Counting (3+1) - Avoiding permutations

A poset is {\it (\3+\1)-free} if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because of their connection with interval orders and their appearance in the (\3+\1)-free Conjecture of Stanley and Stembridge. The dimension 2 posets $P$ are exactly the ones which have an associated permutation $\pi$ where $i\prec j$ in $P$ if and only if $i<j$ as integers and $i$ comes before $j$ in the one-line notation of $\pi$. So we say that a permutation $\pi$ is {\it (\3+\1)-free} or {\it (\3+\1)-avoiding} if its poset is (\3+\1)-free. This is equivalent to $\pi$ avoiding the permutations 2341 and 4123 in the language of pattern avoidance. We give a complete structural characterization of such permutations. This permits us to find their generating function.Comment: 17 page

The Effects of Children's Time Use and Home and Neighborhood Quality on their Body Weight and Cognitive/Behavioral Development

We estimate a directional distance function to assess the impacts of multiple time-varying parent and child inputs on a cluster of jointly produced child outcomes for children aged 7 to 13 years. The directional distance function specification avoids several well-known empirical problems associated with analysis of household production data, namely, the need to aggregate inputs and outputs, assume separability among inputs and outputs, or estimate reduced form equations. Using a balanced panel of families from the National Longitudinal Survey of Youth-Child Sample for 1996 to 2000, we assess the marginal contributions of home and neighborhood environmental quality and children's time allocations, on their math and reading performance, behavior problems, and body mass index. We also measure productivity growth, technical change, efficiency change, and technical efficiency for production of child outcomes. Our results indicate significant jointness among good and bad child outcomes. Significant improvements in children's good outcomes and reductions in bad outcomes are also associated with a better home and parent perceived neighborhood environment, Head Start participation, and increased family time spent together during meals. Children's productivity growth is found to be highest at age 8 years and diminishes thereafter.Health Economics and Policy, Labor and Human Capital,

Characteristics and variability of storm tracks in the north Pacific, Bering Sea, and Alaska

The North Pacific and Bering Sea regions represent loci of cyclogenesis and storm track activity. In this paper climatological properties of extratropical storms in the North Pacific/Bering Sea are presented based upon aggregate statistics of individual storm tracks calculated by means of a feature-tracking algorithm run using NCEP–NCAR reanalysis data from 1948/49 to 2008, provided by the NOAA/Earth System Research Laboratory and the Cooperative Institute for Research in Environmental Sciences, Climate Diagnostics Center. Storm identification is based on the 850-hPa relative vorticity field (ζ) instead of the often-used mean sea level pressure; ζ is a prognostic field, a good indicator of synoptic-scale dynamics, and is directly related to the wind speed. Emphasis extends beyond winter to provide detailed consideration of all seasons. Results show that the interseasonal variability is not as large during the spring and autumn seasons. Most of the storm variables—genesis, intensity, track density—exhibited a maxima pattern that was oriented along a zonal axis. From season to season this axis underwent a north–south shift and, in some cases, a rotation to the northeast. This was determined to be a result of zonal heating variations and midtropospheric moisture patterns. Barotropic processes have an influence in shaping the downstream end of storm tracks and, together with the blocking influence of the coastal orography of northwest North America, result in high lysis concentrations, effectively making the Gulf of Alaska the “graveyard” of Pacific storms. Summer storms tended to be longest in duration. Temporal trends tended to be weak over the study area. SST did not emerge as a major cyclogenesis control in the Gulf of Alaska

The Moon, The Skies And You, Dear

https://digitalcommons.library.umaine.edu/mmb-vp/4411/thumbnail.jp

On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model

We investigate the quantum Jaynes-Cummings model - a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the eigenvalues of the commuting Hamiltonians. A scalar product in the separated variables representation is found for which the commuting Hamiltonians are Hermitian. In the semi classical limit the Bethe roots accumulate on very specific curves in the complex plane. We give the equation of these curves. They build up a system of cuts modeling the spectral curve as a two sheeted cover of the complex plane. Finally, we extend some of these results to the XXX Heisenberg spin chain.Comment: 16 page

Magnetization switching and domain-wall propagation behavior in edge-modulated ferromagnetic nanowire structures

The magnetization reversal processes in ferromagnetic nanowires with sinusoidally modulated edges were investigated as a function of modulation amplitude and wavelength. The reversal processes were studied in two regimes: nucleation controlled reversal and magnetization reversal mediated by domain-wall propagation. In the latter case, domain walls were introduced using both nucleation-pad structures and local pulsed-field injection techniques. The reversal behavior shows that competing effects govern the switching fields in these structures, giving a minimum as a function of modulation wavelength, showing promising results for improved control of domain-wall propagation behavior. The experimental results were interpreted with detailed micromagnetic simulations and an analytical model, based on the demagnetization effects of the modulation upon the spin structure of the wire. The analysis highlights consistent trends in the reversal behavior resulting from modulation, and, significantly, the switching behavior is found to be scalable in relation to the amplitude and wavelength