Interpolation in non-positively curved K\"ahler manifolds

We extend to any simply connected K\"ahler manifold with non-positive sectional curvature some conditions for interpolation in $\mathbb{C}$ and in the unit disk given by Berndtsson, Ortega-Cerd\`a and Seip. The main tool is a comparison theorem for the Hessian in K\"ahler geometry due to Greene, Wu and Siu, Yau.Comment: 9 pages, Late

Torus fibrations and localization of index II

We give a framework of localization for the index of a Dirac-type operator on an open manifold. Suppose the open manifold has a compact subset whose complement is covered by a family of finitely many open subsets, each of which has a structure of the total space of a torus bundle. Under an acyclic condition we define the index of the Dirac-type operator by using the Witten-type deformation, and show that the index has several properties, such as excision property and a product formula. In particular, we show that the index is localized on the compact set.Comment: 47 pages, 2 figures. To appear in Communications in Mathematical Physic

Domestic Rivalry and Export Performance: Theory and Evidence from International Airline Markets

The much-studied relationship between domestic rivalry and export performance consists of those supporting a national-champion rationale, and those supporting a rivalry rationale. While the empirical literature generally supports the positive effects of domestic rivalry, the national-champion rationale actually rests on firmer theoretical ground. We address this inconsistency by providing a theoretical framework that illustrates three paths via which domestic rivalry translates into enhanced international exports. Furthermore, empirical tests on the world airline industry elicit the existence of one particular path - an enhanced firm performance effect - that connects domestic rivalry with improved international exports

Activation and repression of mammalian gene expression by the c-myc protein.

One mechanism by which nuclear-localized oncogenes might transform cells is through an ability to regulate gene expression. We show that the c-myc protein stimulates the level of appropriately initiated expression from the human heat shock protein 70 (hsp70) promoter. Sequences required for full activation lie upstream of the transcription initiation site and are distinct from sequences necessary for basal expression. These sequences also appear distinct from promoter sequences necessary for heat induction, serum induction, and induction by the papovavirus T antigens. The c-myc protein inhibits appropriately initiated expression from the mouse metallothionein I (MT-I) promoter. A mutation that removes 138 amino acids of exon 2 produces a c-myc gene product that is capable of activating the hsp70 promoter but is no longer capable of inhibiting MT-I expression, suggesting that these two properties reside in different domains of the c-myc protein. Expression from the adenovirus EII promoter is slightly inhibited, while expression from the SV40 early promoter is minimally affected by the c-myc protein. Both the spectrum of promoters regulated by the c-myc protein and the sequence requirements for that regulation differ from those of previously characterized viral trans-activating proteins. The data suggest that the c-myc protein can both stimulate and inhibit transcription from mammalian promoters in a novel manner

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group

We study Sobolev-type metrics of fractional order $s\geq0$ on the group \Diff_c(M) of compactly supported diffeomorphisms of a manifold $M$. We show that for the important special case $M=S^1$ the geodesic distance on \Diff_c(S^1) vanishes if and only if $s\leq\frac12$. For other manifolds we obtain a partial characterization: the geodesic distance on \Diff_c(M) vanishes for $M=\R\times N, s<\frac12$ and for $M=S^1\times N, s\leq\frac12$, with $N$ being a compact Riemannian manifold. On the other hand the geodesic distance on \Diff_c(M) is positive for $\dim(M)=1, s>\frac12$ and $\dim(M)\geq2, s\geq1$. For $M=\R^n$ we discuss the geodesic equations for these metrics. For $n=1$ we obtain some well known PDEs of hydrodynamics: Burgers' equation for $s=0$, the modified Constantin-Lax-Majda equation for $s=\frac 12$ and the Camassa-Holm equation for $s=1$.Comment: 16 pages. Final versio

Approximate solution of the Duffin-Kemmer-Petiau equation for a vector Yukawa potential with arbitrary total angular momenta

The usual approximation scheme is used to study the solution of the Duffin-Kemmer-Petiau (DKP) equation for a vector Yukawa potential in the framework of the parametric Nikiforov-Uvarov (NU) method. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for arbitrary total angular momentum in closed form. Further, the approximate energy equation and wave function spinor components are also given for case. A set of parameter values is used to obtain the numerical values for the energy states with various values of quantum levelsComment: 17 pages; Communications in Theoretical Physics (2012). arXiv admin note: substantial text overlap with arXiv:1205.0938, and with arXiv:quant-ph/0410159 by other author

Landau-Ginzburg Description of Boundary Critical Phenomena in Two Dimensions

The Virasoro minimal models with boundary are described in the Landau-Ginzburg theory by introducing a boundary potential, function of the boundary field value. The ground state field configurations become non-trivial and are found to obey the soliton equations. The conformal invariant boundary conditions are characterized by the reparametrization-invariant data of the boundary potential, that are the number and degeneracies of the stationary points. The boundary renormalization group flows are obtained by varying the boundary potential while keeping the bulk critical: they satisfy new selection rules and correspond to real deformations of the Arnold simple singularities of A_k type. The description of conformal boundary conditions in terms of boundary potential and associated ground state solitons is extended to the N=2 supersymmetric case, finding agreement with the analysis of A-type boundaries by Hori, Iqbal and Vafa.Comment: 42 pages, 13 figure

Magnetic trapping of ultracold neutrons

Three-dimensional magnetic confinement of neutrons is reported. Neutrons are loaded into an Ioffe-type superconducting magnetic trap through inelastic scattering of cold neutrons with 4He. Scattered neutrons with sufficiently low energy and in the appropriate spin state are confined by the magnetic field until they decay. The electron resulting from neutron decay produces scintillations in the liquid helium bath that results in a pulse of extreme ultraviolet light. This light is frequency downconverted to the visible and detected. Results are presented in which 500 +/- 155 neutrons are magnetically trapped in each loading cycle, consistent with theoretical predictions. The lifetime of the observed signal, 660 s +290/-170 s, is consistent with the neutron beta-decay lifetime.Comment: 17 pages, 18 figures, accepted for publication in Physical Review