Quadratic maps with a periodic critical point of period 2

We provide a complete classification of possible graphs of rational preperiodic points of endomorphisms of the projective line of degree 2 defined over the rationals with a rational periodic critical point of period 2, under the assumption that these maps have no periodic points of period at least 7. We explain how this extends results of Poonen on quadratic polynomials. We show that there are 13 possible graphs, and that such maps have at most 9 rational preperiodic points. We provide data related to the analogous classification of graphs of endomorphisms of degree 2 with a rational periodic critical point of period 3 or 4.Comment: Updated theorem 2 to rule out the cases of quadratic maps with a rational periodic critical point of period 2 and a rational periodic point of period 5 or

Spin Wave Theory of Spin 1/2 XY Model with Ring Exchange on a Triangular Lattice

We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson $J$-$K$ model with nearest neighbour exchange $J$ and four-particle ring-exchange $K$ at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. We find that the pure $J$ model (XY model) which has a well known uniform superfluid phase with an ordered parameter $M_x=\neq 0$ at zero temperature is quickly destroyed by the inclusion of a negative-$K$ ring-exchange interactions, favouring a state with a $(\frac{4\pi}{3}, 0)$ ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz-Thouless phase transition ($T_{KT}$) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for K \textless 0, the phase boundary monotonically decreases to T=0 at $K/J = -4/3$, where a phase transition is expected and $T_{KT}$ decreases rapidly while for positive $K$, $T_{KT}$ reaches a maximum at some $K\neq 0$. It has been shown on a square lattice using quantum Monte Carlo(QMC) simulations that for small K\textgreater 0 away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased\cite{F}. Our result seems to agree with this trend found in QMC simulations

An economic analysis of five selected LANDSAT assisted information systems in Oregon

A comparative cost analysis was performed on five LANDSAT-based information systems. In all cases, the LANDSAT system was found to have cost advantages over its alternative. The information sets generated by LANDSAT and the alternative method are not identical but are comparable in terms of satisfying the needs of the sponsor. The information obtained from the LANDSAT system in some cases is said to lack precision and detail. On the other hand, it was found to be superior in terms of providing information on areas that are inaccessible and unobtainable through conventional means. There is therefore a trade-off between precision and detail, and considerations of costs. The projects examined were concerned with locating irrigation circles in Morrow County; monitoring tansy ragwort infestation; inventoring old growth Douglas fir near Spotted Owl habitats; inventoring vegetation and resources in all state-owned lands; and determining and use for Columbia River water policies

Long-period intensity pulsations in the solar corona during activity cycle 23

We report on the detection (10 \sigma) of 917 events of long-period (3 to 16 hours) intensity pulsations in the 19.5 nm passband of the SOHO Extreme ultraviolet Imaging Telescope. The data set spans from January 1997 to July 2010, i.e the entire solar cycle 23 and the beginning of cycle 24. The events can last for up to six days and have relative amplitudes up to 100%. About half of the events (54%) are found to happen in active regions, and 50% of these have been visually associated with coronal loops. The remaining 46% are localized in the quiet Sun. We performed a comprehensive analysis of the possible instrumental artifacts and we conclude that the observed signal is of solar origin. We discuss several scenarios which could explain the main characteristics of the active region events. The long periods and the amplitudes observed rule out any explanation in terms of magnetohydrodynamic waves. Thermal nonequilibrium could produce the right periods, but it fails to explain all the observed properties of coronal loops and the spatial coherence of the events. We propose that moderate temporal variations of the heating term in the energy equation, so as to avoid a thermal nonequilibrium state, could be sufficient to explain those long-period intensity pulsations. The large number of detections suggests that these pulsations are common in active regions. This would imply that the measurement of their properties could provide new constraints on the heating mechanisms of coronal loops.Comment: 10 pages, 4 figure

Combinatorial coherent states via normal ordering of bosons

We construct and analyze a family of coherent states built on sequences of integers originating from the solution of the boson normal ordering problem. These sequences generalize the conventional combinatorial Bell numbers and are shown to be moments of positive functions. Consequently, the resulting coherent states automatically satisfy the resolution of unity condition. In addition they display such non-classical fluctuation properties as super-Poissonian statistics and squeezing.Comment: 12 pages, 7 figures. 20 references. To be published in Letters in Mathematical Physic

Some partial-unit-memory convolutional codes

The results of a study on a class of error correcting codes called partial unit memory (PUM) codes are presented. This class of codes, though not entirely new, has until now remained relatively unexplored. The possibility of using the well developed theory of block codes to construct a large family of promising PUM codes is shown. The performance of several specific PUM codes are compared with that of the Voyager standard (2, 1, 6) convolutional code. It was found that these codes can outperform the Voyager code with little or no increase in decoder complexity. This suggests that there may very well be PUM codes that can be used for deep space telemetry that offer both increased performance and decreased implementational complexity over current coding systems

A new look at the problem of gauge invariance in quantum field theory

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.Comment: Accepted by Physica Scripta. 27 page