15,376 research outputs found
Non-unique factorization of polynomials over residue class rings of the integers
We investigate non-unique factorization of polynomials in Z_{p^n}[x] into
irreducibles. As a Noetherian ring whose zero-divisors are contained in the
Jacobson radical, Z_{p^n}[x] is atomic. We reduce the question of factoring
arbitrary non-zero polynomials into irreducibles to the problem of factoring
monic polynomials into monic irreducibles. The multiplicative monoid of monic
polynomials of Z_{p^n}[x] is a direct sum of monoids corresponding to
irreducible polynomials in Z_p[x], and we show that each of these monoids has
infinite elasticity. Moreover, for every positive integer m, there exists in
each of these monoids a product of 2 irreducibles that can also be represented
as a product of m irreducibles.Comment: 11 page
Performance characteristics of wind profiling radars
Doppler radars used to measure winds in the troposphere and lower stratosphere for weather analysis and forecasting are lower-sensitivity versions of mesosphere-stratosphere-troposphere radars widely used for research. The term wind profiler is used to denote these radars because measurements of vertical profiles of horizontal and vertical wind are their primary function. It is clear that wind profilers will be in widespread use within five years: procurement of a network of 30 wind profilers is underway. The Wave Propagation Laboratory (WPL) has operated a small research network of radar wind profilers in Colorado for about two and one-half years. The transmitted power and antenna aperture for these radars is given. Data archiving procedures have been in place for about one year, and this data base is used to evaluate the performance of the radars. One of the prime concerns of potential wind profilers users is how often and how long wind measurements are lacking at a given height. Since these outages constitute an important part of the performance of the wind profilers, they are calculated at three radar frequencies, 50-, 405-, and 915-MHz, (wavelengths of 6-, 0.74-, and 0.33-m) at monthly intervals to determine both the number of outages at each frequency and annual variations in outages
Unusual conductance of polyyne-based molecular wires
We report a full self-consistent ab initio calculation of the current-voltage
curve and the conductance of thiolate capped polyynes in contact with gold
electrodes. We find the conductance of polyynes an order of magnitude larger
compared with other conjugated oligomers. The reason lies in the position of
the Fermi level deep in the HOMO related resonance. With the conductance weakly
dependent on the applied bias and almost independent of the length of the
molecular chain, polyynes appear as nearly perfect molecular wires.Comment: 4 pages, 5 figures, 3 table
Consequences of a Change in the Galactic Environment of the Sun
The interaction of the heliosphere with interstellar clouds has attracted
interest since the late 1920's, both with a view to explaining apparent
quasi-periodic climate "catastrophes" as well as periodic mass extinctions.
Until recently, however, models describing the solar wind - local interstellar
medium (LISM) interaction self-consistently had not been developed. Here, we
describe the results of a two-dimensional (2D) simulation of the interaction
between the heliosphere and an interstellar cloud with the same properties as
currently, except that the neutral H density is increased from the present
value of n(H) ~ 0.2 cm^-3 to 10 cm^-3. The mutual interaction of interstellar
neutral hydrogen and plasma is included. The heliospheric cavity is reduced
considerably in size (approximately 10 - 14 AU to the termination shock in the
upstream direction) and is highly dynamical. The interplanetary environment at
the orbit of the Earth changes markedly, with the density of interstellar H
increasing to ~2 cm^-3. The termination shock itself experiences periods where
it disappears, reforms and disappears again. Considerable mixing of the shocked
solar wind and LISM occurs due to Rayleigh-Taylor-like instabilities at the
nose, driven by ion-neutral friction. Implications for two anomalously high
concentrations of 10Be found in Antarctic ice cores 33 kya and 60 kya, and the
absence of prior similar events, are discussed in terms of density enhancements
in the surrounding interstellar cloud. The calculation presented here supports
past speculation that the galactic environment of the Sun moderates the
interplanetary environment at the orbit of the Earth, and possibly also the
terrestrial climate.Comment: 23 pages, 2 color plates (jpg), 3 figures (eps
Orbiting dynamic compression laboratory
In order to examine the feasibility of carrying out dynamic compression experiments on a space station, the possibility of using explosive gun launchers is studied. The question of whether powders of a refractory metal (molybdenum) and a metallic glass could be well considered by dynamic compression is examined. In both cases extremely good bonds are obtained between grains of metal and metallic glass at 180 and 80 kb, respectively. When the oxide surface is reduced and the dynamic consolidation is carried out in vacuum, in the case of molybdenum, tensile tests of the recovered samples demonstrated beneficial ultimate tensile strengths
An exact relation between Eulerian and Lagrangian velocity increment statistics
We present a formal connection between Lagrangian and Eulerian velocity
increment distributions which is applicable to a wide range of turbulent
systems ranging from turbulence in incompressible fluids to magnetohydrodynamic
turbulence. For the case of the inverse cascade regime of two-dimensional
turbulence we numerically estimate the transition probabilities involved in
this connection. In this context we are able to directly identify the processes
leading to strongly non-Gaussian statistics for the Lagrangian velocity
increments.Comment: 5 pages, 3 figure
Directed Random Walk on the Lattices of Genus Two
The object of the present investigation is an ensemble of self-avoiding and
directed graphs belonging to eight-branching Cayley tree (Bethe lattice)
generated by the Fucsian group of a Riemann surface of genus two and embedded
in the Pincar\'e unit disk. We consider two-parametric lattices and calculate
the multifractal scaling exponents for the moments of the graph lengths
distribution as functions of these parameters. We show the results of numerical
and statistical computations, where the latter are based on a random walk
model.Comment: 17 pages, 8 figure
Universal decay of scalar turbulence
The asymptotic decay of passive scalar fields is solved analytically for the
Kraichnan model, where the velocity has a short correlation time. At long
times, two universality classes are found, both characterized by a distribution
of the scalar -- generally non-Gaussian -- with global self-similar evolution
in time. Analogous behavior is found numerically with a more realistic flow
resulting from an inverse energy cascade.Comment: 4 pages, 3 Postscript figures, submitted to PR
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