High orders of Weyl series for the heat content

This article concerns the Weyl series of spectral functions associated with the Dirichlet Laplacian in a $d$-dimensional domain with a smooth boundary. In the case of the heat kernel, Berry and Howls predicted the asymptotic form of the Weyl series characterized by a set of parameters. Here, we concentrate on another spectral function, the (normalized) heat content. We show on several exactly solvable examples that, for even $d$, the same asymptotic formula is valid with different values of the parameters. The considered domains are $d$-dimensional balls and two limiting cases of the elliptic domain with eccentricity $\epsilon$: A slightly deformed disk ($\epsilon\to 0$) and an extremely prolonged ellipse ($\epsilon\to 1$). These cases include 2D domains with circular symmetry and those with only one shortest periodic orbit for the classical billiard. We analyse also the heat content for the balls in odd dimensions $d$ for which the asymptotic form of the Weyl series changes significantly.Comment: 20 pages, 1 figur

Self-force of a point charge in the space-time of a symmetric wormhole

We consider the self-energy and the self-force for an electrically charged particle at rest in the wormhole space-time. We develop general approach and apply it to two specific profiles of the wormhole throat with singular and with smooth curvature. The self-force for these two profiles is found in manifest form; it is an attractive force. We also find an expression for the self-force in the case of arbitrary symmetric throat profile. Far from the throat the self-force is always attractive.Comment: 18 pages, 3 figures Comments: corrected pdf, enlarged pape

Laplace transform of spherical Bessel functions

We provide a simple analytic formula in terms of elementary functions for the Laplace transform j_{l}(p) of the spherical Bessel function than that appearing in the literature, and we show that any such integral transform is a polynomial of order l in the variable p with constant coefficients for the first l-1 powers, and with an inverse tangent function of argument 1/p as the coefficient of the power l. We apply this formula for the Laplace transform of the memory function related to the Langevin equation in a one-dimensional Debye model.Comment: 5 pages LATEX, no figures. Accepted 2002, Physica Script

Mortality study of 18 000 patients treated with omeprazole.

Background: The long term safety of potent gastric acid suppressive therapy has yet to be established. Method: General practice record review at a median interval of 26 months followed by retrieval of details of all deaths within four years using the UK National Health Service Central Registers in 17 936 patients prescribed omeprazole in 1993–1995. Death rates were compared with general population rates. Results: Records of 17 489 patients (97.5%) were examined. A total of 12 703 patients received further scripts for antisecretory drugs, 8097 for omeprazole only (65.6%): 3097 patients have died. All cause mortality was higher in the first year (observed/expected (O/E) 1.44 (95% confidence intervals (CI) 1.34–1.55); p<0.0001) but had fallen to population expectation by the fourth year. There were significant mortality increases in the first year, falling to or below population expectation by the fourth year, for deaths ascribed to neoplasms (1.82 (95% CI 1.58–2.08); p<0.0001), circulatory diseases (1.27 (95% CI 1.13–1.43); p<0.0001), and respiratory diseases (1.37 (95% CI 1.12–1.64); p<0.001). Increased mortality ascribed to digestive diseases (2.56 (95% CI 1.87–3.43); p<0.0001) persisted, although reduced. Increased mortality rates for cancers of the stomach (4.06 (95% CI 2.60–6.04); p<0.0001), colon and rectum (1.40 (95% CI 0.84–2.18); p=0.075), and trachea, bronchus, and lung (1.64 (95% CI 1.19–2.19); p<0.01) seen in the first year had disappeared by the fourth year but that for cancer of the oesophagus had not (O/E 7.35 (95% CI 5.20–10.09) (p<0.0001) in year 1; 2.88 (95% CI 1.62–4.79) (p<0.001) in year 4). Forty of 78 patients dying of oesophageal cancer had the disease present at registration. Twenty seven of those remaining cases had clinical evidence of Barrett’s disease, stricture, ulcer, or oesophagitis at registration (O/E 3.30 (95% CI 2.17–4.80)). Six deaths occurred in patients with hiatal hernia or reflux only (O/E 1.02 (95% CI 0.37–2.22)) and five in patients without oesophageal disease (O/E 0.77 (95% CI 0.25–1.80)). No relationships were detected with numbers of omeprazole scripts received. Conclusions: Increases in mortality associated with treatment are due to pre- existing illness, including pre-existing severe oesophageal disease. There was no evidence of an increased risk of oesophageal adenocarcinoma in those without oesophageal mucosal damage recorded at registration

