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In this article, we will extend the method of balanced truncation using normalised right coprime factors of the system transfer matrix by Meyer (1990) [3] to balanced truncation with preservation of half line dissipativity. Special cases are preservation of positive realness and bounded realness. We consider a half line dissipative input-output system, with quadratic supply rate given by a nonsingular symmetric matrix Sigma with the property that its positive signature is equal to the number of input components of the system. The transfer matrix of such system allows a Sigma-normalised right coprime factorisation. We associate with such factorisation two Lyapunov equations, one of which is nonstandard, involving the indefinite matrix Sigma. Balancing will be based on making the unique solutions of these two Lyapunov equations equal and diagonal. The diagonal elements will be called the Hankel Sigma-singular values, because their squares are the nonzero eigenvalues of the composition of the 'graph' Hankel operator, multiplication by Sigma, and the adjoint graph Hankel operator. This method of balanced truncation will be shown to preserve stability, minimality, and half line dissipativeness. We will characterize the 'classical' positive real and bounded real characteristic values in terms of the new Hankel Sigma-singular values. Finally, we will derive one-step error bounds for the special case of balanced truncation of bounded real systems. (C) 2009 Elsevier B.V. All rights reserved

Black Holes from Branes: Various string theoretical constructions

In this dissertation we have studied black holes from various perspectives in string theory. One common theme of all the black holes that we have studied, is that they are constructed from branes. In part I we considered supersymmetry breaking Scherk-Schwarz duality twists and their effect on black holes in string theory. Our setup was type IIB string theory compactified on a four-torus and then further compactified on a circle with a duality twist along the circle. In these reductions we have studied several different brane configurations, the D1-D5-P system and dual configurations, that give rise to five-dimensional black holes in the standard untwisted reduction. Scherk-Schwarz reductions can be lifted to string theory so long as the monodromy is an element of the discrete U-duality group. We have worked out the quantization conditions that this requirement imposes on the twist parameters. Moreover, when the duality twist is a T-duality, the theory at the minimum of the potential can be described as an asymmetric orbifold. We have explicitly constructed this orbifold, and we have argued what conditions the survival of certain D-brane configurations puts on the orbifold. In part II we studied M2-branes and D2-branes wrapping Riemann surfaces with non-constant curvature: spindles and topological discs. These give rise to 4d black hole solutions in N=2 STU supergravity, whose near-horizon is a warped product of AdS2 with the Riemann surface. We have shown that the disc and spindle solutions can be obtained from different global completions of the same local solution, and we have analyzed their properties in detail. We have uplifted various truncations of this family of near-horizon solutions to M-theory and to massive type IIA. We found that some of these uplifts yield smooth solutions, while others yield solutions that have singularities associated to smeared branes or monopoles. In part III we have classified the necessary and sufficient conditions for near-horizon geometries of extremal supersymmetric rotating black holes in 11d supergravity, which are associated to rotating M2-branes. These near-horizon geometries contain an AdS2 factor which is fibered by the internal geometry. We have allowed for the most general fibration and flux configuration supporting rotating M2-branes. Due to the generality of our ansatz the black holes covered by our classification can include both electric and magnetic charges as well as angular momentum in 4d. By use of dualities, we have also presented necessary and sufficient conditions for the near-horizon geometry of a class of rotating black string solutions in type IIB. Finally, we have embedded several known 4d black hole solutions from the literature into our classification

Classification of supersymmetric black holes in AdS₅

In this thesis we provide a first systematic framework towards the classification of supersymmetric black holes in d = 5 gauged supergravity. We build our formalism by assuming different isometry groups of spacetimes: SU(2) and U(1)². The first part of this thesis is concerned with supersymmetric solutions to minimal gauged supergravity with SU(2) isometry. Our main result is the first uniqueness theorem for black holes with a cosmological constant in dimensions d > 3. The proof combines a delicate near-horizon analysis with a general form for a Kähler metric with cohomogeneity-1 SU(2) symmetry and makes no global assumptions on the spacetime. The rest of the thesis is dedicated to extensive study of supersymmetric solutions with U(1)² toric symmetry. This reduces to a problem in toric Kähler geometry. In the second part of my thesis we develop the symplectic approach to toric Kähler geometry, which allows us to classify near-horizon and axial structure of toric solutions, including multi-centre configurations and yet to be found black hole solutions with non-trivial topology. We introduce an important subclass of Kähler metrics, which contains all known supersymmetric solutions, and show that the known supersymmetric black hole is unique in this class. In the final part, we further generalise our black hole uniqueness theorem to a gauged supergravity coupled to a number of abelian vector multiplets

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

Light hyperweak new gauge bosons from kinetic mixing in string models

String theory is at the moment our best candidate for a unified quantum theory of gravity, aiming to reconcile all the known (and unknown) interactions with gravity as well as provide insights for currently mysterious phenomena that the Standard Model and the modern Cosmology are not able to explain. In fact, it is believed that most of the problems associated to the Standard Model can indeed be resolved in string theory. Supersymmetry is supposed to be an elegant solution to the Hierarchy problem (even though more and more stringent bounds in this direction are being placed by the fact that we have been unable to experimentally find supersymmetry yet), while all the axions that compactifications bring into play can be used to resolve the strong CP problem as well as provide good candidates for Dark Matter. Inflationary models can also be constructed in string theory, providing, then, the most diffused solution to the Horizon problem. This work, in particular, is formulated in type IIB string theory compactified on an orientifolded Calabi-Yau three-fold in LARGE Volume Scenario (LVS) and focuses on the stabilisation of all the moduli in play compatible with the construction of a hidden gauge sector whose gauge boson kinetically mixes to the visible sector U(1), acquiring a mass via a completely stringy process resulting in the St{\"u}ckelberg mechanism. The "compatibility" regards the fact that certain experimental bounds should be respected combined with recent data extrapolated by Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS) events at the Spallation Neutron Source at Oak Ridge National Laboratory. We are going to see that in this context we will be able to fix all the moduli as well as present a brane and fluxes set-up reproducing the correct mass and coupling of the hidden gauge boson. We also get a TeV scale supersymmetry, since the gravitino in this model will be of order O(TeV), with an uplifted vacuum to reproduce a de Sitter universe as well

Proceedings of the Third International Mobile Satellite Conference (IMSC 1993)

Satellite-based mobile communications systems provide voice and data communications to users over a vast geographic area. The users may communicate via mobile or hand-held terminals, which may also provide access to terrestrial cellular communications services. While the first and second International Mobile Satellite Conferences (IMSC) mostly concentrated on technical advances, this Third IMSC also focuses on the increasing worldwide commercial activities in Mobile Satellite Services. Because of the large service areas provided by such systems, it is important to consider political and regulatory issues in addition to technical and user requirements issues. Topics covered include: the direct broadcast of audio programming from satellites; spacecraft technology; regulatory and policy considerations; advanced system concepts and analysis; propagation; and user requirements and applications