Angular reduction in multiparticle matrix elements

A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of the spherical harmonics. For non-scalar couplings, the reduction gives Cartesian tensor forms for the spherical harmonic products, with tensors built from the physical vectors in the original expression. The reduction for arbitrary couplings is given in closed form, making it amenable to symbolic manipulation on a computer. The final expressions do not depend on a special choice of coordinate axes, nor do they contain azimuthal quantum number summations, nor do they have complex tensor terms for couplings to a scalar. Consequently, they are easily interpretable from the properties of the physical vectors they contain.Comment: This version contains added comments and typographical corrections to the original article. Now 27 pages, 0 figure

Effects of Government Programs on Corn, Soybeans, and Wheat Production in the U.S.

Agricultural Finance, Farm Management, Production Economics,

Importance of Baryon-Baryon Coupling in Hypernuclei

The $\Lambda N - \Sigma N$ coupling in $\Lambda$--hypernuclei and $\Lambda \Lambda - \Xi N$ coupling in $\Lambda \Lambda$--hypernuclei produce novel physics not observed in the conventional, nonstrange sector. Effects of $\Lambda \leftrightarrow \Sigma$ conversion in $^3_{\Lambda}$H are reviewed. The role of $\Lambda N - \Sigma N$ coupling suppression in the $A=4,5$ $\Lambda$--hypernuclei due to Pauli blocking is highlighted, and the implications for the structure of $^{10}_{\;\, \Lambda}$B are explored. Suppression of $\Lambda \Lambda - \Xi N$ conversion in $^{\;\;\, 6}_{\Lambda \Lambda}$He is hypothesized as the reason that the $$ matrix element is small. Measurement of $^{\;\;\, 4}_{\Lambda \Lambda}$H is proposed to investigate the full $\Lambda \Lambda - \Xi N$ interaction. The implication for $\Lambda \Lambda$ analog states is discussed.Comment: 17 pages LATEX, 1 figure uuencoded postscrip

Assessing statistical significance of periodogram peaks

The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate periodicities for different periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are given. They include an upper limit to the false alarm probability (or a lower limit to the significance). These estimations are tested numerically in order to establish regions of their practical applicability.Comment: 7 pages, 6 figures, 1 table; To be published in MNRA

Abundances of Disk Planetary Nebulae in M31 and the Radial Oxygen Gradient

We have obtained spectra of 16 planetary nebulae in the disk of M31 and determined the abundances of He, N, O, Ne, S and Ar. Here we present the median abundances and compare them with previous M31 PN disk measurements and with PNe in the Milky Way. We also derive the radial oxygen gradient in M31, which is shallower than that in the Milky Way, even accounting for M31's larger disk scale length.Comment: 2 pages, 1 figure, 1 table, to appear in the proceedings of IAU Symposium No. 283, Planetary Nebulae: An Eye to the Futur

Abundances of PNe in the Outer Disk of M31

We present spectroscopic observations and chemical abundances of 16 planetary nebulae (PNe) in the outer disk of M31. The [O III] 4363 line is detected in all objects, allowing a direct measurement of the nebular temperature essential for accurate abundance determinations. Our results show that the abundances in these M31 PNe display the same correlations and general behaviors as Type II PNe in the Milky Way Galaxy. We also calculate photoionization models to derive estimates of central star properties. From these we infer that our sample PNe, all near the peak of the Planetary Nebula Luminosity Function, originated from stars near 2 M_sun. Finally, under the assumption that these PNe are located in M31's disk, we plot the oxygen abundance gradient, which appears shallower than the gradient in the Milky Way.Comment: 48 pages, including 12 figures and 8 tables, accepted by Astrophysical Journa