The Multiplicity of Eigenvalues of the Hodge Laplacian on 5-Dimensional Compact Manifolds

We study multiplicity of the eigenvalues of the Hodge Laplacian on smooth, compact Riemannian manifolds of dimension five for generic families of metrics. We prove that generically the Hodge Laplacian, restricted to the subspace of co-exact two-forms, has nonzero eigenvalues of multiplicity two. The proof is based on the fact that Hodge Laplacian restricted to the subspace of co-exact two-forms is minus the square of the Beltrami operator, a first-order operator. We prove that for generic metrics the spectrum of the Beltrami operator is simple. Because the Beltrami operator in this setting is a skew-adjoint operator, this implies the main result for the Hodge Laplacian

Solving the Coulomb scattering problem using the complex scaling method

Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex scaling method, applied to a specially constructed inhomogeneous Schr\"odinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.Comment: 3 pages, 3 figure

Silvopastoral Agroforestry in Upland and Lowland UK Grassland: Tree Growth and Animal Performance

Trees, individually protected from herbivore damage using plastic shelters, were planted at two densities (100 and 400 stems/ha) into sheepgrazed pasture in upland and lowland UK grassland sites in 1988. Tree and animal performance were compared with conventional forestry (no sheep) and pasture (no tree) systems. Effects on tree growth and survival are highly species and site dependent although some treatment effects did emerge. Tree shelters encouraged rapid early height growth compared to forestry controls although in some cases tree form was also adversely affected. Generally tree performance within agroforestry treatments was better at the higher planting density. Eight years after planting there has been no reduction in animal production despite interception of up to 10% of total photosynthetically active radiation by the developing tree canopy

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

Surficial Geologic Map of the Millerstown 7.5-Minute Quadrangle, Kentucky

The Millerstown 7.5-minute quadrangle is located south of Louisville and southwest of Elizabethtown along the boundaries between Hardin, Grayson, and Hart Counties and within the Mississippian Plateau physiographic region (McDowell, 1986). Topography is characterized by the low relief Pennyroyal plain that sits at altitudes below about 650 ft above sea level, the low relief Mammoth Cave plateau at altitudes above about 650 ft, and steep slopes of and isolated knobs of the incised Dripping Springs escarpment that separates the two plains. Moore (1965) mapped the bedrock geology of the quadrangle, which was later digitized by Johnson (2006). Mississippian bedrock and local areas of Pennsylvanian bedrock are exposed throughout most of the quadrangle, all, of which, are cut by several vertical faults. The Ste. Genevieve Limestone is the oldest lithology and underlies the Pennyroyal region in the northeast and southwest corners of the quadrangle, and locally along the Nolin River. The Beaver Bend Limestone, Mooretown Formation, Paoli Limestone, Sample Sandstone, and Reelsville Limestone stratigraphic sequence underlie most of the remaining Pennyroyal plain and several steep slopes of the Dripping Springs escarpment. The Beech Creek Limestone, Big Clifty Sandstone, and Haney Limestone Members of the Golconda Formation are exposed along the Dripping Springs escarpment the edges of the Mammoth Cave plateau region. Most of the Mammoth Cave plateau is underlain by the Hardinsburg Limestone, and, locally in the southwest corner of the quadrangle, the Glen Dean Limestone, Leitchfield Formation, and Pennsylvanian Caseyville Formation. Previously mapped surficial deposits include minor areas of alluvium in tributaries across the Millerstown quadrangle (Moore, 1964)

Epitope-specific Evolution of Human CD8+ T Cell Responses from Primary to Persistent Phases of Epstein-Barr Virus Infection

Primary virus infection often elicits a large CD8+ T cell response which subsequently contracts to a smaller memory T cell pool; the relationship between these two virus-specific populations is not well understood. Here we follow the human CD8+ T cell response to Epstein-Barr virus (EBV) from its primary phase in infectious mononucleosis (IM) through to the persistent carrier state. Using HLA-A2.1 or B8 tetramers specific for four lytic cycle and three latent cycle epitopes, we find marked differences in the epitope-specific composition of the T cell populations between the two phases of infection. The primary response is dominated by lytic epitope specificities which are severely culled (and in one case extinguished) with resolution of the acute infection; in contrast latent epitope specificities are less abundant, if present at all, in acute IM but often then increase their percentage representation in the CD8 pool. Even comparing epitopes of the same type, the relative size of responses seen in primary infection does not necessarily correlate with that seen in the longer term. We also follow the evolution of phenotypic change in these populations and show that, from a uniform CD45RA−RO+CCR7− phenotype in IM, lytic epitope responses show greater reversion to a CD45RA+RO− phenotype whereas latent epitope responses remain CD45RA−RO+ with a greater tendency to acquire CCR7. Interestingly these phenotypic distinctions reflect the source of the epitope as lytic or latent, and not the extent to which the response has been amplified in vivo

