1,990 research outputs found
Design Criteria for Zero Leakage Connectors for Launch Vehicles. Mathematical Model of Interface Sealing Phenomenon, Volume 2 Final Report
Mathematical model of interface sealing phenomenon in determining design criteria for zero leakage connectors for launch vehicle
Four-qubit entanglement from string theory
We invoke the black hole/qubit correspondence to derive the classification of
four-qubit entanglement. The U-duality orbits resulting from timelike reduction
of string theory from D=4 to D=3 yield 31 entanglement families, which reduce
to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references
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Polarizations and Nullcone of Representations of Reductive Groups
The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.
Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions
We consider invariant Riemannian metrics on compact homogeneous spaces G/H
where an intermediate subgroup K between G and H exists, so that the
homogeneous space G/H is the total space of a Riemannian submersion. We study
the question as to whether enlarging the fibers of the submersion by a constant
scaling factor retains the nonnegative curvature in the case that the
deformation starts at a normal homogeneous metric. We classify triples of
groups (H,K,G) where nonnegative curvature is maintained for small
deformations, using a criterion proved by Schwachh\"ofer and Tapp. We obtain a
complete classification in case the subgroup H has full rank and an almost
complete classification in the case of regular subgroups.Comment: 23 pages; minor revisions, to appear in Geometriae Dedicat
Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions
It is well known that in four or more dimensions, there exist exotic
manifolds; manifolds that are homeomorphic but not diffeomorphic to each other.
More precisely, exotic manifolds are the same topological manifold but have
inequivalent differentiable structures. This situation is in contrast to the
uniqueness of the differentiable structure on topological manifolds in one, two
and three dimensions. As exotic manifolds are not diffeomorphic, one can argue
that quantum amplitudes for gravity formulated as functional integrals should
include a sum over not only physically distinct geometries and topologies but
also inequivalent differentiable structures. But can the inclusion of exotic
manifolds in such sums make a significant contribution to these quantum
amplitudes? This paper will demonstrate that it will. Simply connected exotic
Einstein manifolds with positive curvature exist in seven dimensions. Their
metrics are found numerically; they are shown to have volumes of the same order
of magnitude. Their contribution to the semiclassical evaluation of the
partition function for Euclidean quantum gravity in seven dimensions is
evaluated and found to be nontrivial. Consequently, inequivalent differentiable
structures should be included in the formulation of sums over histories for
quantum gravity.Comment: AmsTex, 23 pages 5 eps figures; replaced figures with ones which are
hopefully viewable in pdf forma
A general form of Gelfand-Kazhdan criterion
We formalize the notion of matrix coefficients for distributional vectors in
a representation of a real reductive group, which consist of generalized
functions on the group. As an application, we state and prove a Gelfand-Kazhdan
criterion for a real reductive group in very general settings.Comment: 16 pages, to appear in Manuscripta Mathematic
Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories
The computer-mechanization of an ambitious explicit ethical theory, Gewirth's
Principle of Generic Consistency, is used to showcase an approach for
representing and reasoning with ethical theories exhibiting complex logical
features like alethic and deontic modalities, indexicals, higher-order
quantification, among others. Harnessing the high expressive power of Church's
type theory as a meta-logic to semantically embed a combination of quantified
non-classical logics, our work pushes existing boundaries in knowledge
representation and reasoning. We demonstrate that intuitive encodings of
complex ethical theories and their automation on the computer are no longer
antipodes.Comment: 14 page
Transfer of K-types on local theta lifts of characters and unitary lowest weight modules
In this paper we study representations of the indefinite orthogonal group
O(n,m) which are local theta lifts of one dimensional characters or unitary
lowest weight modules of the double covers of the symplectic groups. We apply
the transfer of K-types on these representations of O(n,m), and we study their
effects on the dual pair correspondences. These results provide examples that
the theta lifting is compatible with the transfer of K-types. Finally we will
use these results to study subquotients of some cohomologically induced
modules
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