Computer program determines exact two-sided tolerance limits for normal distributions

Computer program determines by numerical integration the exact statistical two-sided tolerance limits, when the proportion between the limits is at least a specified number. The program is limited to situations in which the underlying probability distribution for the population sampled is the normal distribution with unknown mean and variance

The scalar complex potential and the Aharonov-Bohm effect

The Aharonov-Bohm effect is traditionally attributed to the effect of the electromagnetic 4-potential $A$, even in regions where both the electric field $\mathbf{E}$ and the magnetic field $\mathbf{B}$ are zero. The AB effect reveals that multiple-valued functions play a crucial role in the description of an electromagnetic field. We argue that the quantity measured by AB experiments is a difference in values of a multiple-valued complex function, which we call a complex potential or {pre-potential. We show that any electromagnetic field can be described by this pre-potential, and give an explicit expression for the electromagnetic field tensor through this potential. The pre-potential is a modification of the two scalar potential functions.Comment: 10 pages 2 figure

Necrotic tumor growth: an analytic approach

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.Comment: 14 pages, 3 figure

A numerical study of the r-mode instability of rapidly rotating nascent neutron stars

The first results of numerical analysis of classical r-modes of {\it rapidly} rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity are numerically solved without the slow rotation approximation. A critical curve of gravitational wave emission induced instability which restricts the rotational frequencies of hot young neutron stars is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the `evolutionary curves' along which neutron stars are supposed to evolve as cooling and spinning-down proceed. Rotational frequencies of $1.4M_{\odot}$ stars suffering from this instability decrease to around 100Hz when the standard cooling mechanism of neutron stars is employed. This result confirms the results of other authors who adopted the slow rotation approximation.Comment: 4 pages, 2 figures; MNRAS,316,L1(2000

The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of a Time Machine

We study the propagator of a non-relativistic, non-interacting particle in any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an external, flat spacetime in which two spatial regions, $V_-$ at time $t_-$ and $V_+$ at time $t_+$, are connected by two temporal wormholes, one leading from the past side of $V_-$ to t the future side of $V_+$ and the other from the past side of $V_+$ to the future side of $V_-$. We express the propagator explicitly in terms of those for ordinary, flat spacetime and for the two wormholes; and from that expression we show that the propagator satisfies completeness and unitarity in the initial and final ``chronal regions'' (regions without closed timelike curves) and its propagation from the initial region to the final region is unitary. However, within the time machine it satisfies neither completeness nor unitarity. We also give an alternative proof of initial-region-to-final-region unitarity based on a conserved current and Gauss's theorem. This proof can be carried over without change to most any non-relativistic time-machine spacetime; it is the non-relativistic version of a theorem by Friedman, Papastamatiou and Simon, which says that for a free scalar field, quantum mechanical unitarity follows from the fact that the classical evolution preserves the Klein-Gordon inner product

Elastic scattering of low energy pions by nuclei and the in-medium isovector pi N amplitude

Measurements of elastic scattering of 21.5 MeV pi+ and pi- by Si, Ca, Ni and Zr were made using a single arm magnetic spectrometer. Absolute calibration was made by parallel measurements of Coulomb scattering of muons. Parameters of a pion-nucleus optical potential were obtained from fits to all eight angular distributions put together. The `anomalous' s-wave repulsion known from pionic atoms is clearly observed and could be removed by introducing a chiral-motivated density dependence of the isovector scattering amplitude, which also greatly improved the fits to the data. The empirical energy dependence of the isoscalar amplitude also improves the fits to the data but, contrary to what is found with pionic atoms, on its own is incapable of removing the anomaly.Comment: 20 pages, 5 figures, 5 tables. V2 added details on uncertainties,extended discussion. To appear in PR

Plaintiff Estate\u27s Motion for Sanctions Against Cuyahoga County Prosecutor William D. Mason

Estate’s motion for sanctions against William D. Mason for violation of Disciplinary Rule 7-107, which provides in pertinent part that “A lawyer who is participating. . . in. . . a matter shall not make an extra judicial statement that a reasonable person would expect to be disseminated. . . if the lawyer knows or. . . should know. . . will. . . materially prejudice an adjudicated procedure.” The Estate alleged that Prosecutor Mason violated D.R. 7-107 in a press conference interview on February 22, 2000, which resulted in the following Plain Dealer headline: “Sheppard Sought $3.25 Million, Mason Says.” The Estate argued that Mason improperly and inaccurately revealed details of a failed settlement agreement between the parties and that this could have had a prejudicial effect on the jury, which in fact caused the court to voir dire all eleven jurists, one of which actually saw the headline

Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

Recent studies have raised doubts about the occurrence of r modes in Newtonian stars with a large degree of differential rotation. To assess the validity of this conjecture we have solved the eigenvalue problem for Rossby-Haurwitz waves (the analogues of r waves on a thin-shell) in the presence of differential rotation. The results obtained indicate that the eigenvalue problem is never singular and that, at least for the case of a thin-shell, the analogues of r modes can be found for arbitrarily large degrees of differential rotation. This work clarifies the puzzling results obtained in calculations of differentially rotating axi-symmetric Newtonian stars.Comment: 8pages, 3figures. Submitted to CQ

Influence of the Coulomb Interaction on the Chemical Equilibrium of Nuclear Systems at Break-Up

The importance of a Coulomb correction to the formalism proposed by Albergo et al. for determining the temperatures of nuclear systems at break-up and the ensities of free nucleon gases is discussed. While the proposed correction has no effect on the temperatures extracted based on double isotope ratios, it becomes non-negligible when such temperatures or densities of free nucleon gases are extracted based on multiplicities of heavier fragments of different atomic numbers

The rotational modes of relativistic stars: Numerical results

We study the inertial modes of slowly rotating, fully relativistic compact stars. The equations that govern perturbations of both barotropic and non-barotropic models are discussed, but we present numerical results only for the barotropic case. For barotropic stars all inertial modes are a hybrid mixture of axial and polar perturbations. We use a spectral method to solve for such modes of various polytropic models. Our main attention is on modes that can be driven unstable by the emission of gravitational waves. Hence, we calculate the gravitational-wave growth timescale for these unstable modes and compare the results to previous estimates obtained in Newtonian gravity (i.e. using post-Newtonian radiation formulas). We find that the inertial modes are slightly stabilized by relativistic effects, but that previous conclusions concerning eg. the unstable r-modes remain essentially unaltered when the problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure