Almost Hermitian Geometry on Six Dimensional Nilmanifolds

The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)xU(1) on complex projective 3-space. This leads to a combinatorial description of the classes of almost Hermitian structures on the Iwasawa and other nilmanifolds.Comment: 22 pages, 2 figure

Torsion, TQFT, and Seiberg-Witten invariants of 3-manifolds

We prove a conjecture of Hutchings and Lee relating the Seiberg-Witten invariants of a closed 3-manifold X with b_1 > 0 to an invariant that `counts' gradient flow lines--including closed orbits--of a circle-valued Morse function on the manifold. The proof is based on a method described by Donaldson for computing the Seiberg-Witten invariants of 3-manifolds by making use of a `topological quantum field theory,' which makes the calculation completely explicit. We also realize a version of the Seiberg-Witten invariant of X as the intersection number of a pair of totally real submanifolds of a product of vortex moduli spaces on a Riemann surface constructed from geometric data on X. The analogy with recent work of Ozsvath and Szabo suggests a generalization of a conjecture of Salamon, who has proposed a model for the Seiberg-Witten-Floer homology of X in the case that X is a mapping torus.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper2.abs.htm

Reversible Superconductivity in Electrochromic Indium-Tin Oxide Films

Transparent conductive indium tin oxide (ITO) thin films, electrochemically intercalated with sodium or other cations, show tunable superconducting transitions with a maximum $T_c$ at 5 K. The transition temperature and the density of states, $D(E_F)$ (extracted from the measured Pauli susceptibility $\chi_p$ exhibit the same dome shaped behavior as a function of electron density. Optimally intercalated samples have an upper critical field $\approx 4$ T and $\Delta/{k_BT_c} \approx 2.0$. Accompanying the development of superconductivity, the films show a reversible electrochromic change from transparent to colored and are partially transparent (orange) at the peak of the superconducting dome. This reversible intercalation of alkali and alkali earth ions into thin ITO films opens diverse opportunities for tunable, optically transparent superconductors

Nanoscale magnetic structure of ferromagnet/antiferromagnet manganite multilayers

Polarized Neutron Reflectometry and magnetometry measurements have been used to obtain a comprehensive picture of the magnetic structure of a series of La{2/3}Sr{1/3}MnO{3}/Pr{2/3}Ca{1/3}MnO{3} (LSMO/PCMO) superlattices, with varying thickness of the antiferromagnetic (AFM) PCMO layers (0<=t_A<=7.6 nm). While LSMO presents a few magnetically frustrated monolayers at the interfaces with PCMO, in the latter a magnetic contribution due to FM inclusions within the AFM matrix was found to be maximized at t_A~3 nm. This enhancement of the FM moment occurs at the matching between layer thickness and cluster size, where the FM clusters would find the optimal strain conditions to be accommodated within the "non-FM" material. These results have important implications for tuning phase separation via the explicit control of strain.Comment: 4 pages, submitted to PR

EUV and X-ray spectroheliograph study

The results of a program directed toward the definition of an EUV and X-ray spectroheliograph which has significant performance and operational improvements over the OSO-7 instrument are documented. The program investigated methods of implementing selected changes and incorporated the results of the study into a set of drawings which defines the new instrument. The EUV detector performance degradation observed during the OSO-7 mission was investigated and the most probable cause of the degradation identified

Comment on ``Cosmological Gamma Ray Bursts and the Highest Energy Cosmic Rays''

In a letter with the above title, published some time ago in PRL, Waxman made the interesting suggestion that cosmological gamma ray bursts (GRBs) are the source of the ultra high energy cosmic rays (UHECR). This has also been proposed independently by Milgrom and Usov and by Vietri. However, recent observations of GRBs and their afterglows and in particular recent data from the Akeno Great Air Shwoer Array (AGASA) on UHECR rule out extragalactic GRBs as the source of UHECR.Comment: Comment on a letter with the above title published by E. Waxman in PRL 75, 386 (1995). Submitted for publication in PRL/Comment

Observation of the spontaneous vortex phase in the weakly ferromagnetic superconductor ErNi2_{2}B2_{2}C: A penetration depth study

The coexistence of weak ferromagnetism and superconductivity in ErNi$_{2}$B$_{2}$C suggests the possibility of a spontaneous vortex phase (SVP) in which vortices appear in the absence of an external field. We report evidence for the long-sought SVP from the in-plane magnetic penetration depth $\Delta \lambda (T)$ of high-quality single crystals of ErNi$_{2}$B$_{2}$C. In addition to expected features at the N\'{e}el temperature $T_{N}$ = 6.0 K and weak ferromagnetic onset at $T_{WFM}=2.3$K, $\Delta \lambda (T)$ rises to a maximum at $T_{m}=0.45$ K before dropping sharply down to $\sim$0.1 K. We assign the 0.45 K-maximum to the proliferation and freezing of spontaneous vortices. A model proposed by Koshelev and Vinokur explains the increasing $\Delta \lambda (T)$ as a consequence of increasing vortex density, and its subsequent decrease below $T_{m}$ as defect pinning suppresses vortex hopping.Comment: 5 pages including figures; added inset to Figure 2; significant revisions to tex

A 2k2k-Vertex Kernel for Maximum Internal Spanning Tree

We consider the parameterized version of the maximum internal spanning tree problem, which, given an $n$-vertex graph and a parameter $k$, asks for a spanning tree with at least $k$ internal vertices. Fomin et al. [J. Comput. System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a $3k$-vertex kernel. Here we propose a novel way to use the same reduction rule, resulting in an improved $2k$-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a deterministic algorithm for the problem running in time $4^k \cdot n^{O(1)}$