A Spectral Bernstein Theorem

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface $M$ in $\R^{n+1}$. (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that $M$ has only essential spectrum consisting of the half line $[0, +\infty)$. This is the case when $\lim_{\tilde{r}\to +\infty}\tilde{r}\kappa_i=0$, where $\tilde{r}$ is the extrinsic distance to a point of $M$ and $\kappa_i$ are the principal curvatures. (2) If the $\kappa_i$ satisfy the decay conditions $|\kappa_i|\leq 1/\tilde{r}$, and strict inequality is achieved at some point $y\in M$, then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces.Comment: 16 pages. v2. Final version: minor revisions, we add Proposition 3.2. Accepted for publication in the Annali di Matematica Pura ed Applicata, on the 05/03/201

Relativistic Effects in the Electromagnetic Current at GeV Energies

We employ a recent approach to the non-relativistic reduction of the electromagnetic current operator in calculations of electronuclear reactions. In contrast to the traditional scheme, where approximations are made for the transferred momentum, transferred energy and initial momentum of the struck nucleon in obtaining an on-shell inspired form for the current, we treat the problem exactly for the transferred energy and transferred momentum. We calculate response functions for the reaction $^2H(e,e'p)n$ at CEBAF (TJNAF) energies and find large relativistic corrections. We also show that in Plane Wave Impulse Approximation, it is always possible to use the full operator, and we present a comparison of such a limiting case with the results incorporating relativistic effects to the first order in the initial momentum of the struck nucleon.Comment: 31 pages, 8 figures, Revte

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Vortex precession in Bose-Einstein condensates: observations with filled and empty cores

We have observed and characterized the dynamics of singly quantized vortices in dilute-gas Bose-Einstein condensates. Our condensates are produced in a superposition of two internal states of 87Rb, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the precession frequency of the vortex core about the condensate axis changes by only a factor of two.Comment: 4 pages, 3 figure

Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space

The Casimir stress on a cylinderical shell in background of conformally flat space-time for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.Comment: 10 pages, no figur

Inelastic nucleon contributions in (e,e′)(e,e^\prime) nuclear response functions

We estimate the contribution of inelastic nucleon excitations to the $(e,e^\prime)$ inclusive cross section in the CEBAF kinematic range. Calculations are based upon parameterizations of the nucleon structure functions measured at SLAC. Nuclear binding effects are included in a vector-scalar field theory, and are assumed have a minimal effect on the nucleon excitation spectrum. We find that for q\lsim 1 GeV the elastic and inelastic nucleon contributions to the nuclear response functions are comparable, and can be separated, but with roughly a factor of two uncertainty in the latter from the extrapolation from data. In contrast, for q\rsim 2 GeV this uncertainty is greatly reduced but the elastic nucleon contribution is heavily dominated by the inelastic nucleon background.Comment: 20 pages, 7 figures available from the authors at Department of Physics and Astronomy, University of Rochester, Rochester NY 1462

Parity Violating Measurements of Neutron Densities

Parity violating electron nucleus scattering is a clean and powerful tool for measuring the spatial distributions of neutrons in nuclei with unprecedented accuracy. Parity violation arises from the interference of electromagnetic and weak neutral amplitudes, and the $Z^0$ of the Standard Model couples primarily to neutrons at low $Q^2$. The data can be interpreted with as much confidence as electromagnetic scattering. After briefly reviewing the present theoretical and experimental knowledge of neutron densities, we discuss possible parity violation measurements, their theoretical interpretation, and applications. The experiments are feasible at existing facilities. We show that theoretical corrections are either small or well understood, which makes the interpretation clean. The quantitative relationship to atomic parity nonconservation observables is examined, and we show that the electron scattering asymmetries can be directly applied to atomic PNC because the observables have approximately the same dependence on nuclear shape.Comment: 38 pages, 7 ps figures, very minor changes, submitted to Phys. Rev.

SU(3) symmetry breaking in lower fp-shell nuclei

Results of shell-model calculations for lower fp-shell nuclei show that SU(3) symmetry breaking in this region is driven by the single-particle spin-orbit splitting. However, even though states of the yrast band exhibit SU(3) symmetry breaking, the results also show that the yrast band B(E2) values are insensitive to this fragmentation of the SU(3) symmetry; specifically, the quadrupole collectivity as measured by B(E2) transition strengths between low lying members of the yrast band remain high even though SU(3) appears to be broken. Results for $^{44,46,48}Ti$ and $^{48}Cr$ using the Kuo-Brown-3 two-body interaction are given to illustrate these observations.Comment: Updated to the published versio

Revision and Update of the Consensus Definitions of Invasive Fungal Disease From the European Organization for Research and Treatment of Cancer and the Mycoses Study Group Education and Research Consortium.

BACKGROUND: Invasive fungal diseases (IFDs) remain important causes of morbidity and mortality. The consensus definitions of the Infectious Diseases Group of the European Organization for Research and Treatment of Cancer and the Mycoses Study Group have been of immense value to researchers who conduct clinical trials of antifungals, assess diagnostic tests, and undertake epidemiologic studies. However, their utility has not extended beyond patients with cancer or recipients of stem cell or solid organ transplants. With newer diagnostic techniques available, it was clear that an update of these definitions was essential. METHODS: To achieve this, 10 working groups looked closely at imaging, laboratory diagnosis, and special populations at risk of IFD. A final version of the manuscript was agreed upon after the groups' findings were presented at a scientific symposium and after a 3-month period for public comment. There were several rounds of discussion before a final version of the manuscript was approved. RESULTS: There is no change in the classifications of "proven," "probable," and "possible" IFD, although the definition of "probable" has been expanded and the scope of the category "possible" has been diminished. The category of proven IFD can apply to any patient, regardless of whether the patient is immunocompromised. The probable and possible categories are proposed for immunocompromised patients only, except for endemic mycoses. CONCLUSIONS: These updated definitions of IFDs should prove applicable in clinical, diagnostic, and epidemiologic research of a broader range of patients at high-risk

On the Existence of Undistorted Progressive Waves (UPWs) of Arbitrary Speeds 0≤v<∞0 \leq v< \infty in Nature

We present the theory, the experimental evidence, and fundamental physical consequences concerning the existence of families of undistorted progressive waves (UPWs) of arbitrary speeds $0\leq v < \infty$, which are solutions of the homogeneous wave equation, Maxwell equations, and Dirac and Weyl equations.Comment: 77 pages, Latex article, with figures. Includes corrections to the published versio