Rigorous simulations of quantum tunneling dynamics in model systems with up to 20 coupled degrees of freedom are reported. The simulations implement an extension of the recently developed matching-pursuit/split-operator Fourier-transform method to complex-valued coherent-state representations. The resulting method recursively applies the time-evolution operator, as defined by the Trotter expans...

Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension G̃ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we focus our attention on the development of the theory of principal series representations for G̃ and its applications to the study of Hecke algebras via a Satake is...

Birkhoff (or lacunary) interpolation is an extension of polynomial interpolation that appears when observation gives irregular information about function and its derivatives. A Birkhoff interpolation problem is not always solvable even in the appropriate polynomial or rational space. In this paper we split up the initial problem in subproblems having a unique polynomial solution and use multino...

We study the existence of almost split sequences in tri-exact categories, that is, extension-closed subcategories triangulated categories. Our results unify and extend a number theorems for abelian categories exact (that categories), those triangles by numerous researchers. As applications, we obtain some new on derived all modules over an algebra with unity or locally finite dimensional given ...

A “Storage-Area Network” (SAN) comprises computers (“Initiators”), storage “block devices” (“Targets”), and a Controller(s). Most SANs use the SCSI protocol over various communication infrastructures. Presently, all Initiator Target traffic must pass through the Controller, severely limiting scalability. We extend the SCSI-3 Transport layer to support distribution, and combine this with SCSI's ...

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation o...

For Ω an infinite set, k ≥ 2 and W the set of k-sets from Ω, there is a natural closed permutation group Γk which is a non-split extension 0 → Z 2 → Γk → Sym(Ω) → 1. We classify the closed subgroups of Γk which project onto Sym(Ω). The question arises in model theory as a problem about finite covers, but here we formulate and solve it in algebraic terms.

We associate to every algebraic number field K/Q a hyperbolic surface lamination and an external fundamental group IΓK : a generalization of the fundamental germ construction of [3], [4] that necessarily contains external (not first order definable) elements. The external fundamental group IΓQ is a split extension of the absolute Galois group ÎΓQ, that conjecturally contains a subgroup whose ab...

Let G be the group of points of a split reductive group over a finite extension of Qp. In this paper, we compute the dimensions of certain classes of locally analytic G-representations. This includes principal series representations and certain representations coming from homogeneous line bundles on p-adic symmetric spaces. As an application, we compute the dimensions of the unitary GL2pQpq-rep...

Let m be the least cardinal θ such that MA θ fails. The only known model for " m is singular " was constructed by Kunen [K1]. In Kunen's model cof (m) = ω 1. It is unknown whether " ω 1 < cof (m) < m " is consistent. The purpose of this paper is to present a proof of Kunen's result and to identify the difficulties of generalizing this result to an arbitrary uncountable cofinality. The following...