A Spectral Analysis for Self-Adjoint Operators Generated by a Class of Second Order Difference Equations

AbstractA qualitative spectral analysis for a class of second order difference equations is given. Central to the analysis of equations in this class is the observation that real-valued solutions exhibit a type of stable asymptotic behavior for certain real values of the spectral parameter. This asymptotic behavior leads to the characterization of the limit point and limit circle nature of these equations, and is used to show that a strong nonsubordinacy criterion is satisfied on subintervals ofRfor equations of limit point type. These subintervals are part of the absolutely continuous spectrum of the self-adjoint realization of these equations. By other means, the nature of the discrete spectrum for these self-adjoint realizations is also discussed

The Effective Action For Brane Localized Gauge Fields

The low energy effective action including gauge field degrees of freedom on a non-BPS p=2 brane embedded in a N=1, D=4 target superspace is obtained through the method of nonlinear realizations of the associated super-Poincare symmetries. The invariant interactions of the gauge fields and the brane excitation modes corresponding to the Nambu-Goldstone degrees of freedom resulting from the broken space translational symmetry and the target space supersymmetries are determined. Brane localized matter field interactions with the gauge fields are obtained through the construction of the combined gauge and super-Poincare covariant derivatives for the matter fields.Comment: 12 pages, no figure

Clarifying Some Remaining Questions in the Anomaly Puzzle

We discuss several points that may help to clarify some questions that remain about the anomaly puzzle in supersymmetric theories. In particular, we consider a general N=1 supersymmetric Yang-Mills theory. The anomaly puzzle concerns the question of whether there is a consistent way to put the R-current and the stress tensor in a single supercurrent, even though in the classical theory they are in the same supermultiplet. As is well known, the classically conserved supercurrent bifurcates into two supercurrents having different anomalies in the quantum regime. The most interesting result we obtain is an explicit expression for the lowest component of one of the two supercurrents in 4-dimensional spacetime, namely the supercurrent that has the energy-momentum tensor as one of its components. This expression for the lowest component is an energy-dependent linear combination of two chiral currents, which itself does not correspond to a classically conserved chiral current. The lowest component of the other supercurrent, namely, the R-current, satisfies the Adler-Bardeen theorem. The lowest component of the first supercurrent has an anomaly that we show is consistent with the anomaly of the trace of the energy-momentum tensor. Therefore, we conclude that there is no consistent way to put the R-current and the stress tensor in a single supercurrent in the quantized theory. We also discuss and try to clarify some technical points in the derivations of the two-supercurrents in the literature. These latter points concern the significance of infrared contributions to the NSVZ beta-function and the role of the equations of motion in deriving the two supercurrents.Comment: 22 pages, no figure. v2: minor changes. v3: sections re-organized. new subsections (IVA, IVB) added. references adde

A Detailed Monte-Carlo Simulation for the Belle TOF System

We have developed a detailed Monte Carlo simulation program for the Belle TOF system. Based on GEANT simulation, it takes account of all physics processes in the TOF scintillation counters and readout electronics. The simulation reproduces very well the performance of the Belle TOF system, including the dE/dx response, the time walk effect, the time resolution, and the hit efficiency due to beam background. In this report, we will describe the Belle TOF simulation program in detail.Comment: To be submitted to NI

Reconstruction of the palaeo‐sea level of Britain and Ireland arising from empirical constraints of ice extent: implications for regional sea level forecasts and North American ice sheet volume

Reconstructions of palaeo-sea level are vital for predicting future sea level change and constraining palaeo-ice sheet reconstructions, as well as being useful for a wide array of applications across Quaternary Science. Previous reconstructions of the palaeo-sea level of Britain and Ireland relied on a circular tuning of glacio-isostatic models: input ice sheet thicknesses and extents were iteratively altered to fit relative sea level data. Here we break that circularity by utilizing new data from the BRITICE-CHRONO project, which constrains the position of the British–Irish ice sheet margin through time, and we compare derived glacio-isostatic modelling to the rich relative sea level record. We test a combination of plausible ice thickness scenarios which account for the uncertainty of ice margin position over the North Sea, demonstrating the region where regional sea level data could distinguish between different glaciation scenarios. Our optimal reconstruction is then combined with several global-scale reconstructions. As the signal of the British–Irish Ice Sheet is constrained, we demonstrate how the relative sea level record of Britain and Ireland can be used to test reconstructions of far-field ice sheets (e.g. Antarctica, Eurasia and the Laurentide). The derived palaeo-topography data are likely to be useful for multiple disciplines. Finally, our improved method of sea level reconstruction impacts predictions of contemporary vertical land motion

B-1a cells acquire their unique characteristics by bypassing the pre-BCR selection stage

B-1a cells are long-lived, self-renewing innate-like B cells that predominantly inhabit the peritoneal and pleural cavities. In contrast to conventional B-2 cells, B-1a cells have a receptor repertoire that is biased towards bacterial and self-antigens, promoting a rapid response to infection and clearing of apoptotic cells. Although B-1a cells are known to primarily originate from fetal tissues, the mechanisms by which they arise has been a topic of debate for many years. Here we show that in the fetal liver versus bone marrow environment, reduced IL-7R/STAT5 levels promote immunoglobulin kappa gene recombination at the early pro-B cell stage. As a result, differentiating B cells can directly generate a mature B cell receptor (BCR) and bypass the requirement for a pre-BCR and pairing with surrogate light chain. This 'alternate pathway' of development enables the production of B cells with self-reactive, skewed specificity receptors that are peculiar to the B-1a compartment. Together our findings connect seemingly opposing lineage and selection models of B-1a cell development and explain how these cells acquire their unique properties

Using the surface profiles of modern ice masses to inform palaeo-glacier reconstructions

Morphometric study of modern ice masses is useful because many reconstructions of glaciers traditionally draw on their shape for guidance Here we analyse data derived from the surface profiles of 200 modern ice masses-valley glaciers icefields ice caps and ice sheets with length scales from 10(0) to 10(3) km-from different parts of the world Four profile attributes are investigated relief span and two parameters C* and C that result from using Nye s (1952) theoretical parabola as a profile descriptor C* and C respectively measure each profile s aspect ratio and steepness and are found to decrease in size and variability with span This dependence quantifies the competing influences of unconstrained spreading behaviour of ice flow and bed topography on the profile shape of ice masses which becomes more parabolic as span Increases (with C* and C tending to low values of 2 5-3 3 m(1/2)) The same data reveal coherent minimum bounds in C* and C for modern ice masses that we develop into two new methods of palaeo glacier reconstruction In the first method glacial limits are known from moraines and the bounds are used to constrain the lowest palaeo ice surface consistent with modern profiles We give an example of applying this method over a three-dimensional glacial landscape in Kamchatka In the second method we test the plausibility of existing reconstructions by comparing their C* and C against the modern minimum bounds Of the 86 published palaeo ice masses that we put to this test 88% are found to be plausible The search for other morphometric constraints will help us formalise glacier reconstructions and reduce their uncertainty and subjectiveness (C) 2010 Elsevier Ltd All rights reserve