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Arxiv.org
by Burchard Kaup; Hans-Jörg Reiffen
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The leaves in singular holomorphic foliation theory are examples of quasi-analytic layers. In the first part of our publication we are concerned with a theory of these subjects. A quasi-analytic decomposition of a complex manifold is a decomposition into pairwise disjoint connected quasi-analytic layers. These are holomorphic foliations in the sense of P. Stefan and K. Spallek. A very different but more usual conception of holomorphic foliations is develloped by P. Baum and R. Bott. It is based...
Source: http://arxiv.org/abs/0808.3893v1
Arxiv.org
by V. P. Nair
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K\"ahler-Chern-Simons theory describes antiself-dual gauge fields on a four- dimensional K\"ahler manifold. The phase space is the space of gauge potentials, the symplectic reduction of which by the constraints of antiself-duality leads to the moduli space of antiself-dula instantons. We outline the theory highlighting the symmetries, their canonical realization and some properties of the quantum wave functions. The relationship to integrable systems via dimensional reduction is...
Source: http://arxiv.org/abs/hep-th/9110042v1
Arxiv.org
by K. S. Virbhadra; George F. R. Ellis
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We study strong gravitational lensing due to a Schwarzschild black hole. Apart from the primary and the secondary images we find a sequence of images on both sides of the optic axis; we call them {\em relativistic images}. These images are formed due to large bending of light near r = 3M (the closest distance of approach r_o is greater than 3M). The sources of the entire universe are mapped in the vicinity of the black hole by these images. For the case of the Galactic supermassive ``black...
Source: http://arxiv.org/abs/astro-ph/9904193v2
Arxiv.org
by Mariusz P. Dabrowski; Arne. L. Larsen
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The null string equations of motion and constraints in the Schwarzschild spacetime are given. The solutions are those of the null geodesics of General Relativity appended by a null string constraint in which the "constants of motion" depend on the world-sheet spatial coordinate. Because of the extended nature of a string, the physical interpretation of the solutions is completely different from the point particle case. In particular, a null string is generally not propagating in a...
Source: http://arxiv.org/abs/hep-th/9610243v1
Arxiv.org
by Abid H. Mujtaba
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It is known that every compact simple Lie group admits a bi-invariant homogeneous Einstein metric. In this paper we use two ansatz to probe the existence of additional inequivalent Einstein metrics on the Lie group SU (n) for arbitrary n. We provide an explicit construction of (2k+1) inequivalent Einstein metrics on SU (2k) and 2k inequivalent Einstein metrics on SU (2k + 1).
Source: http://arxiv.org/abs/1110.1978v1
Arxiv.org
by O. Mendoza; E. C. Saenz; V. Santiago; M. J. Souto Salorio
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We show that the relative Auslander-Buchweitz context on a triangulated category $\T$ coincides with the notion of co-$t$-structure on certain triangulated subcategory of $\T$ (see Theorem \ref{M2}). In the Krull-Schmidt case, we stablish a bijective correspondence between co-$t$-structures and cosuspended, precovering subcategories (see Theorem \ref{correspond}). We also give a characterization of bounded co-$t$-structures in terms of relative homological algebra. The relationship between...
Source: http://arxiv.org/abs/1002.4604v3
Arxiv.org
by Ruediger Lunde; Claus-Peter Wirth
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Maintaining the main aspects of the algebraic specification language ASF as presented in [Bergstra&al.89] we have extend ASF with the following concepts: While once exported names in ASF must stay visible up to the top the module hierarchy, ASF+ permits a more sophisticated hiding of signature names. The erroneous merging of distinct structures that occurs when importing different actualizations of the same parameterized module in ASF is avoided in ASF+ by a more adequate form of parameter...
Source: http://arxiv.org/abs/0902.2995v1
Arxiv.org
by Lorenzo Cornalba; Miguel S. Costa; Joao Penedones
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It is well known that spherical D-branes are nucleated in the presence of an external RR electric field. Using the description of D-branes as solitons of the tachyon field on non-BPS D-branes, we show that the brane nucleation process can be seen as the decay of the tachyon false vacuum. This process can describe the decay of flux-branes in string theory or the decay of quintessence potentials arising in flux compactifications.
Source: http://arxiv.org/abs/hep-th/0501151v1
Arxiv.org
by Ding Wang; R. B. Zhang; Xiao Zhang
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A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $\Lambda$ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The metrics and curvatures of the quantum Schwarzschild spacetime and the quantum Schwarzschild-de Sitter spacetime are computed. It is shown that up to the second order in the deformation parameter, the quantum spacetimes are solutions of a noncommutative Einstein...
Source: http://arxiv.org/abs/0809.0614v2
Arxiv.org
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For G=SL_n or GL_n we construct representations V such that the invariant ring K[V]^G is not Cohen-Macaulay.
Source: http://arxiv.org/abs/0711.2737v1
Arxiv.org
by A. G. Agnese; M. La Camera
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We introduce the concept of "quasi-universe" and describe the Einstein-Rosen bridge as an extreme wormhole connecting two quasi-universes.
Source: http://arxiv.org/abs/astro-ph/0110373v1
Arxiv.org
by H. O. Girotti; M. Gomes; V. O. Rivelles; A. J. da Silva
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The continuous extension of the discrete duality symmetry of the Schwarz-Sen model is studied. The corresponding infinitesimal generator $Q$ turns out to be local, gauge invariant and metric independent. Furthermore, $Q$ commutes with all the conformal group generators. We also show that $Q$ is equivalent to the non---local duality transformation generator found in the Hamiltonian formulation of Maxwell theory. We next consider the Batalin--Fradkin-Vilkovisky formalism for the Maxwell theory...
