The Eguchi–Hanson, Taub–NUT and Atiyah–Hitchin metrics are the only complete non–singular SO(3)–invariant hyper–Kahler metrics in four dimensions. The presence of a rotational SO(2) isometry allows for their unified treatment based on solutions of the 3–dim continual Toda equation. We determine the Toda potential in each case and examine the free field realization of the corresponding solutions...

This article investigates stationary surfaces with boundaries, which arise as the critical points of functionals dependent on curvature. Precisely, a generalized “bending energy” functional $$\mathcal {W}$$ is considered involves Lagrangian that symmetric in principal curvatures. The first variation computed, and stress tensor extracted whose divergence quantifies deviation from -criticality. B...

We show that the violation of rotational symmetry for differential cross section for Aharonov-Bohm effect with nonstandard boundary conditions has been known for some time. Moreover, the results were applied to discuss the Hall effect and persistent currents of fermions in a plane pierced by a flux tube. PACS: 03.65.Bz Nonrelativistic scattering theory PACS: 72.20.My Galvanomagnetic and other m...

New explicit solutions to the incompressible Navier-Stokes equations in R2 \ {0} are determined, which generalize the scale-invariant solutions found by Hamel. These new solutions are invariant under a particular combination of the scaling and rotational symmetries. They are the only solutions invariant under this new symmetry in the same way as the Hamel solutions are the only scaleinvariant s...

The antecedent of Einstein field equations with Euclidean signature is the complex elliptic Monge-Ampère equation, CMA2. For elliptic CMA2 solutions determine hyper-Kähler, self-dual and therefore Ricci-flat metrics with Euclidean signature. We shall consider a symmetry reduction of CMA2 to solutions that admit only a single Killing vector. Systematic studies of vacuum metrics with one Killing ...

INTRODUCTION: The choice of gradient sampling orientations for DT-MRI experiments has exercised many groups in the field. Of particular interest is the design of sampling schemes that will ensure that the error / variance in tensor estimates is independent of the relative orientation of the tensor to the reference frame established by the sampling vectors, which others have termed ‘statistical ...