4,415 research outputs found
Oscillation of Fourier Integrals with a spectral gap
Suppose that Fourier transform of a function f is zero on the interval
[-a,a]. We prove that the lower density of sign changes of f is at least a/pi,
provided that f is a locally integrable temperate distribution in the sense of
Beurling, with non-quasianalytic weight. We construct an example showing that
the last condition cannot be omitted.Comment: 1 Figur
Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point
A parametric oscillator with damping driven by white noise is studied. The
mean square displacement (MSD) in the long-time limit is derived analytically
for the case that the static force vanishes, which was not treated in the past
work \cite{tashiro07}. The formula is asymptotic but is applicable to a general
periodic function. On the basis of this formula, some periodic functions
reducing MSD remarkably are proposed
A cosmological bound on mass difference
We demonstrate that CPT-violation due to mass difference generates
a non-zero photon mass. As a result the cosmological bounds on the photon mass
lead to the bounds on mass difference which are at least by 10 orders
of magnitude stronger than the direct experimental bound.Comment: 8 page
Time machines and the Principle of Self-Consistency as a consequence of the Principle of Stationary Action (II): the Cauchy problem for a self-interacting relativistic particle
We consider the action principle to derive the classical, relativistic motion
of a self-interacting particle in a 4-D Lorentzian spacetime containing a
wormhole and which allows the existence of closed time-like curves. In
particular, we study the case of a pointlike particle subject to a
`hard-sphere' self-interaction potential and which can traverse the wormhole an
arbitrary number of times, and show that the only possible trajectories for
which the classical action is stationary are those which are globally
self-consistent. Generically, the multiplicity of these trajectories (defined
as the number of self-consistent solutions to the equations of motion beginning
with given Cauchy data) is finite, and it becomes infinite if certain
constraints on the same initial data are satisfied. This confirms the previous
conclusions (for a non-relativistic model) by Echeverria, Klinkhammer and
Thorne that the Cauchy initial value problem in the presence of a wormhole
`time machine' is classically `ill-posed' (far too many solutions). Our results
further extend the recent claim by Novikov et al. that the `Principle of
self-consistency' is a natural consequence of the `Principle of minimal
action.'Comment: 39 pages, latex fil
New global stability estimates for the Gel'fand-Calderon inverse problem
We prove new global stability estimates for the Gel'fand-Calderon inverse
problem in 3D. For sufficiently regular potentials this result of the present
work is a principal improvement of the result of [G. Alessandrini, Stable
determination of conductivity by boundary measurements, Appl. Anal. 27 (1988),
153-172]
Oscillation of linear ordinary differential equations: on a theorem by A. Grigoriev
We give a simplified proof and an improvement of a recent theorem by A.
Grigoriev, placing an upper bound for the number of roots of linear
combinations of solutions to systems of linear equations with polynomial or
rational coefficients.Comment: 16 page
Geometry and Statistics of Cosmic Microwave Polarization
Geometrical and statistical properties of polarization of CMB are analyzed.
Singular points of the vector field which describes CMB polarization are found
and classified. Statistical distribution of the singularities is studied. A
possible signature of tensor perturbations in CMB polarization is discussed.
For a further analysis of CMB statistics Minkowski functionals are used, which
present a technically simple method to search for deviations from a Gaussian
distribution.Comment: 37 pages, 5 figures, submitted in Int.J.Mod.Phys.
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