Source: http://arxiv.org/abs/hep-th/9702065v2
Arxiv.org
by Andreas Doering
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The Kochen-Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models. In this paper, we first offer a new, non-combinatorial proof for quantum systems with a type $I_{n}$ factor as algebra of observables, including $I_{\infty}$. Afterwards, we give a proof of the Kochen-Specker theorem for an arbitrary von Neumann algebra $\mathcal{R}$ without...
Source: http://arxiv.org/abs/quant-ph/0408106v1
Arxiv.org
by M. Merkl; F. E. Zimmer; G. Juzeliunas; P. Öhberg
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Ultra-cold atoms which are subject to ultra-relativistic dynamics are investigated. By using optically induced gauge potentials we show that the dynamics of the atoms is governed by a Dirac type equation. To illustrate this we study the trembling motion of the centre of mass for an effective two level system, historically called Zitterbewegung. Its origin is described in detail, where in particular the role of the finite width of the atomic wave packets is seen to induce a damping of both the...
Source: http://arxiv.org/abs/0803.4189v2
Arxiv.org
by Craig Citro; Alexandru Ghitza
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We describe an algorithm for enumerating the set of level 1 systems of Hecke eigenvalues arising from modular forms (mod p).
Source: http://arxiv.org/abs/1102.3321v2
Arxiv.org
by Wolfram Koepf
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Ich m\"ochte in diesem Bericht algorithmische Methoden vorstellen, die im wesentlichen in diesem Jahrzehnt Einzug in die Computeralgebra gefunden haben. Die haupts\"achlichen Ideen gehen auf Stanley \cite{Sta} und Zeilberger \cite{Zei1}--\cite{Zei4} zur\"uck, vgl.\ die Beschreibung \cite{Strehl1}, und haben ihre Wurzeln teilweise bereits im letzten Jahrhundert (siehe z.\ B.\ \cite{Beke1}--\cite{Beke2}), gerieten aber auf Grund der Komplexit\"at der auftretenden Algorithmen...
Source: http://arxiv.org/abs/math/9412226v1
Arxiv.org
by M. Friedland; G. K. Sankaran
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We calculate Tits buildings for certain arithmetic subgroups of Sp(4). These give information about the boundary of the corresponding moduli spaces of abelian surfaces. More pictures (in colour) and a summary of the results (in English) can be found at http://www.bath.ac.uk/~masgks/Buildings/
Source: http://arxiv.org/abs/math/0002249v2
Arxiv.org
by Yang Han
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In 1989 Happel conjectured that for a finite-dimensional algebra $A$ over an algebraically closed field $k$, $\gl A < \infty$ if and only if $\hch A < \infty$. Recently Buchweitz-Green-Madsen-Solberg gave a counterexample to Happel's conjecture. They found a family of pathological algebra $A_q$ for which $\gl A_q = \infty$ but $\hch A_q=2$. These algebras are pathological in many aspects, however their Hochschild homology behaviors are not pathological any more, indeed one has $\hh A_q =...
Source: http://arxiv.org/abs/math/0408402v1
Arxiv.org
by Ansgar Schneider
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We show that the $C^*$-algebraic approach to T-duality of Mathai and Rosenberg is equivalent to the topological approach of Bunke and Schick.
Source: http://arxiv.org/abs/0712.0260v1
Arxiv.org
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When de Sitter first introduced his celebrated spacetime, he claimed, following Schwarzschild, that its spatial sections have the topology of the real projective space RP^3 (that is, the topology of the group manifold SO(3)) rather than, as is almost universally assumed today, that of the sphere S^3. (In modern language, Schwarzschild was disturbed by the non-local correlations enforced by S^3 geometry.) Thus, what we today call "de Sitter space" would not have been accepted as such...
Source: http://arxiv.org/abs/hep-th/0308022v3
Arxiv.org
by Wolfgang Steimle
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This work treats on the question whether a given map f: M -> B of smooth closed manifolds is homotopic to a smooth fiber bundle. We define a first obstruction in H^1(B;Wh(\pi_1(E))) and, provided that this obstruction vanishes and one additional condition is verified, a second obstruction in Wh(\pi_1(E)) >. Both elements vanish if the answer to the above question is positive. In the case where B is the 1-sphere and the dimension of M exceeds five, we show that the converse is also true,...
Source: http://arxiv.org/abs/0706.3973v1
Arxiv.org
by Paweł Duch; Ryszard Paweł Kostecki
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Using new approach to construction of space-times emerging from quantum information theory, we identify the space of quantum states that generates the Schwarzschild space-time. No quantisation procedure is used. The emergent space-time is obtained by the Poincar\'{e}-Wick rotation and Fronsdal embedding of certain submanifold of the riemanian manifold of six-dimensional strictly positive matrices with the Bogolyubov-Kubo-Mori metric.
Source: http://arxiv.org/abs/1110.6566v3
Arxiv.org
by Uchida Gen; Tetsuya Shiromizu
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It is shown that if an asymptotically flat spacetime is asymptotically stationary, in the sense that $\Lie_{\xi} g_{ab}$ vanishes at the rate $\sim t^{-3}$ for asymptotically timelike vector field $\xi^a$, and the energy-momentum tensor vanishes at the rate $\sim t^{-4}$, then the spacetime is an asymptotically Schwarzschild spacetime. This gives a new aspect of the uniqueness theorem of a black hole.