Comment on:"The effect of prehospital critical care on survival following out of hospital cardiac arrest: A prospective observational study"

We read the article “The effect of pre-hospital critical care on survival following out of hospital cardiac arrest: A prospective observational study”1 with great interest. The authors should be complimented for their effort to answer the question whether or not pre-hospital critical care teams contribute to the survival of out-of-hospital cardiac arrest (OHCA) patients. In their study, they could not demonstrate a positive association between pre-hospital critical care and survival to hospital discharge, which was their primary endpoint. Although a couple of reasons for the lack of benefit from pre-hospital critical care for OHCA are provided, we think several important explanations remain unmentioned in the article

Relativistic and Radiative Corrections to the Mollow Spectrum

The incoherent, inelastic part of the resonance fluorescence spectrum of a laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. Starting from this level of description, we discuss theoretical foundations of high-precision spectroscopy using the resonance fluorescence light of strongly laser-driven atoms. Specifically, we evaluate the leading relativistic and radiative corrections to the Mollow spectrum, up to the relative orders of (Z alpha)^2 and alpha(Z alpha)^2, respectively, and Bloch-Siegert shifts as well as stimulated radiative corrections involving off-resonant virtual states. Complete results are provided for the hydrogen 1S-2P_{1/2} and 1S-2P_{3/2} transitions; these include all relevant correction terms up to the specified order of approximation and could directly be compared to experimental data. As an application, the outcome of such experiments would allow for a sensitive test of the validity of the dressed-state basis as the natural description of the combined atom-laser system.Comment: 20 pages, 1 figure; RevTe

Green's function of a finite chain and the discrete Fourier transform

A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered as an example. Comparison to Bethe ansatz clarifies the relation between the two approaches.Comment: preprint of the paper published in Int. J. Modern Physics B Vol. 20, No. 5 (2006) 593-60

Global Electric Circuit Diurnal Variation Derived from Storm Overflight and Satellite Optical Lightning Datasets

We have combined analyses of over 1000 high altitude aircraft observations of electrified clouds with diurnal lightning statistics from the Lightning Imaging Sensor (LIS) and Optical Transient Detector (OTD) to produce an estimate of the diurnal variation in the global electric circuit. Using basic assumptions about the mean storm currents as a function of flash rate and location, and the global electric circuit, our estimate of the current in the global electric circuit matches the Carnegie curve diurnal variation to within 4% for all but two short periods of time. The agreement with the Carnegie curve was obtained without any tuning or adjustment of the satellite or aircraft data. Mean contributions to the global electric circuit from land and ocean thunderstorms are 1.1 kA (land) and 0.7 kA (ocean). Contributions to the global electric circuit from ESCs are 0.22 kA for ocean storms and 0.04 kA for land storms. Using our analysis, the mean total conduction current for the global electric circuit is 2.0 kA

Probe method and a Carleman function

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions which is called a {\it needle sequence}. The needle sequence blows up on a special curve which connects a given point inside the domain with a point on the boundary of the domain and is convergent locally outside the curve. The sequence yields a reconstruction formula of unknown discontinuity, such as cavity, inclusion in a given medium from the Dirichlet-to-Neumann map. In this paper, an explicit needle sequence in {\it three dimensions} is given in a closed form. It is an application of a Carleman function introduced by Yarmukhamedov. Furthermore, an explicit needle sequence in the probe method applied to the reduction of inverse obstacle scattering problems with an {\it arbitrary} fixed wave number to inverse boundary value problems for the Helmholtz equation is also given.Comment: 2 figures, final versio