Identifying an \u3cem\u3em\u3c/em\u3e-Ary Partition Identity through an \u3cem\u3em\u3c/em\u3e-Ary Tree

The Calkin-Wilf tree is well-known as one way to enumerate the rationals, but also may be used to count hyperbinary partitions of an integer, h2(n). We present an m-ary tree which is a generalization of the Calkin-Wilf tree and show how it may be used to count the hyper m-ary partitions of an integer, hm(n). We then use properties of the m-ary tree to prove an identity relating values of h2 to values of hm, showing that one sequence is a subsequence of the other. Finally, we give a bijection between the partitions to reprove our identity

Thirty four Galloway Lochs: bathymetry, water quality and surface sediment diatom assemblages

Bathymetric descriptions of thirty four Galloway lochs are given together with water quality data for 1983-85. Results of diatom analysis of surface sediment collected from each loch are presented in tabular form. Lake water pH is generally lower in November samples than in samples collected in summer months. Cation exchange, following deposition of sea salts on peaty catchments, is suggested as a partial winter period. cause of pH depression in the winter period. Where lakes are deep enough, summer thermal stratification usually occurs between 5 and 8 m depth. Floristic diversity of the periphyton component of surface sediment diatom assemblages is shown to increase generally with pH

Volcanology from Space: Interpreting Volcanic Processes Using Space-Borne Remote Sensing Imagery

No abstract availabl

Teacher Knowledge and Selection of Evidence-Based Practices: A survey study

Federal legislation and state and local policies mandate the use of evidence-based practices (EBPs) and aim to improve the quality of education for all students. Federal mandates (No Child Left Behind (NCLB) Act of 2001) coupled with teacher training requirements and the need for identifying effective practices for use with students with and without disabilities, highlight the need for teachers to not only implement EBPs but to identify such practices for implementation. The passage of NCLB marked the first time in education that the use of scientific research to inform instructional decisions was mandated

Analysis of Chaos-Induced Pulse Trains in the Ionization of Hydrogen

We examine excitation (by a short laser pulse) of a hydrogen atom in parallel electric and magnetic fields, from an initial tightly bound state to a state above the classical ionization threshold. We predict that the atom ionizes by emitting a train of electron pulses. This prediction is based on the classical dynamics of electron escape. In particular, the pulse train is due to classical chaos, which occurs for nonvanishing magnetic field. We connect the structure of the pulse train to fractal structure in the escape dynamics, and discuss several issues of experimental interest, with a particular emphasis on understanding the resolution of individual pulses. A brief account of this work appeared previously as a Letter [Phys. Rev. Lett. 92, 073001 (2004)]

Chaos-Induced Pulse Trains in the Ionization of Hydrogen

We predict that a hydrogen atom in parallel electric and magnetic fields, excited by a short laser pulse to an energy above the classical saddle, ionizes via a train of electron pulses. These pulses are a consequence of classical chaos induced by the magnetic field. We connect the structure of this pulse train (e.g., pulse size and spacing) to fractal structure in the classical dynamics. This structure displays a weak self-similarity, which we call “epistrophic self-similarity.” We demonstrate how this self-similarity is reflected in the pulse train

Processing and Transmission of Information

Contains reports on five research projects.National Aeronautics and Space Administration (Grant NGL 22-009-013)National Science Foundation (Grant GK-5800

Periodic Heart Rate Decelerations in Premature Infants

The pacemaking system of the heart is complex; a healthy heart constantly integrates and responds to extracardiac signals, resulting in highly complex heart rate patterns with a great deal of variability. In the laboratory and in some pathological or age-related states, however, dynamics can show reduced complexity that is more readily described and modeled. Reduced heart rate complexity has both clinical and dynamical significance - it may provide warning of impending illness or clues about the dynamics of the heart\u27s pacemaking system. In this paper, we describe simple and interesting heart rate dynamics that we have observed in premature human infants - reversible transitions to large-amplitude periodic oscillations - and we show that the appearance and disappearance of these periodic oscillations can be described by a simple mathematical model, a Hopf bifurcation

The CHESS survey of the L1157-B1 shock: the dissociative jet shock as revealed by Herschel--PACS

Outflows generated by protostars heavily affect the kinematics and chemistry of the hosting molecular cloud through strong shocks that enhance the abundance of some molecules. L1157 is the prototype of chemically active outflows, and a strong shock, called B1, is taking place in its blue lobe between the precessing jet and the hosting cloud. We present the Herschel-PACS 55--210 micron spectra of the L1157-B1 shock, showing emission lines from CO, H2O, OH, and [OI]. The spatial resolution of the PACS spectrometer allows us to map the warm gas traced by far-infrared (FIR) lines with unprecedented detail. The rotational diagram of the high-Jup CO lines indicates high-excitation conditions (Tex ~ 210 +/- 10 K). We used a radiative transfer code to model the hot CO gas emission observed with PACS and in the CO (13-12) and (10-9) lines measured by Herschel-HIFI. We derive 20010^5 cm-3. The CO emission comes from a region of about 7 arcsec located at the rear of the bow shock where the [OI] and OH emission also originate. Comparison with shock models shows that the bright [OI] and OH emissions trace a dissociative J-type shock, which is also supported by a previous detection of [FeII] at the same position. The inferred mass-flux is consistent with the "reverse" shock where the jet is impacting on the L1157-B1 bow shock. The same shock may contribute significantly to the high-Jup CO emission.Comment: 7 pages, 9 figures, accepted for publication in Astronomy and Astrophysic

The ortho-to-para ratio of ammonia in the L1157 outflow

We have measured the ortho-to-para ratio of ammonia in the blueshifted gas of the L1157 outflow by observing the six metastable inversion lines from (J, K) = (1, 1) to (6, 6). The highly excited (5, 5) and (6, 6) lines were first detected in the low-mass star forming regions. The rotational temperature derived from the ratio of four transition lines from (3, 3) to (6, 6) is 130-140 K, suggesting that the blueshifted gas is heated by a factor of ~10 as compared to the quiescent gas. The ortho-to-para ratio of the NH3 molecules in the blueshifted gas is estimated to be 1.3--1.7, which is higher than the statistical equilibrium value. This ratio provides us with evidence that the NH3 molecules have been evaporated from dust grains with the formation temperature between 18 and 25 K. It is most likely that the NH3 molecules on dust grains have been released into the gas phase through the passage of strong shock waves produced by the outflow. Such a scenario is supported by the fact that the ammonia abundance in the blueshifted gas is enhanced by a factor of ~5 with respect to the dense quiescent gas.Comment: 16 pages, including 3 PS figures. To appear in the ApJ (Letters). aastex macro