Source: http://arxiv.org/abs/gr-qc/9810040v1
Arxiv.org
by Peter Collas; David Klein
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We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.
Source: http://arxiv.org/abs/gr-qc/0603086v3
Arxiv.org
by Varghese Mathai; Danny Stevenson
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The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby generalizing some fundamental results of Connes and Hochschild-Kostant-Rosenberg. The Connes-Chern character is also...
Source: http://arxiv.org/abs/math/0404329v2
Arxiv.org
by Jose Luis Hernandez-Pastora; Jesus Martin; Eduardo Ruiz
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Global harmonic coordinates for the complete Schwarzschild metric are found for a more general case than that addressed in a previous work by Quan-Hui Liu. The supplementary constant that appears, in addition to the mass, is related to the stress quadrupole moment of a singular energy--momentum tensor. Similar calculations are also carried out in q--harmonic coordinates.
Source: http://arxiv.org/abs/gr-qc/0109031v3
Arxiv.org
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We give examples of Non-Cohen-Macaulay invariant rings.
Source: http://arxiv.org/abs/0711.2738v1
Arxiv.org
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Gravity with incorporation of additional dimensions and noncommutative geometry.
Source: http://arxiv.org/abs/0803.2308v1
Arxiv.org
by Shao-shiung Lin; Shi-shyr Roan
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We investigate Bethe Ansatz equations for the one-dimensional spin-$\frac{1}{2}$ Heisenberg XXX chain with a special interest in a finite system. Solutions for the two-particle sector are obtained. The ground state in antiferromagnetic case has been analytically studied through the logarithmic form of Bethe Ansatz equations.
Source: http://arxiv.org/abs/cond-mat/9509183v1
Arxiv.org
by Holger Brenner
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We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.
Source: http://arxiv.org/abs/math/0302235v1
Arxiv.org
by Patrizia Berti; Irene Crimaldi; Luca Pratelli; Pietro Rigo
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Let (X_n) be a sequence of random variables (with values in a separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well. Key words and phrases: Anscombe theorem, Exchangeability, Random indices, Random sums, Stable convergence
Source: http://arxiv.org/abs/1209.6473v1
Arxiv.org
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Schwarzschild's solution of Einstein's field equations in vacuum can be written in many different forms. Unfortunately Schwarzschild's own original form is less nice looking and simple than that latter derived by Droste and Hilbert. We prove here that we can have both: a nice looking simple form and the meaning that Schwarzschild wanted to give to his solution, i.e., that of describing the gravitational field of a massive point particle.
Source: http://arxiv.org/abs/0709.2257v2
Arxiv.org
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Let k be a global field, p an odd prime number different from char(k) and S, T disjoint, finite sets of primes of k. Let G_S^T(k)(p)=Gal(k_S^T(p)|k) be the Galois group of the maximal p-extension of k which is unramified outside S and completely split at T. We prove the existence of a finite set of primes S_0, which can be chosen disjoint from any given set M of Dirichlet density zero, such that the cohomology of G_{S\cup S_0}^T(k)(p) coincides with the etale cohomology of the associated marked...
Source: http://arxiv.org/abs/0806.0772v3
Arxiv.org
by A. G. Agnese; M. La Camera
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The exterior and interior Schwarzschild solutions are rewritten replacing the usual radial variable with an angular one. This allows to obtain some results otherwise less apparent or even hidden in other coordinate systems.
Source: http://arxiv.org/abs/gr-qc/0007041v1
Arxiv.org
by Tobias Brandes; Jun'ichi Inoue; Akira Shimizu
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We present theoretical results for superradiance, i.e. the collective coherent decay of a radiating system, in a semiconductor heterostructure under a strong quantizing magnetic field. We predict a strong peak (`Dicke-peak') in the emission intensity as a function of time, which should be observable after a short initial excitation of electrons into the conduction band. This peak has a characteristic dependence on the magnetic field and should be observable on sub-picosecond time scales....
Source: http://arxiv.org/abs/cond-mat/9908448v1
Arxiv.org
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In my diploma thesis I calculate a lower mass bound of the lightest nutralino assuming an additional supernova cooling mechanism. I consider elektron-positron annihilation and nucleon-nucleon bremsstrahlung as cooling processes. These cooling processes must not be too effective because they would destroy the neutrino signal (SN 1987a). From this requirement I derive an upper bound for the emitted energy and as a consequence I get a lower bound for the mass of the lightest neutralino.
Source: http://arxiv.org/abs/hep-ph/0407341v1
Arxiv.org
by Thomas P. Kling; Ezra T. Newman
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Light cones of Schwarzschild geometry are studied in connection to the Null Surface Formulation and gravitational lensing. The paper studies the light cone cut function's singularity structure, gives exact gravitational lensing equations, and shows that the "pseudo-Minkowski" coordinates are well defined within the model considered.
Source: http://arxiv.org/abs/gr-qc/9809037v1
Arxiv.org
by C. A. Serino; K. F. Tiampo; W. Klein
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We introduce a new model for an earthquake fault system that is composed of non-interacting simple lattice models with different levels of damage denoted by $q$. The undamaged lattice models ($q=0$) have Gutenberg-Richter scaling with a cumulative exponent $\beta=1/2$, whereas the damaged models do not have well defined scaling. However, if we consider the "fault system" consisting of all models, damaged and undamaged, we get excellent scaling with the exponent depending on the...
