8,443 research outputs found
Resolutions of Cones over Einstein-Sasaki Spaces
Recently an explicit resolution of the Calabi-Yau cone over the inhomogeneous
five-dimensional Einstein-Sasaki space Y^{2,1} was obtained. It was constructed
by specialising the parameters in the BPS limit of recently-discovered
Kerr-NUT-AdS metrics in higher dimensions. We study the occurrence of such
non-singular resolutions of Calabi-Yau cones in a more general context.
Although no further six-dimensional examples arise as resolutions of cones over
the L^{pqr} Einstein-Sasaki spaces, we find general classes of non-singular
cohomogeneity-2 resolutions of higher-dimensional Einstein-Sasaki spaces. The
topologies of the resolved spaces are of the form of an R^2 bundle over a base
manifold that is itself an bundle over an Einstein-Kahler manifold.Comment: Latex, 23 page
The Hierarchy of Stable Distributions and Operators to Trade Off Stability and Performance
Recent work addressing model reliability and generalization has resulted in a
variety of methods that seek to proactively address differences between the
training and unknown target environments. While most methods achieve this by
finding distributions that will be invariant across environments, we will show
they do not necessarily find the same distributions which has implications for
performance. In this paper we unify existing work on prediction using stable
distributions by relating environmental shifts to edges in the graph underlying
a prediction problem, and characterize stable distributions as those which
effectively remove these edges. We then quantify the effect of edge deletion on
performance in the linear case and corroborate the findings in a simulated and
real data experiment
SU(3)-structures on submanifolds of a Spin(7)-manifold
Local SU(3)-structures on an oriented submanifold of Spin(7)-manifold are
determined and their types are characterized in terms of the shape operator and
the type of the Spin(7)-structure. An application to Bryant \cite{MR89b:53084}
and Calabi \cite{MR24 #A558} examples is given. It is shown that the product of
a Cayley plane and a minimal surface lying in a four-dimensional orthogonal
Cayley plane with the induced complex structure from the octonions described by
Bryant in \cite{MR89b:53084} admits a holomorphic local complex volume form
exactly when it lies in a three-plane, i.e. it coincides with the example
constructed by Calabi in \cite{MR24 #A558}. In this case the holomorphic
(3,0)-form is parallel with respect to the unique Hermitian connection with
totally skew-symmetric torsion.Comment: 25 pages, no figures, some improvements and clarifications are made,
final version to appear in Diff. Geom. App
Tipping the Scale to Bring a Balanced Approach: Evidence Disclosure in Chinese International Arbitration
Due to the ever-increasing trade between China and the rest of the world, commercial disputes have risen dramatically. Many foreign companies choose to resolve these disputes through arbitration to circumvent the Chinese courts and to retain more autonomy and control. Arbitration itself can also be a problem because rules and laws differ, depending on the jurisdiction and the institution involved. Under China’s civil law tradition, arbitrators are restricted in their ability to force parties to disclose evidence that may be detrimental to their case. Additionally, arbitrators have no authority to obtain evidence from uncooperative third parties. This Article seeks to provide some guidance for parties engaged in arbitration proceedings in China
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