Bound states in two spatial dimensions in the non-central case

We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting the number of bound states in a potential gV for g=1 is replaced by counting the number of g_i's for which zero energy bound states exist, and then the kernel of the integral equation for the zero-energy wave functon is symmetrized. One of the keys of the solution is the replacement of an inhomogeneous integral equation by a homogeneous integral equation.Comment: Work supported in part by the U.S. Department of Energy under Grant No. DE-FG02-84-ER4015

Generalization of the Calogero-Cohn Bound on the Number of Bound States

It is shown that for the Calogero-Cohn type upper bounds on the number of bound states of a negative spherically symmetric potential $V(r)$, in each angular momentum state, that is, bounds containing only the integral $\int^\infty_0 |V(r)|^{1/2}dr$, the condition $V'(r) \geq 0$ is not necessary, and can be replaced by the less stringent condition $(d/dr)[r^{1-2p}(-V)^{1-p}] \leq 0, 1/2 \leq p < 1$, which allows oscillations in the potential. The constants in the bounds are accordingly modified, depend on $p$ and $\ell$, and tend to the standard value for $p = 1/2$.Comment: 1 page. Correctly formatted version (replaces previous version

Leaky vessels as a potential source of stromal acidification in tumours

Malignant tumours are characterised by higher rates of acid production and a lower extracellular pH than normal tissues. Previous mathematical modelling has indicated that the tumour-derived production of acid leads to a gradient of low pH in the interior of the tumour extending to a normal pH in the peritumoural tissue. This paper uses mathematical modelling to examine the potential of leaky vessels as an additional source of stromal acidification in tumours. We explore whether and to what extent increasing vascular permeability in vessels can lead to the breakdown of the acid gradient from the core of the tumour to the normal tissue, and a progressive acidification of the peritumoural stroma. We compare our mathematical simulations to experimental results found in vivo with a tumour implanted in the mammary fat pad of a mouse in a window chamber construct. We find that leaky vasculature can cause a net acidification of the normal tissue away from the tumour boundary, though not a progressive acidification over time as seen in the experiments. Only through progressively increasing the leakiness can the model qualitatively reproduce the experimental results. Furthermore, the extent of the acidification predicted by the mathematical model is less than as seen in the window chamber, indicating that although vessel leakiness might be acting as a source of acid, it is not the only factor contributing to this phenomenon. Nevertheless, tumour destruction of vasculature could result in enhanced stromal acidification and invasion, hence current therapies aimed at buffering tumour pH should also examine the possibility of preventing vessel disruption

Barefoot running improves economy at high intensities and peak treadmill velocity

Aim: Barefoot running can improve running economy (RE) compared to shod running at low exercise intensities, but data is lacking for the higher intensities typical during many distance running competitions. The influence of barefoot running on the velocity at maximal oxygen uptake (vVO2max) and peak incremental treadmill test velocity (vmax) is unknown. The present study tested the hypotheses that barefoot running would improve RE, vVO2max and vmax relative to shod running. Methods: Using a balanced within-subject repeated measures design, eight male runners (aged 23.1±4.5 years, height 1.80±0.06 m, mass 73.8±11.5 kg, VO2max 4.08±0.39 L·min-1) completed a familiarization followed by one barefoot and one shod treadmill running trial, 2-14 days apart. Trial sessions consisted of a 5 minute warm-up, 5 minute rest, followed by 4×4 minute stages, at speeds corresponding to ~67, 75, 84 and 91% shod VO2max respectively, separated by a 1 minute rest. After the 4th stage treadmill speed was incremented by 0.1 km·h-1 every 15 s until participants reached volitional exhaustion. Results: RE was improved by 4.4±7.0% across intensities in the barefoot condition (P=0.040). The improvement in RE was related to removed shoe mass (r2=0.80, P=0.003) with an intercept at 0% improvement for RE at 0.520 kg total shoe mass. Both vVO2max (by 4.5±5.0%, P=0.048) and vmax (by 3.9±4.0%, P=0.030) also improved but VO2max was unchanged (p=0.747). Conclusion: Barefoot running improves RE at high exercise intensities and increases vVO2max and vmax, but further research is required to clarify the influence of very light shoe weights on RE

Estimating Monthly GDP In A General Kalman Filter Framework: Evidence From Switzerland

In this paper, we estimate deseasonalized monthly series for Swiss Gross Domestic Product at constant prices of 1990 for the period 1980-1998. They are consistent with the quarterly figures estimated by the Federal Office for Economic Development and Labour and are obtained by including information contained in related series. We present a general approach using the Kalman Filter technique nesting a great variety of interpolation setups. We evaluate competing models and provide a time series that can be used by other researchers.Interpolation, Kalman filter, National accounting.

Distributions associated with general runs and patterns in hidden Markov models

This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general classes of patterns (competing patterns and generalized later patterns), and thus, the theory includes as special cases results for a large class of problems that have wide application. The unobserved state sequence is assumed to be Markovian with a general order of dependence. An auxiliary Markov chain is associated with the state sequence and is used to simplify the computations. Two examples are given to illustrate the use of the methodology. Whereas the first application is more to illustrate the basic steps in applying the theory, the second is a more detailed application to DNA sequences, and shows that the methods can be adapted to include restrictions related to biological knowledge.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS125 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Suppressing Super-Horizon Curvature Perturbations?

We consider the possibility of suppressing superhorizon curvature perturbations after the end of the ordinary slow-roll inflationary stage. This is the opposite of the curvaton limit. We assume that large curvature perturbations are created by the inflaton and investigate if they can be diluted or suppressed by a second very homogeneous field which starts to dominate the energy density of the universe shortly after the end of inflation. We show explicit that the gravitational sourcing of inhomogeneities from the more inhomogeneous fluid to the more homogeneous fluid makes the suppression difficult if not impossible to achieve.Comment: 10 pages, 1 figure. Important revision. Conclusions more negativ

Tunneling Spectroscopy of Two-level Systems Inside Josephson Junction

We consider a two-level (TL) system with energy level separation Omega_0 inside a Josephson junction. The junction is shunted by a resistor R and is current I (or voltage V = RI) biased. If the TL system modulates the Josephson energy and/or is optically active, it is Rabi driven by the Josephson oscillations in the running phase regime near the resonance 2eV = Omega_0. The Rabi oscillations, in turn, translate into oscillations of current and voltage which can be detected in noise measurements. This effect provides an option to fully characterize the TL systems and to find the TL's contribution to the decoherence when the junction is used as a qubit.Comment: 4 page