Source: http://arxiv.org/abs/1012.1260v1
Arxiv.org
by Morteza Rahmani; Mohammad H. Faroughi
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In this paper we introduce the concept of Bochner pg-frames for Banach spaces. We characterize the Bochner pg-frames and specify the optimal bounds of a Bochner pg- frames. Then we define a Bochner qg-Riesz basis and verify the relations between Bochner pg-frames and Bochner qg-Riesz bases. Finally, we discuss the perturbation of Bochner pg-frames.
Source: http://arxiv.org/abs/1205.2323v1
Arxiv.org
by Denise Nakiboglu
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Looking at the cartesian product of a topological space with itself, a natural map to be considered on that object is the involution that interchanges the coordinates, i.e. that maps (x,y) to (y,x). The so-called halfsquaring construction, now also called "symmetric squaring construction", in Cech homology with Z/2-coefficients was introduced in [arXiv:0709.1774] as a map from the k-th Cech homology group of a space X to the 2k-th Cech homology group of X \times X divided by the above...
Source: http://arxiv.org/abs/1002.1449v1
Arxiv.org
by Thomas Scanlon
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Using the theory of o-minimality we show that the $p$-adic method of Skolem-Mahler-Lech-Chabauty may be adapted to prove instances of the dynamical Mordell-Lang conjecture for some real analytic dynamical systems. For example, we show that if $f_1,...,f_n$ is a finite sequence of real analytic functions $f_i:(-1,1) \to (-1,1)$ for which $f_i(0) = 0$ and $|f_i'(0)| \leq 1$ (possibly zero), $a = (a_1,...,a_n)$ is an $n$-tuple of real numbers close enough to the origin and $H(x_1,...,x_n)$ is a...
Source: http://arxiv.org/abs/1010.0482v1
Arxiv.org
by Martin Chuaqui
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Let $f$ be a Schwarz-Christoffel mapping of the disk $\D$ onto a polygon. In this paper, we prove that in the formula $f"/f'=(B_1/B_2)/(1-zB_1/B_2)$ obtained recently in [3], the degrees $d_1, d_2$ of the finite Blaschke products $B_1, B_2$ are equal, respectively, to the number of convex vertices minus 1, and the number of concave vertices. A similar result is obtained for the corresponding representation formula for mappings onto the exterior of polygons.
Source: http://arxiv.org/abs/1207.6143v1
Arxiv.org
by Jaemo Park; Soo-Jong Rey
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Green-Schwarz action of Type IIB string on $AdS_3 \times S^3$ is constructed via coset superspace approach. The construction relies exclusively on symplectically Majorana-Weyl spinor formalism, thus permitting it easier to prove $\kappa$-symmetry for on-shell Type IIB supergravity backgrounds.
Source: http://arxiv.org/abs/hep-th/9812062v1
Arxiv.org
by Hitoshi Shiraishi; Toshio Hayami
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Let $\mathcal{B}$ be the class of functions $w(z)$ of the form $w(z)=\sum\limits_{k=1}^{\infty}b_k z^k$ which are analytic and satisfy the condition $|w(z)|
Source: http://arxiv.org/abs/1302.6916v1
Arxiv.org
by Hiroyuki Abe; Yutaka Sakamura
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We reinterpret the Scherk-Schwarz (SS) boundary condition for SU(2)_R in a compactified five-dimensional (5D) Poincare supergravity in terms of the twisted SU(2)_U gauge fixing in 5D conformal supergravity. In such translation, only the compensator hypermultiplet is relevant to the SS twist, and various properties of the SS mechanism can be easily understood. Especially we show the equivalence between the SS twist and boundary constant superpotentials at the full supergravity level.
Source: http://arxiv.org/abs/hep-th/0610279v1
Arxiv.org
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The jet parton correlation has been studied for different cut scenarios and various jet algorithms. These migrations are getting important for measuring the strong coupling constant alpha_s and the NLO gluon density g(xi,Q^2) from jet rates in DIS at HERA.
Source: http://arxiv.org/abs/hep-ex/9709011v1
Arxiv.org
by S. Deser; G. W. Gibbons
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We present some obvious physical requirements on gravitational avatars of non-linear electrodynamics and illustrate them with explicit determinantal Born-Infeld-Einstein models. A related procedure, using compensating Weyl scalars, permits us to formulate conformally invariant versions of these systems as well.
Source: http://arxiv.org/abs/hep-th/9803049v1
Arxiv.org
by Anne V. Shepler; Sarah Witherspoon
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We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V)#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer subgroups, focusing on the infinite family of complex reflection groups G(r,p,n) to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give information about deformations of S(V)#G and, in particular, about graded Hecke algebras. We expand the...
Source: http://arxiv.org/abs/math/0603231v2
Arxiv.org
by Pavel Etingof; Wee Liang Gan; Victor Ginzburg
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We study a generalization of graded Hecke algebras introduced by Drinfeld in 1986, in which the role of a finite group G is played by a reductive algebraic group. This includes continuous generalizations of symplectic reflection algebras and of rational Cherednik algebras. We prove direct and converse PBW theorems, and also study versions of our algebras in which the group G is replaced with its Lie algebra. We also begin to develop the representation theory of continuous Hecke algebras, which...
Source: http://arxiv.org/abs/math/0501192v3
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by Jean-Louis Colliot-Th'el`ene
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Given a smooth, projective irreducible variety over the reals, various algebraic formulas have been given for the number of real connected components of the set of real points. In this note I compare a formula of E. Becker and D. Gondard (1995) with a formula I gave in 1978. I show how one may deduce one from the other by using a purity theorem of M. Rost (1990). ----- E. Becker und D. Gondard haben eine algebraische Formel fuer die Anzahl von Zusammenhangskomponenten des Raumes der reellen...
