Hermitian structures on six dimensional nilmanifolds

Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong K\"ahler with torsion, balanced or locally conformal K\"ahler structures (J,g).Comment: LaTeX, 24 pages, 1 figur

A canonical structure on the tangent bundle of a pseudo- or para-K\"ahler manifold

It is a classical fact that the cotangent bundle T^* \M of a differentiable manifold \M enjoys a canonical symplectic form $\Omega^*$. If (\M,\j,g,\omega) is a pseudo-K\"ahler or para-K\"ahler $2n$-dimensional manifold, we prove that the tangent bundle T\M also enjoys a natural pseudo-K\"ahler or para-K\"ahler structure (\J,\G,\Omega), where $\Omega$ is the pull-back by $g$ of $\Omega^*$ and \G is a pseudo-Riemannian metric with neutral signature $(2n,2n)$. We investigate the curvature properties of the pair (\J,\G) and prove that: \G is scalar-flat, is not Einstein unless $g$ is flat, has nonpositive (resp.\ nonnegative) Ricci curvature if and only if $g$ has nonpositive (resp.\ nonnegative) Ricci curvature as well, and is locally conformally flat if and only if $n=1$ and $g$ has constant curvature, or $n>2$ and $g$ is flat. We also check that (i) the holomorphic sectional curvature of (\J,\G) is not constant unless $g$ is flat, and (ii) in $n=1$ case, that \G is never anti-self-dual, unless conformally flat.Comment: Clarified the statements on the cotangent bundle. Corrected various typo

Twisted modules and co-invariants for commutative vertex algebras of jet schemes

Let Z⊂k be an affine scheme over \C and \J Z its jet scheme. It is well-known that \mathbb{C}[\J Z], the coordinate ring of \J Z, has the structure of a commutative vertex algebra. This paper develops the orbifold theory for \mathbb{C}[\J Z]. A finite-order linear automorphism g of Z acts by vertex algebra automorphisms on \mathbb{C}[\J Z]. We show that \mathbb{C}[\J^g Z], where \J^g Z is the scheme of g--twisted jets has the structure of a g-twisted \mathbb{C}[\J Z] module. We consider spaces of orbifold coinvariants valued in the modules \mathbb{C}[\J^g Z] on orbicurves [Y/G], with Y a smooth projective curve and G a finite group, and show that these are isomorphic to ℂ[ZG]

Technological development of cylindrical and flat shaped high energy density capacitors

Cylindrical wound metallized film capacitors rated 2 micron F 500 VDC that had an energy density greater than 0.3 J/g, and flat flexible metallized film capacitors rated at 2 micron F 500 VDC that had an energy density greater than 0.1 J/g were developed. Polysulfone, polycarbonate, and polyvinylidene fluoride (PVF2) were investigated as dielectrics for the cylindrical units. PVF2 in 6.0 micron m thickness was employed in the final components of both types. Capacitance and dissipation factor measurements were made over the range 25 C to 100 C, and 10 Hz to 10 kHz. No pre-life-test burning was performed, and six of ten cylindrical units survived a 2500 hour AC plus DC lift test. Three of the four failures were infant mortality. All but two of the flat components survived 400 hours. Finished energy densities were 0.104 J/g at 500 V and 0.200 J/g at 700 V, the energy density being limited by the availability of thin PVF2 films