Proof of the Double Bubble Conjecture in R^n

The least-area hypersurface enclosing and separating two given volumes in R^n is the standard double bubble.Comment: 20 pages, 22 figure

Experiences in deploying metadata analysis tools for institutional repositories

Current institutional repository software provides few tools to help metadata librarians understand and analyze their collections. In this article, we compare and contrast metadata analysis tools that were developed simultaneously, but independently, at two New Zealand institutions during a period of national investment in research repositories: the Metadata Analysis Tool (MAT) at The University of Waikato, and the Kiwi Research Information Service (KRIS) at the National Library of New Zealand. The tools have many similarities: they are convenient, online, on-demand services that harvest metadata using OAI-PMH; they were developed in response to feedback from repository administrators; and they both help pinpoint specific metadata errors as well as generating summary statistics. They also have significant differences: one is a dedicated tool wheres the other is part of a wider access tool; one gives a holistic view of the metadata whereas the other looks for specific problems; one seeks patterns in the data values whereas the other checks that those values conform to metadata standards. Both tools work in a complementary manner to existing Web-based administration tools. We have observed that discovery and correction of metadata errors can be quickly achieved by switching Web browser views from the analysis tool to the repository interface, and back. We summarize the findings from both tools' deployment into a checklist of requirements for metadata analysis tools

On the geometry of mixed states and the Fisher information tensor

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant-Kirillov-Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.Comment: 27 pages; Accepted Manuscrip

Dynamics of drop deformation and formation during secondary breakup in the bag breakup regime

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77016/1/AIAA-1997-797-833.pd

Exotic torus manifolds and equivariant smooth structures on quasitoric manifolds

In 2006 Masuda and Suh asked if two compact non-singular toric varieties having isomorphic cohomology rings are homeomorphic. In the first part of this paper we discuss this question for topological generalizations of toric varieties, so-called torus manifolds. For example we show that there are homotopy equivalent torus manifolds which are not homeomorphic. Moreover, we characterize those groups which appear as the fundamental groups of locally standard torus manifolds. In the second part we give a classification of quasitoric manifolds and certain six-dimensional torus manifolds up to equivariant diffeomorphism. In the third part we enumerate the number of conjugacy classes of tori in the diffeomorphism group of torus manifolds. For torus manifolds of dimension greater than six there are always infinitely many conjugacy classes. We give examples which show that this does not hold for six-dimensional torus manifolds.Comment: 21 pages, 2 figures, results about quasitoric manifolds adde

Puzzles in BB physics

I discuss some puzzles observed in exclusive $B$ meson decays, concentrating on the large difference between the direct CP asymmetries in the $B^0\to \pi^\mp K^\pm$ and $B^\pm\to \pi^0 K^\pm$ modes, the large $B^0\to\pi^0\pi^0$ branching ratio, and the large deviation of the mixing-induced CP asymmetries in the $b\to sq\bar q$ penguins from those in the $b\to c\bar c s$ trees.Comment: 6 pages, 1 figure, talk presented at the 9th Workshop on High Energy Physics Phenomenology, Bhubaneswar, Orissa, India, Jan. 3-14, 2006; reference adde

Influence on electron coherence from quantum electromagnetic fields in the presence of conducting plates

The influence of electromagnetic vacuum fluctuations in the presence of the perfectly conducting plate on electrons is studied with an interference experiment. The evolution of the reduced density matrix of the electron is derived by the method of influence functional. We find that the plate boundary anisotropically modifies vacuum fluctuations that in turn affect the electron coherence. The path plane of the interference is chosen either parallel or normal to the plate. In the vicinity of the plate, we show that the coherence between electrons due to the boundary is enhanced in the parallel configuration, but reduced in the normal case. The presence of the second parallel plate is found to boost these effects. The potential relation between the amplitude change and phase shift of interference fringes is pointed out. The finite conductivity effect on electron coherence is discussed.Comment: 29 pages, 3 figure

GALEX J201337.6+092801: The lowest gravity subdwarf B pulsator

We present the recent discovery of a new subdwarf B variable (sdBV), with an exceptionally low surface gravity. Our spectroscopy of J20136+0928 places it at Teff = 32100 +/- 500, log(g) = 5.15 +/- 0.10, and log(He/H) = -2.8 +/- 0.1. With a magnitude of B = 12.0, it is the second brightest V361 Hya star ever found. Photometry from three different observatories reveals a temporal spectrum with eleven clearly detected periods in the range 376 to 566 s, and at least five more close to our detection limit. These periods are unusually long for the V361 Hya class of short-period sdBV pulsators, but not unreasonable for p- and g-modes close to the radial fundamental, given its low surface gravity. Of the ~50 short period sdB pulsators known to date, only a single one has been found to have comparable spectroscopic parameters to J20136+0928. This is the enigmatic high-amplitude pulsator V338 Ser, and we conclude that J20136+0928 is the second example of this rare subclass of sdB pulsators located well above the canonical extreme horizontal branch in the HR diagram.Comment: 5 pages, accepted for publication in ApJ Letter

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Exotic smooth structures and symplectic forms on closed manifolds

We give a short proof of the (known) result that there are no Kaehler structures on exotic tori. This yields a negative solution to a problem posed by Benson and Gordon. W discuss the symplectic version of the problem and analyze results which yield an evidence for the conjecture that there are no symplectic structures on exotic tori.Comment: AMSLaTeX, 16 pages, a new version. A survey of the symplectic version of the problem is adde