Source: http://arxiv.org/abs/math/0502538v1
Arxiv.org
by Reynier Peletier
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This is a summary of my lectures during the 2011 IAC Winter School in Puerto de la Cruz. I give an introduction to the field of stellar populations in galaxies, and highlight some new results. Since the title of the Winter School was {\it Secular Evolution of Galaxies} I mostly concentrate on nearby galaxies, which are best suited to study this theme. Of course, the understanding of stellar populations is intimately connected to understanding the formation and evolution of galaxies, one of the...
Source: http://arxiv.org/abs/1210.2127v1
Arxiv.org
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This is my diploma thesis in german language. In the context of formal deformation theorie of assoziative observables in classical field theory I consider the symmetric algebra S(V) on an arbitrary-dimensional R- or C-vectorspace V as a prototype of comprehensive observables algebras in quantum field theory. In this framework I calculate the Hochschild cohomologies of S(V) with values in S(V)-S(V)-bimodules M. In the case that V is a locally convex vectorspace I compute the continuous...
Source: http://arxiv.org/abs/1009.4365v2
Arxiv.org
by F. M. Paiva; A. F. F. Teixeira
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Motion of bodies and light rays are studied in the gravitational field of Schwarzschild. Several Doppler effects are described. ----- Movado de korpoj kaj lumo estas studitaj en gravita kampo de Schwarzschild. Pluraj Doppleraj efikoj estas priskribitaj.
Source: http://arxiv.org/abs/0912.1229v1
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by Ivan Marin
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We refine the infinitesimal Hecke algebra associated to a 2-reflection group into a $\Z/2\Z$-graded Lie algebra, as a first step towards a global understanding of a natural $\mathbbm{N}$-graded object. We provide an interpretation of this Lie algebra in terms of the image of the braid group into the Hecke algebra, in connection with unitary structures. This connection is particularly strong when $W$ is a Coxeter group, and when in addition we can use generalizations of Drinfeld's rational even...
Source: http://arxiv.org/abs/1212.1279v1
Arxiv.org
by Yungui Gong
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We studied the Einstein-Brans-Dicke cosmology in detail. The difference of the evolution of the universe is significant between Einstein-Brans-Dicke cosmology and standard big-bang model during the radiation-dominated era. The power-law evolution of the scale factor is fast enough to solve the cosmological puzzles and slow enough to avoid the graceful exit problem. However, the constraints from the satisfactory bubble distribution (beta^2>0.25) and the solar system observations (beta^2
Source: http://arxiv.org/abs/gr-qc/9809015v2
Arxiv.org
by Deepak Naidu; Sarah Witherspoon
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Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit connection to Hochschild cohomology. We compute the relevant part of Hochschild cohomology for actions of many reflection groups and we exploit computations from our paper with Shroff for diagonal actions. By combining our work with recent results of Levandovskyy...
Source: http://arxiv.org/abs/1111.5243v1
Arxiv.org
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The ground state energy of the Mueller functional of large (neutral) atoms of atomic number Z agrees with the quantum mechanical ground state energy up to order o(Z to the 5/3). ----- Die Grundzustandsenergie des Muellerfunktionals von grossen (neutralen) Atomen der Ordnungszahl Z stimmt mit der quantenmechanischen Grundzustandsenergie bis zur Ordnung o(Z hoch 5/3) ueberein.
Source: http://arxiv.org/abs/0811.2453v2
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Our conception of a generalized ergodic theory shall exceed the generality of general topology: In this first part of the generalized ergodic theory we investigate the logical constitution of the conception of attractors. We prepare a general theory of sensitivity of flows, which we intend to present in the second part of the generalized ergodic theory. As a result of this first part take the theorem 3.3 and the theorem 3.8: We show a very general ergodic theorem, however it concerns insensitve...
Source: http://arxiv.org/abs/0902.2818v4
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Periodenbereiche sind gewisse offene Unterraeume von verallgemeinerten Flaggenvarietaeten, welche durch Semistabilitaetsbedingungen beschrieben werden. In dem Fall eines endlichen Grundkoerpers bilden diese eine Zariski-offene Untervarietaet, im Fall eines lokalen Koerpers einen zulaessigen offenen Unterraum im Sinne der rigiden algebraischen Geometrie. In dieser Arbeit berechnen wir fuer den Fall eines endlichen Grundkoerpers die l-adische Kohomologie mit kompaktem Traeger dieser...
Source: http://arxiv.org/abs/math/9907098v1
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by E. N. Glass; J. P. Krisch
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Recently, Glass and Krisch have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid [1999 Class. Quantum Grav. vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was studied. The continuous solutions of classical diffusive transport are believed to describe the envelope of underlying fractal behavior. In this work we examine the classical picture at scales on which fractal behavior might be evident.
Source: http://arxiv.org/abs/gr-qc/0006020v1
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We comment on the paper [1] by Albert Einstein from 1918 to Willem De Sitter's solution [2] of the Einstein field equation from today's point of view. To this end, we start by describing the geometry of the De Sitter space-time and present its importance for the inflationary cosmological model.
Source: http://arxiv.org/abs/gr-qc/0506121v1
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by Bruce Margon; Eric W. Deutsch
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Four high-latitude slow variable stars have been noted by Meinunger (1972) as "nicht rote" ("not red") objects and thus curious. We have previously reported (Margon & Deutsch 1997) that one of these objects, CC Boo, is in fact a QSO. Here we present observations demonstrating that the remaining three are also highly variable active galactic nuclei. The most interesting object of the four is perhaps S 10765 (= NGP9 F324-0276706), which proves to be a resolved galaxy at...