Surficial Geologic Map of the Summit 7.5-Minute Quadrangle, Kentucky

The Summit 7.5-minute quadrangle is located south of Louisville and west of Elizabethtown along the boundary between Hardin and Grayson Counties and within the Mississippian Plateau physiographic region (McDowell, 1986). Topography is characterized by the low relief Pennyroyal region that sits at elevations between 560 to 650 ft above sea level, the low relief Mammoth Cave plateau at elevations between 750 to 900 ft, and the steep Dripping Springs escarpment that separates the two plains. Moore (1964) mapped the bedrock geology of the quadrangle, which was later digitized by Conley (2002). Mississippian bedrock is exposed throughout the quadrangle and is cut by several vertical faults. The St. Louis Limestone and overlying Ste. Genevieve Limestone underlie the Pennyroyal region and are the oldest bedrock units in the quadrangle. The Beaver Bend and Paoli Limestones, Sample Sandstone, Reelsville Limestone, and Beech Creek Limestone Member of the Golconda Formation are exposed along the Dripping Springs escarpment. The Mammoth Cave plateau region is underlain by the Big Clifty Sandstone and, locally, Haney Limestone Members of the Golconda Formation east of the Summit Fault, and Hardinsburg Sandstone west of the fault. Previously mapped surficial deposits include minor areas of alluvium in tributaries across the Summit quadrangle, and areas of “slumped sandstone” (colluvium) in the Pennyroyal region (Moore, 1964)

Shapes of leading tunnelling trajectories for single-electron molecular ionization

Based on the geometrical approach to tunnelling by P.D. Hislop and I.M. Sigal [Memoir. AMS 78, No. 399 (1989)], we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single-active-electron models of molecular tunnelling ionization (i.e., theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short range interactions and "almost" linear in the case of long range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the obtained results are discussed.Comment: 14 pages, 5 figure

Stage-Specific Inhibition of MHC Class I Presentation by the Epstein-Barr Virus BNLF2a Protein during Virus Lytic Cycle

gamma-herpesvirus Epstein-Barr virus (EBV) persists for life in infected individuals despite the presence of a strong immune response. During the lytic cycle of EBV many viral proteins are expressed, potentially allowing virally infected cells to be recognized and eliminated by CD8+ T cells. We have recently identified an immune evasion protein encoded by EBV, BNLF2a, which is expressed in early phase lytic replication and inhibits peptide- and ATP-binding functions of the transporter associated with antigen processing. Ectopic expression of BNLF2a causes decreased surface MHC class I expression and inhibits the presentation of indicator antigens to CD8+ T cells. Here we sought to examine the influence of BNLF2a when expressed naturally during EBV lytic replication. We generated a BNLF2a-deleted recombinant EBV (ΔBNLF2a) and compared the ability of ΔBNLF2a and wild-type EBV-transformed B cell lines to be recognized by CD8+ T cell clones specific for EBV-encoded immediate early, early and late lytic antigens. Epitopes derived from immediate early and early expressed proteins were better recognized when presented by ΔBNLF2a transformed cells compared to wild-type virus transformants. However, recognition of late antigens by CD8+ T cells remained equally poor when presented by both wild-type and ΔBNLF2a cell targets. Analysis of BNLF2a and target protein expression kinetics showed that although BNLF2a is expressed during early phase replication, it is expressed at a time when there is an upregulation of immediate early proteins and initiation of early protein synthesis. Interestingly, BNLF2a protein expression was found to be lost by late lytic cycle yet ΔBNLF2a-transformed cells in late stage replication downregulated surface MHC class I to a similar extent as wild-type EBV-transformed cells. These data show that BNLF2a-mediated expression is stage-specific, affecting presentation of immediate early and early proteins, and that other evasion mechanisms operate later in the lytic cycle