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AdS(2) holographic dictionary
Mirjam Cvetič, Ioannis Papadimitriou, 2016, izvirni znanstveni članek

Opis: We construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well de fined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetries and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Comp ere, Song and Strominger [1], in agreement with the results of Castro and Song [2]. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS(2) x S-2 or conformally AdS(2) x S-2 solutions of the STU model in four dimensions, including non extremal black holes. The four dimensional solutions obtained by uplifting the running dilaton solutions coincide with the so called 'subtracted geometries', while those obtained from the uplift of the constant dilaton ones are new.
Ključne besede: 2D gravity, AdS-CFT correspondence, black holes, space-time symmetries
Objavljeno: 27.06.2017; Ogledov: 204; Prenosov: 78
.pdf Celotno besedilo (1,01 MB)
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On the solvability of second-order impulsive differential equations with antiperiodic boundary value conditions
Yepeng Xing, Valery Romanovski, 2008, izvirni znanstveni članek

Opis: We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
Ključne besede: second-order impulsive differential equations, antiperiodic boundary value conditions, Green's function
Objavljeno: 26.06.2017; Ogledov: 262; Prenosov: 70
.pdf Celotno besedilo (241,29 KB)
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Some basic difference equations of Schrodinger boundary value problems
Andreas Ruffing, Maria Meiler, Andrea Bruder, 2009, izvirni znanstveni članek

Opis: We consider special basic difference equations which are related to discretizations of Schrödinger equations on time scales with special symmetry properties, namely, so-called basic discrete grids. These grids are of an adaptive grid type. Solving the boundary value problem of suitable Schrödinger equations on these grids leads to completely new and unexpected analytic properties of the underlying function spaces. Some of them are presented in this work.
Ključne besede: differential equations, discretization, Schrödinger equations, value problems
Objavljeno: 26.06.2017; Ogledov: 140; Prenosov: 93
.pdf Celotno besedilo (278,92 KB)
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Oscillatory difference equations and moment problems
José M. Ferreira, Sandra Pinelas, Andreas Ruffing, 2014, izvirni znanstveni članek

Opis: In this paper, we first consider some new oscillatory results with respect to the discrete Hermite polynomials of type I, respectively, type II and the Heim-Lorek polynomials. In the second part, we investigate the oscillatory and boundedness properties of the related orthogonality measures and the functions representing them. The polynomials considered so far in this article are closely related to the concept of theWess-Ruffing discretization.
Ključne besede: difference equations, Hermite polynomials, polynomials, discretization
Objavljeno: 26.06.2017; Ogledov: 151; Prenosov: 99
.pdf Celotno besedilo (331,56 KB)
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Difference-differential operators for basic adaptive discretizations and their central function systems
Lucia Birk, Sophia Roßkopf, Andreas Ruffing, 2012, izvirni znanstveni članek

Opis: The concept of inherited orthogonality is motivated and an optimality statement for it is derived. Basic adaptive discretizations are introduced. Various properties of difference operators which are directly related to basic adaptive discretizations are looked at. A Lie-algebraic concept for obtaining basic adaptive discretizations is explored. Some of the underlying moment problems of basic difference equations are investigated in greater detail.
Ključne besede: discretization, difference operator, Lie algebra, difference equations
Objavljeno: 26.06.2017; Ogledov: 132; Prenosov: 79
.pdf Celotno besedilo (408,24 KB)
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Comparing algebraic and numerical solutions of classical diffusion process equations in computational financial mathematics
Andreas Ruffing, Patrick Windpassinger, Stefan Panig, 2001, izvirni znanstveni članek

Opis: We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics.
Ključne besede: diffusion processes, diffusion equations
Objavljeno: 14.06.2017; Ogledov: 136; Prenosov: 84
.pdf Celotno besedilo (2,80 MB)
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Mirjam Cvetič, G. W. Gibbons, Christopher N. Pope, 2015, izvirni znanstveni članek

Opis: We present explicit solutions of the time-symmetric initial value constraints, expressed in terms of freely specifiable harmonic functions for examples of supergravity theories, which emerge as effective theories of compactified string theory. These results are a prerequisite for the study of the time-evolution of topologically non-trivial initial data for supergravity theories, thus generalising the "Geometrodynamics" program of Einstein-Maxwell theory to that of supergravity theories. Specifically, we focus on examples of multiple electric Maxwell and scalar fields, and analyse the initial data problem for the general Einstein-Maxwell-Dilaton theory both with one and two Maxwell fields, and the STU model. The solutions are given in terms of up to eight arbitrary harmonic functions in the STU model. As a by-product, in order compare our results with known static solutions, the metric in isotropic coordinates and all the sources of the non-extremal black holes are expressed entirely in terms of harmonic functions. We also comment on generalizations to time-nonsymmetric initial data and their relation to cosmological solutions of gauged so-called fake supergravities with positive cosmological constant.
Ključne besede: black holes, supergravity, string theory, conformal field models, string duality
Objavljeno: 14.06.2017; Ogledov: 202; Prenosov: 36
.pdf Celotno besedilo (581,40 KB)
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Entanglement entropy of subtracted geometry black holes
Mirjam Cvetič, Zain H. Saleem, Alejandro Satz, 2015, polemika, diskusijski prispevek, komentar

Opis: We compute the entanglement entropy of minimally coupled scalar fields on subtracted geometry black hole backgrounds, focusing on the logarithmic corrections. We notice that matching between the entanglement entropy of original black holes and their subtracted counterparts is only at the order of the area term. The logarithmic correction term is not only different but also, in general, changes sign in the subtracted case. We apply Harrison transformations to the original black holes and find out the choice of the Harrison parameters for which the logarithmic corrections vanish.
Ključne besede: black holes, string theory
Objavljeno: 14.06.2017; Ogledov: 160; Prenosov: 98
.pdf Celotno besedilo (378,41 KB)
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General U(1) x U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure
Mirjam Cvetič, Denis Klevers, Hernan Piragua, Washington Taylor, 2015, izvirni znanstveni članek

Opis: We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1) x U(1) gauge symmetry. Generic U(1) x U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2) x SU(2) x SU(3), SU(2)(3) x SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. The construction suggests a generalization to U(1)(k) factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.
Ključne besede: F-theory, differential geometry, algebraic geometry, gauge symmetry
Objavljeno: 14.06.2017; Ogledov: 213; Prenosov: 91
.pdf Celotno besedilo (1,36 MB)
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Application of Mawhin’s coincidence degree and matrix spectral theory to a delayed system
Yong-Hui Xia, Xiang Gu, Patricia Wong J. Y., Syed Abbas, 2012, izvirni znanstveni članek

Opis: This paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model with M-predators and N-preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability of the periodic solution. The existence and stability conditions are given in terms of spectral radius of explicit matrices which are much different from the conditions given by the algebraic inequalities. Finally, an example is given to show the feasibility of our results.
Ključne besede: coincidence degree, Jean Mawhin, predator-prey model, spectral theory
Objavljeno: 12.06.2017; Ogledov: 333; Prenosov: 39
.pdf Celotno besedilo (2,05 MB)

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