Source: http://arxiv.org/abs/astro-ph/9810202v1
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Both the distribution of hydrogen and the rotation curve of the Milky Way indicate the existence of a ring of Cold Dark Matter in the galactic plane with a radius of 14 kiloparsecs around the galactic centre. Using a semianalytical model, the formation of such a structure by the accretion of dwarf galaxies is simulated. The formation of the ring can be explained by the infall of a single dwarf galaxy, as well as by the infall of several dwarf galaxies under the condition that the eccentricity...
Source: http://arxiv.org/abs/0810.5300v3
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by Dov Gabbay; Karl Schlechta
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We investigate several technical and conceptual questions. Our main subject is the investigation of independence as a ternary relation in the context of non-monotonic logic. In the context of probability, this investigation was started by W.Spohn et al., and then followed by J.Pearl. We look at products of function sets, and thus continue our own investigation of independence in non-monotonic logic. We show that a finite characterization of this relation in our context is impossible, and...
Source: http://arxiv.org/abs/1108.3033v6
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by Hubert Karl; Sebstian Karl
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It is well known that a fixed point iteration for solving a linear equation system converges if and only if the spectral radius of the iteration matrix is less than one. A method is presented which guarantees the Fixed Point, even if this condition is not ("spectral radius
Source: http://arxiv.org/abs/1301.2481v1
Let F be a rational quaternion algebra, and let k be an imaginary quadratic splitting field of F. If one extends F to a 2x2 matrix algebra over k, then every maximal order of F can be embedded into a maximal order of this extension. We show that all embedding maximal orders are isomorphic to each another, and that and how their isomorphism type (in relation to the 2x2 matrix algebra over the maximal order of k) depends only on the ramification behavior of F (theorem 6.2). This enables us to...
Source: http://arxiv.org/abs/1207.6460v1
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by F. M. Paiva; A. F. F. Teixeira
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Geodesic of simultaneity is a spacelike geodesic in which every pair of neighbour events are simultaneous ($g_{0\mu}\dd x^\mu=0$). These geodesics are studied in the exterior region of \Sch's metric.
Source: http://arxiv.org/abs/1006.4654v1
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The Exodus was causally connected to the eruption of Thera. The time of this geological event is determined by C14 dating as 1627-1600 BC. The chaos that followed this catastrophe led to upheavals which distorted the chronologies. Taking periods of foreign domination into account leads to an agreement between the chronologies of Egypt and Israel. ----- Der Exodus wurde durch den Ausbruch von Thera ermoeglicht, welcher als geologisches Ereignis durch C14 Datierungen auf die Zeit 1627-1600 BC...
Source: http://arxiv.org/abs/0909.1473v1
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by Gérard H. E. Duchamp; Christophe Tollu
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We describe the problem of Sweedler's duals for bialgebras as essentially characterizing the domain of the transpose of the multiplication. This domain is the set of what could be called ``representative linear forms'' which are the elements of the algebraic dual which are also representative on the multiplicative semigroup of the algebra. When the algebra is free, this notion is indeed equivalent to that of rational functions of automata theory. For the sake of applications, the range of...
Source: http://arxiv.org/abs/0712.0125v3
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by D. Wilczak; P. Zgliczyński
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We present a Lohner type algorithm for the computation of rigorous bounds for solutions of ordinary differential equations and its derivatives with respect to initial conditions up to arbitrary order. As an application we prove the existence of multiple invariant tori around some elliptic periodic orbits for the pendulum equation with periodic forcing and for Michelson system.
Source: http://arxiv.org/abs/0704.0720v1
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by Xiaolan Yu; Yinhuo Zhang
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Let $R$ be a Nichols algebra of Hecke type. In this paper, we show that if $R$ is Noetherian and of finite global dimension, then $R$ has a rigid dualizing complex. We then give a necessary and sufficient condition for $R$ to be a Calabi-Yau algebra.
Source: http://arxiv.org/abs/1212.4289v1
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by Alexandru Ghitza
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We show that the systems of Hecke eigenvalues occurring in the spaces of Siegel modular forms (mod p) of fixed dimension g, fixed level N, and varying weight, are the same as the systems occurring in the spaces of Siegel cusp forms with the same parameters and varying weight. In particular, in the case g=1, this says that the Hecke eigensystems (mod p) coming from classical modular forms are the same as those coming from cusp forms. The proof uses restriction to the superspecial locus. We also...
Source: http://arxiv.org/abs/math/0511728v2
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by Tony Rothman; George F. R. Ellis; Jeff Murugan
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Parallel transport of vectors in curved spacetimes generally results in a deficit angle between the directions of the initial and final vectors. We examine such holonomy in the Schwarzschild-Droste geometry and find a number of interesting features that are not widely known. For example, parallel transport around circular orbits results in a quantized band structure of holonomy invariance. We also examine radial holonomy and extend the analysis to spinors and to the Reissner-Nordstr\"om...
Source: http://arxiv.org/abs/gr-qc/0008070v4
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by S. Deser; J. Franklin
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We provide a simple derivation of the Schwarzschild solution in General Relativity, generalizing an early approach by Weyl, to include Birkhoff's theorem: constancy of the mass; its deeper, Hamiltonian, basis is also given. Our procedure is illustrated by a parallel derivation of the Coulomb field and constancy of electric charge, in electrodynamics.
