivement le recours à la lex et quelques décennies après la disparition d’Auguste, la loi recevait comme seule fonction de sanctionner les pouvoirs et honneurs décidés par le Sénat et conférés à l’empereur à chaque début de principat. Cette loi était la dernière traduction formelle de la volonté du populus Romanus : parce qu’elle émanait du peuple et qu’elle établissait un fondement entre le prince et son statut, ses pouvoirs et les activités auxquelles elle donnait lieu, elle retint particulièrement l’attention des Prudents. S’ils constatèrent le bouleversement général des sources du droit que l’enracinement du prince dans l’édifice constitutionnel républicain et le développement de ses interventions normatives avaient entraînés, seule la partie des Prudents que le prince avait associée à l’exercice de sa justice et de sa production normative, amplifia la normativité des formes qu’empruntait la volonté impériale. La formulation de l’identité de la constitution impériale à la lex marqua l’avènement d’un ordre juridique dont la cohérence reposait sur le consensus, non plus des divers organes de la République mais de l’empereur et des Prudents. Le recours à l’autorité de la loi pour caractériser les constitutions impériales leur assurait, au-delà des mutations dont ils surent prendre la mesure, la continuité d’une activité qui s’originait dans les premiers temps de la civitas. / The restoration of the Republic led by Octavian marked a new start of legislative activity, said to be "flourishing" by Ovid (Met.,2.141), "under the leadership of the righteous" Augustus (Met.,2.141). As part of his funeral honours, Augustus being so closely related to his legislative work was made clear when it was suggested that the name of each law were to be inscribed on the banners for the funeral procession. The lex accompanied Augustus to his tomb. Little by little his successors no longer resorted to the lex and a few decades after Augustus decease, the unique function of the law was to acknowledge the powers and honours decided by the Senate and conferred to the Emperor at the beginning of his reign. That law was the last formal expression of the will of the populus Romanus: because it originated from the people and established the basis between the Prince and his status, his power and the activities that rose from it, it particularly caught the attention of the Prudentes. Though they may have noted the general disruption of the sources of the Law, resulting from the normative interventions of the emperor, it was only the part of jurisprudence that the prince had associated with his justice and therefore the production of norms,, that enhanced the normativity of the forms expressing the imperial will. The identity of the imperial constitution formed on the lex was the beginning of a new legal order, coherently based upon the consensus between the emperor and the Prudentes rather than upon the various organs of the Republic. Their resorting to the authority of the Law to characterize the imperial constitutions and their ability to assess change, ensured that an activity that started at the beginning of the civitas could continue.

Multisymplectic integrators like Preissman and six-point schemes and a semi-explicit symplectic method are applied to the coupled nonlinear Schr&ouml / dinger equations (CNLSE). Energy, momentum and additional conserved quantities are preserved by the multisymplectic integrators, which are shown using modified equations. The multisymplectic schemes are backward stable and non-dissipative. A semi-explicit method which is symplectic in the space variable and based on linear-nonlinear, even-odd splitting in time is derived. These methods are applied to the CNLSE with plane wave and soliton solutions for various combinations of the parameters of the equation. The numerical results confirm the excellent long time behavior of the conserved quantities and preservation of the shape of the soliton solutions in space and time.