What a classical r-matrix really is

The notion of classical $r$-matrix is re-examined, and a definition suitable to differential (-difference) Lie algebras, -- where the standard definitions are shown to be deficient, -- is proposed, the notion of an ${\mathcal O}$-operator. This notion has all the natural properties one would expect form it, but lacks those which are artifacts of finite-dimensional isomorpisms such as not true in differential generality relation \mbox{End}\, (V) \simeq V^* \otimes V for a vector space $V$. Examples considered include a quadratic Poisson bracket on the dual space to a Lie algebra; generalized symplectic-quadratic models of such brackets (aka Clebsch representations); and Drinfel'd's 2-cocycle interpretation of nondegenate classical $r$-matrices

Interferometric imaging of the high-redshift radio galaxy, 4C60.07: An SMA, Spitzer and VLA study reveals a binary AGN/starburst

‘The definitive version is available at www3.interscience.wiley.com '. Copyright Blackwell / RAS. DOI: 10.1111/j.1365-2966.2008.13811.xPeer reviewe

ρ\rho Polarization and `Model Independent' Extraction of ∣Vub∣/∣Vcd∣|V_{ub}|/|V_{cd}| from D→ρℓνD\to\rho\ell\nu and B→ρℓνB\to\rho\ell\nu

We briefly discuss the predictions of the heavy quark effective theory for the semileptonic decays of a heavy pseudoscalar to a light one, or to a light vector meson. We point out that measurement of combinations of differential helicity decay rates at Cleo-c and the $B$ factories can provide a model independent means of extracting the ratio $|V_{ub}|/|V_{cd}|$. We briefly discuss the corrections to this prediction.Comment: 8 pages, LaTeX, 1 figur

Stability conditions and positivity of invariants of fibrations

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthda

Virtual Structure Constants as Intersection Numbers of Moduli Space of Polynomial Maps with Two Marked Points

In this paper, we derive the virtual structure constants used in mirror computation of degree k hypersurface in CP^{N-1}, by using localization computation applied to moduli space of polynomial maps from CP^{1} to CP^{N-1} with two marked points. We also apply this technique to non-nef local geometry O(1)+O(-3)->CP^{1} and realize mirror computation without using Birkhoff factorization.Comment: 10 pages, latex, a minor change in Section 4, English is refined, Some typing errors in Section 3 are correcte

Colossal dielectric permittivity of BaTiO3-based nanocrystalline ceramics sintered by spark plasma sintering

In pursuit of high permittivity materials for electronic application, there has been a considerable interest recently in the dielectric properties of various perovskite oxides like calcium copper titanate or lanthanum doped barium titanate. When processed in a particular way, this later material present at ambient temperature and at f=1 kHz unusual interesting dielectric properties, a so called “colossal” permittivity value up to several 106 with relatively low dielectric losses. Moreover and contrary to what is classically expected and evidenced for this type of materials, no temperature dependence is observed. This behavior is observed in nanopowders based ceramics. An assumption to explain the observed properties is proposed. These results have important technological applications, since these nanoceramics open a new route to the fabrication of very thin dielectric films

M2-branes on M-folds

We argue that the moduli space for the Bagger-Lambert A_4 theory at level k is (R^8 \times R^8)/D_{2k}, where D_{2k} is the dihedral group of order 4k. We conjecture that the theory describes two M2-branes on a Z_{2k} ``M-fold'', in which a geometrical action of Z_{2k} is combined with an action on the branes. For k=1, this arises as the strong coupling limit of two D2-branes on an O2^- orientifold, whose worldvolume theory is the maximally supersymmetric SO(4) gauge theory. Finally, in an appropriate large-k limit we show that one recovers compactified M-theory and the M2-branes reduce to D2-branes.Comment: 16 pages, LaTeX, v2: typos corrected, included appendices on Chern-Simons level quantization and monopole charge quantizatio

Fictional first memories

YesIn a large-scale survey, 6,641 respondents provided descriptions of their first memory and their age when they encoded that memory, and they completed various memory judgments and ratings. In good agreement with many other studies, where mean age at encoding of earliest memories is usually found to fall somewhere in the first half of the 3rd year of life, the mean age at encoding here was 3.2 years. The established view is that the distribution around mean age at encoding is truncated, with very few or no memories dating to the preverbal period, that is, below about 2 years of age. However, we found that 2,487 first memories (nearly 40% of the entire sample) dated to an age at encoding of 2 years and younger, with 893 dating to 1 year and younger. We discuss how such improbable, fictional first memories could have arisen and contrast them with more probable first memories, those with an age at encoding of 3 years and older

Marginal Deformations of Field Theories with AdS_4 Duals

We generate new AdS_4 solutions of D=11 supergravity starting from AdS_4 x X_7 solutions where X_7 has U(1)^3 isometry. We consider examples where X_7 is weak G_2, Sasaki-Einstein or tri-Sasakian, corresponding to d=3 SCFTs with N=1,2 or 3 supersymmetry, respectively, and where the deformed solutions preserve N=1,2 or 1 supersymmetry, respectively. For the special cases when X_7 is M(3,2), Q(1,1,1) or N(1,1)_I we identify the exactly marginal deformation in the dual field theory. We also show that the volume of supersymmetric 5-cycles of N(1,1)_I agrees with the conformal dimension predicted by the baryons of the dual field theory.Comment: 28 pages, 2 figures; v2. typos correcte