Source: http://arxiv.org/abs/gr-qc/0408067v2
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In the first part of our generalized ergodic theory we introduced Cantor-systems, when we managed to prove the generalized ergodic theorem 3.3. The first component of a Cantor-system is a group of the flow and its second component is a set of sets covering the phase-space. Now we continue and we first come across the resistence of the term of metric sensitivity against further generalization. Finding a way of generalization of sensitivity, we understand, that generalized chaos can come out of...
Source: http://arxiv.org/abs/0904.1211v1
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by Steffen Krusch; Paul Sutcliffe
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We study the motion of vortices in the planar Ginzburg-Landau model with Schrodinger-Chern-Simons dynamics. We compare the moduli space approximation with the results of numerical simulations of the full field theory and find that there is agreement if the coupling constant is very close to the critical value separating Type I from Type II superconductors. However, there are significant qualitative differences even for modest deviations from the critically coupled regime. Radiation effects...
Source: http://arxiv.org/abs/cond-mat/0511053v2
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by Andreas Johann Raab
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If and only if each point of a set of the phase-space is in the topological hull of a trajectory running through any other point of this set, we call this set a quasiergodic set. But which are these so defined quasiergodic sets in the case of a given continuous dynamical system, which has piecewise differentiable trajectories in a finit-dimensional real phase-space, which is compact? Let its trajectories define a field of normed tangents, which is continuous in almost each point of the...
Source: http://arxiv.org/abs/0810.5099v8
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by Alessandro Ardizzoni; Gabriella Böhm; Claudia Menini
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Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions B\subseteq A by H, are studied. Assuming that a lifted canonical map is a split epimorphism of modules of the non-commutative base algebra of H, relative injectivity of the H-comodule algebra A is related to the Galois property of the extension B\subseteq A and also to the equivalence of the category of relative Hopf modules to the category of B-modules. This extends a classical theorem by H.-J. Schneider...
Source: http://arxiv.org/abs/math/0612633v2
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by X. X. Chen; G. Tian
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In our previous paper math.DG/0010008, we develop some new techniques in attacking the convergence problems for the K\"ahler Ricci flow. The one of main ideas is to find a set of new functionals on curvature tensors such that the Ricci flow is the gradient like flow of these functionals. We successfully find such functionals in case of Kaehler manifolds. On K\"ahler-Einstein manifold with positive scalar curvature, if the initial metric has positive bisectional curvature, we prove...
Source: http://arxiv.org/abs/math/0108179v2
We introduce the universal complex elliptic genus phi_ell as the ring homomorphism from the complex cobordism ring Omega^U to the polynomial ring C[A,B,C,D] associated to the characteristic power series Q(x)=x/f(x), where f is the solution of the differential equation (f'/f)'=S(f'/f), S(y) = (y+A/2)^4-B/4*(y+A/2)^2+4C*(y+A/2)+B^2/64-2D. Formally, phi_ell arises as the index of the Dolbeault operator of the loop space of a manifold. For manifolds with vanishing first Chern class, phi_ell becomes...
Source: http://arxiv.org/abs/math/0405232v1
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by Wu Zhong Chao
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In the No-Boundary Universe a primordial black hole is created from a constrained gravitational instanton. The black hole created is immersed in the de Sitter background with a positive cosmological constant. The constrained instanton is characterized not only by the external parameters, the mass parameter, charge and angular momentum, but also by one more internal parameter, the identification period in the imaginary time coordinate. Although the period has no effect on the black hole...
Source: http://arxiv.org/abs/gr-qc/9712066v1
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In this work we generalize some of the previously known adiabatic theorems to situations with non-unitary evolutions in Banach spaces. We prove adiabatic theorems with uniform gap condition (generalizing a theorem of Abou Salem), adiabatic theorems with non-uniform gap condition (generalizing a theorem of Kato) and qualitative as well as quantitative adiabatic theorems without gap condition (generalizing theorems of Avron and Elgart, and Teufel). Additionally, we give a generalized version of...
Source: http://arxiv.org/abs/1112.6338v1
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This master thesis discusses the Reissner-Nordstr\"om metric and the dirac equation in curved spaces in the pseudo-complex General Relativity (pc-GR) and reviews the original ansatz of pc-GR. It is written in German.
Source: http://arxiv.org/abs/1106.2653v1
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by J. P. Krisch; E. N. Glass
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We discuss Israel layers collapsing inward from rest at infinity along Schwarzschild-Lemaitre geodesics. The dynamics of the collapsing layer and its equation of state are developed. There is a general equation of state which is approximately polytropic in the limit of very low pressure. The equation of state establishes a new limit on the stress-density ratio.
Source: http://arxiv.org/abs/0710.4058v1
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by Wolfgang Soergel
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This is an attempt to model ambient space as a three-dimensional real affine space with a distinguished group of automorphisms containing the translations and acting freely and transitively on pairs consisting of a half-plane together with a half-line on its boundary. From there the existence of an invariant scalar product is deduced, which then also implies Pythagoras theorem in a quite precise form. This is in contrast to the usual procedure to model ambient space by asking for a...
Source: http://arxiv.org/abs/0806.4052v1
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by Alexander Zuevsky
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Using the second Drinfeld formulation of the quantized universal enveloping algebra $U_q(\widehat{sl_2})$ we introduce a family of its Heisenberg-type elements which are endowed with a deformed commutator and satisfy properties similar to generators of a Heisenberg subalgebra. Explicit expressions for new family of generators are found.
Source: http://arxiv.org/abs/0901.2335v1
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by A. V. Smilga
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The known calculations of the fermion condensate $ $ and the correlator $ $ have been interpreted in terms of {\em localized} instanton solutions minimizing the {\em effective} action. Their size is of order of massive photon Compton wavelength $\mu^{-1}$. At high temperature, these instantons become quasistatic and present the 2-dimensional analog of the `walls' found recently in 4-dimensional gauge theories. In spite of the static nature of these solutions, they should not be interpreted as...
Source: http://arxiv.org/abs/hep-th/9312110v1
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Let K be an algebraically closed field. For a graded K-Algebra R, we write cmdef R:=dim R -depth R. We show that for each reductive group G (over K) which is not linearly reductive, there exists a faithful G-module V such that cmdef K[\sum_i=1^k V]^G >= k-2 for all k. We will give such a V explicitly.
Source: http://arxiv.org/abs/0711.4730v1
Slowly convergent or divergent sequences and series occur abundantly in quantum physics and quantum chemistry. These convergence problems can be overcome with the help of nonlinear sequence transformations (Wynn's epsilon or rho algorithm, Brezinski's theta algorithm, Levin's transformation, etc.) as for instance described in E. J. Weniger, "Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series", Comput. Phys. Rep. Vol. 10, 189 -...
Source: http://arxiv.org/abs/math-ph/0306048v1
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by Kazuki Sasaki; Naoya Suzuki; Hiroki Saito
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Vortex shedding from an obstacle potential moving in a Bose-Einstein condensate is investigated. Long-lived alternately aligned vortex pairs are found to form in the wake, as for the von K\'arm\'an vortex street in classical viscous fluids. Various patterns of vortex shedding are systematically studied and the drag force on the obstacle is calculated. It is shown that the phenomenon can be observed in a trapped system.
Source: http://arxiv.org/abs/1002.2058v1
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by Eugenii Shustin; Zur Izhakian
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We suggest a version of Nullstellensatz over the tropical semiring, the real numbers equipped with operations of maximum and addition.
Source: http://arxiv.org/abs/math/0508413v2
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by L. Borsten; M. J. Duff; S. Ferrara; A. Marrani
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Freudenthal duality (F-duality) was originally introduced as a non-polynomial anti-involution acting on the electromagnetic charges carried by extremal black hole solutions in the broad class of supergravity theories with U-duality groups of type E7. In this context F-duality is a symmetry of the Bekenstein-Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions,...
Source: http://arxiv.org/abs/1212.3254v1
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The German motorway, or 'autobahn', is characterised by long traditions, meticulous state planning, historical misbalance between West and East Germany's transport networks, and highest increase in traffic in modern Europe, posing a need for expansion and/or restructuring. We attempt to evaluate the structure of autobahns using principles of intrinsic optimality of biological networks in experiments with slime mould of Physarum polycephalum. In laboratory experiments with living slime mould we...
Source: http://arxiv.org/abs/1209.3474v1
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A striking characteristic of non-Schwarzschild vacuum exteriors is that they contain not only the total gravitational mass of the source, but also an {\it arbitrary} constant. In this work, we show that the constants appearing in the "temporal Schwarzschild", "spatial Schwarzschild" and "Reissner-Nordstr{\"o}m-like" exteriors are not arbitrary but are completely determined by star's parameters, like the equation of state and the gravitational potential....
Source: http://arxiv.org/abs/0711.0998v1
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by L. Friess
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Let G be a finite planar connected graph without loops or multiple edges. All minimal circuits except atmost one - say C* - are triangles. Let k be the number of vertices of C*. There are at least 2**(k-3) colorings of the vertices of G with four colors, vertices connected by edges colored differently. These colorings are different on C*.
Source: http://arxiv.org/abs/math/0410319v1
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Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear recurrences tries to fill a gap in the literature by giving many extensive examples.
Source: http://arxiv.org/abs/0704.2481v2
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by Subir Ghosh
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A new model for anyon is proposed, which exhibits the classical analogue of the quantum phenomenon - Zitterbewegung. The model is derived from existing spinning particle model and retains the essential features of anyon in the non-relativistic limit.
Source: http://arxiv.org/abs/hep-th/9710200v1
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In this thesis we solve the coboundary equation $\delta c=d$ with bounds for cochains with values in a coherent subsheaf of some $\mathcal{O}^p_{\Omega}$, where $\Omega$ is a Stein manifold. In particular the existence of a finite set of global generators is not assumed. Our result applies therefore to the ideal sheaf $\mathcal{J}_V\subset \mathcal{O}_{\C^N}$ of germs of holomorphic functions vanishing on a closed analytic submanifold $V\subset\C^N$. Although we are mainly interested in the...
Source: http://arxiv.org/abs/math/0202263v1
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We show that the apparently periodic Charap-Duff Yang-Mills `instantons' in time-compactified Euclidean Schwarzschild space are actually time independent. For these solutions, the Yang-Mills potential is constant along the time direction (no barrier) and therefore, there is no tunneling. We also demonstrate that the solutions found to date are three dimensional monopoles and dyons. We conjecture that there are no time-dependent solutions in the Euclidean Schwarzschild background.
Source: http://arxiv.org/abs/hep-th/0201050v2
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by F. W. Bessel; Charles F. F. Karney; Rodney E. Deakin
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The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is a transcription of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825). The text follows the original; however the mathematical notation has been updated to conform to current conventions. Several errors have been corrected and the tables have been recomputed.]
Source: http://arxiv.org/abs/0908.1823v3