31,895 research outputs found
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 , even in regions where both the electric field
and the magnetic field 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 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, at time and
at time , are connected by two temporal wormholes, one leading from
the past side of to t the future side of and the other from the
past side of to the future side of . 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
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