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Torsions of connections on tangent bundles of higher order

Kureš, Miroslav (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

The torsions of a general connection Γ on the r th-order tangent bundle of a manifold M are defined as the Frölicher-Nijenhuis bracket of Γ with the natural affinors. The author deduces the basic properties of these torsions. Then he compares them with the classical torsion of a principal connection on the r th-order frame bundle of M .

Transfer matrices and transport for Schrödinger operators

François Germinet, Alexander Kiselev, Serguei Tcheremchantsev (2004)

Annales de l’institut Fourier

We provide a general lower bound on the dynamics of one dimensional Schrödinger operators in terms of transfer matrices. In particular it yields a non trivial lower bound on the transport exponents as soon as the norm of transfer matrices does not grow faster than polynomially on a set of energies of full Lebesgue measure, and regardless of the nature of the spectrum. Applications to Hamiltonians with a) sparse, b) quasi-periodic, c) random decaying potential are provided....

Transfer of conditions for singular boundary value problems

Petr Přikryl, Jiří Taufer, Emil Vitásek (1989)

Aplikace matematiky

Numerical solution of linear boundary value problems for ordinary differential equations by the method of transfer of conditions consists in replacing the problem under consideration by a sequence of initial value problems. The method of transfer for systems of equations of the first order with Lebesque integrable coefficients was studied by one of the authors before. The purpose of this paper is to extend the idea of the transfer of conditions to singular boundary value problems for a linear second-order...

Tree algebras: An algebraic axiomatization of intertwining vertex operators

Igor Kříž, Yang Xiu (2012)

Archivum Mathematicum

We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a tree algebra. Using the Riemann-Hilbert correspondence, we further prove that a vertex tensor category in the sense of Huang and Lepowsky gives rise to a tree algebra over ℂ . We also show that the chiral WZW model of a simply connected simple compact Lie group gives rise to a tree algebra over ℚ .

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