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Abstract: The behavior of the divergent part of the bulk AdS/CFT effective action is considered with respect to the special finite diffeomorphism transformations acting on the boundary as a Weyl transformation of the boundary metric. The resulting 1-cocycle of the Weyl group is in full agreement with the 1-cocycle of the Weyl group obtained from the cohomological consideration of the effective action of the corresponding CFT.
Iterative methods to solve linear equation systems are widely used in computational physics, engineering and many areas of applied mathematics. In recent works, performance improvements have been achieved based on modifications of several classes of iterative algorithms by various research communities driven by different perspectives and applications. This note presents a brief analysis of conventional and unifying perspectives by highlighting relations between several well-known iterative methods to solve linear equation systems and explicit Euler approximations of the associated parabolic regularized equations. Special cases of equivalence and general relations between different iterative methods such as Jacobi iterations, Richardson iterations, Steepest Descent and Quasi-Newton methods are shown and discussed. The results and discussion extend the conventional perspectives on these iterative methods and give way to intuitive physical interpretations and analogies. The accessibly presented relations give complementary educational insights and aim to inspire transdisciplinary developments of new iterative methods, solvers and preconditioners.
The light-cone Hamiltonian approach is applied to the super D2- brane, and the equivalent area-preserving and U(1) gauge-invariant effective Lagrangian, which is quadratic in the U(1) gauge field, is derived. The latter is recognised to be that of the three- dimensional U(1) gauge theory, interacting with matter supermultiplets, in a special external induced supergravity metric and the gravitino field, depending on matter fields. The duality between this theory and 11d supermembrane theory is demonstrated in the light-cone gauge.
Bei der Erprobung sicherheitsrelevanter Bauteile von Nutzfahrzeugen steht man vor der Aufgabe, die sehr vielfältige Belastung durch die Kunden abschätzen zu müssen und daraus ein Prüfprogramm für die Bauteile abzuleiten, das mehreren gegenläufigen Anforderungen gerecht werden muss: Das Programm muss scharf genug sein, damit bei erfolgreicher Prüfung ein Ausfall im Feld im Rahmen eines bestimmungsgemäßen Gebrauchs ausgeschlossen werden kann, es soll aber nicht zu einer Überdimensionierung der Bauteile führen, und es soll mit relativ wenigen Bauteilversuchen eine ausreichende Aussagesicherheit erreicht werden. Wegen der hohen Anforderungen bzgl. Sicherheit müssen bei der klassischen statistischen Vorgehensweise – Schätzen der Verteilung der Kundenbeanspruchung aus Messdaten, Schätzen der Verteilung der Bauteilfestigkeit aus Versuchsergebnissen und Ableiten einer Ausfallwahrscheinlichkeit – die Verteilungen in den extremen Rändern bekannt sein. Dazu reicht aber das Datenmaterial in der Regel bei weitem nicht aus. Bei der klassischen „empirischen“ Vorgehensweise werden Kennwerte der Beanspruchung und der Festigkeit verglichen und ein ausreichender Sicherheitsabstand gefordert. Das hier vorgeschlagene Verfahren kombiniert beide Methoden, setzt dabei die Möglichkeiten der statistischen Modellierung soweit aufgrund der Datenlage vertretbar ein und ergänzt die Ergebnisse durch empirisch begründete Sicherheitsfaktoren. Dabei werden bei der Lastfestlegung die im Versuch vorhandenen Möglichkeiten berücksichtigt. Hauptvorteile dieses Verfahrens sind a) die Transparenz bzgl. der mit statistischen Mitteln erreichbaren Aussagen und des Zusammenspiels zwischen Lastermittlung und Versuch und b) die Möglichkeit durch entsprechenden Aufwand bei Messungen und Erprobung die empirischen zugunsten der statistischen Anteile zu reduzieren.
Abstract: The self-duality of chiral p-forms was originally investigated by Pasti, Sorokin and Tonin in a manifestly Lorentz covariant action with non-polynomial auxiliary fields. The investigation was then extended to other chiral p-form actions. In this paper we point out that the self-duality appears in a wider context of theoretical models that relate to chiral p-forms. We demonstrate this by considering the interacting model of Floreanini- Jackiw chiral bosons and gauge fields, the generalized chiral Schwinger model (GCSM) and the latter's gauge invariant formulation, and discover that the self-duality of the GCSM corresponds to the vector and axial vector current duality.
Abstract: It has recently been shown that the equation of motion of a massless scalar field in the background of some specific p branes can be reduced to a modified Mathieu equation. In the following the absorption rate of the scalar by a D3 brane in ten dimensions is calculated in terms of modified Mathieu functions of the first kind, using standard Mathieu coefficients. The relation of the latter to Dougall coefficients (used by others) is investigated. The S-matrix obtained in terms of modified Mathieu functions of the first kind is easily evaluated if known rapidly convergent low energy expansions of these in terms of products of Bessel functions are used. Leading order terms, including the interesting logarithmic contributions, can be obtained analytically.
We consider a (2 + 1)-dimensional mechanical system with the Lagrangian linear in the torsion of a light-like curve. We give Hamiltonian formulation of this system and show that its mass and spin spectra are defined by one-dimensional nonrelativistic mechanics with a cubic potential. Consequently, this system possesses the properties typical of resonance-like particles.
Safety and reliability requirements on the one side and short development cycles, low costs and lightweight design on the other side are two competing aspects of truck engineering. For safety critical components essentially no failures can be tolerated within the target mileage of a truck. For other components the goals are to stay below certain predefined failure rates. Reducing weight or cost of structures often also reduces strength and reliability. The requirements on the strength, however, strongly depend on the loads in actual customer usage. Without sufficient knowledge of these loads one needs large safety factors, limiting possible weight or cost reduction potentials. There are a lot of different quantities influencing the loads acting on the vehicle in actual usage. These ‘influencing quantities’ are, for example, the road quality, the driver, traffic conditions, the mission (long haulage, distribution or construction site), and the geographic region. Thus there is a need for statistical methods to model the load distribution with all its variability, which in turn can be used for the derivation of testing specifications.