20,848 research outputs found
An analogue of Ryser's Theorem for partial Sudoku squares
In 1956 Ryser gave a necessary and sufficient condition for a partial latin
rectangle to be completable to a latin square. In 1990 Hilton and Johnson
showed that Ryser's condition could be reformulated in terms of Hall's
Condition for partial latin squares. Thus Ryser's Theorem can be interpreted as
saying that any partial latin rectangle can be completed if and only if
satisfies Hall's Condition for partial latin squares.
We define Hall's Condition for partial Sudoku squares and show that Hall's
Condition for partial Sudoku squares gives a criterion for the completion of
partial Sudoku rectangles that is both necessary and sufficient. In the
particular case where , , , the result is especially simple, as
we show that any partial -Sudoku rectangle can be completed
(no further condition being necessary).Comment: 19 pages, 10 figure
A note on higher-dimensional magic matrices
We provide exact and asymptotic formulae for the number of unrestricted,
respectively indecomposable, -dimensional matrices where the sum of all
matrix entries with one coordinate fixed equals 2.Comment: AmS-LaTeX, 9 page
The instability of stellar structures intermediate between white dwarfs and neutron stars
Instability of stellar structures intermediate between dwarfs and neutron star
Rotation in the Orion Nebula Cluster
Eighteen fields in the Orion Nebula Cluster (ONC) have been monitored for one
or more observing seasons from 1990-99 with a 0.6-m telescope at Wesleyan
University. Photometric data were obtained in Cousins I on 25-40 nights per
season. Results from the first 3 years of monitoring were analyzed by Choi &
Herbst (1996; CH). Here we provide an update based on 6 more years of
observation and the extensive optical and IR study of the ONC by Hillenbrand
(1997) and Hillenbrand et al. (1998). Rotation periods are now available for
134 ONC members. Of these, 67 were detected at multiple epochs with identical
periods by us and 15 more were confirmed by Stassun et al. (1999) in their
study of Ori OBIc/d. The bimodal period distribution for the ONC is confirmed,
but we also find a clear dependence of rotation period on mass. This can be
understood as an effect of deuterium burning, which temporarily slows the
contraction and thus spin-up of stars with M <0.25 solar masses and ages of ~1
My. Stars with M <0.25 solar masses have not had time to bridge the gap in the
period distribution at ~4 days. Excess H-K and I-K emission, as well as CaII
infrared triplet equivalent widths (Hillenbrand et al. 1998), show weak but
significant correlations with rotation period among stars with M >0.25 solar
masses. Our results provide new observational support for the importance of
disks in the early rotational evolution of low mass stars. [abridged]Comment: 18 pages of text, 17 figures, and 4 tables; accepted for publication
in The Astronomical Journa
Terrestrial Planet Formation I. The Transition from Oligarchic Growth to Chaotic Growth
We use a hybrid, multiannulus, n-body-coagulation code to investigate the
growth of km-sized planetesimals at 0.4-2 AU around a solar-type star. After a
short runaway growth phase, protoplanets with masses of roughly 10^26 g and
larger form throughout the grid. When (i) the mass in these `oligarchs' is
roughly comparable to the mass in planetesimals and (ii) the surface density in
oligarchs exceeds 2-3 g/sq cm at 1 AU, strong dynamical interactions among
oligarchs produce a high merger rate which leads to the formation of several
terrestrial planets. In disks with lower surface density, milder interactions
produce several lower mass planets. In all disks, the planet formation
timescale is roughly 10-100 Myr, similar to estimates derived from the
cratering record and radiometric data.Comment: Astronomical Journal, accepted; 22 pages + 15 figures in ps format;
eps figures at http://cfa-www.harvard.edu/~kenyon/dl/ revised version
clarifies evolution and justifies choice of promotion masse
Rapid neutron capture in supernova explosions
Rapid neutron capture in supernova explosion
MIMO nonlinear PID predictive controller
A class of nonlinear generalised predictive controllers (NGPC) is derived for multi-input multi-output (MIMO) nonlinear systems with offset or steady-state response error. The MIMO composite controller consists of an optimal NGPC and a nonlinear disturbance observer. The design of the nonlinear disturbance observer to estimate the offset is particularly simple, as is the associated proof of overall nonlinear closed-loop system stability. Moreover, the transient error response of the disturbance observer can be arbitrarily specified by simple design parameters. Very satisfactory performance of the proposed MIMO nonlinear predictive controller is demonstrated for a three-link nonlinear robotic manipulator example
An investigation of pulsar searching techniques with the Fast Folding Algorithm
Here we present an in-depth study of the behaviour of the Fast Folding
Algorithm, an alternative pulsar searching technique to the Fast Fourier
Transform. Weaknesses in the Fast Fourier Transform, including a susceptibility
to red noise, leave it insensitive to pulsars with long rotational periods (P >
1 s). This sensitivity gap has the potential to bias our understanding of the
period distribution of the pulsar population. The Fast Folding Algorithm, a
time-domain based pulsar searching technique, has the potential to overcome
some of these biases. Modern distributed-computing frameworks now allow for the
application of this algorithm to all-sky blind pulsar surveys for the first
time. However, many aspects of the behaviour of this search technique remain
poorly understood, including its responsiveness to variations in pulse shape
and the presence of red noise. Using a custom CPU-based implementation of the
Fast Folding Algorithm, ffancy, we have conducted an in-depth study into the
behaviour of the Fast Folding Algorithm in both an ideal, white noise regime as
well as a trial on observational data from the HTRU-S Low Latitude pulsar
survey, including a comparison to the behaviour of the Fast Fourier Transform.
We are able to both confirm and expand upon earlier studies that demonstrate
the ability of the Fast Folding Algorithm to outperform the Fast Fourier
Transform under ideal white noise conditions, and demonstrate a significant
improvement in sensitivity to long-period pulsars in real observational data
through the use of the Fast Folding Algorithm.Comment: 19 pages, 15 figures, 3 table
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