On the t-Term Rank of a Matrix

For t a positive integer, the t-term rank of a (0,1)-matrix A is defined to be the largest number of 1s in A with at most one 1 in each column and at most t 1s in each row. Thus the 1-term rank is the ordinary term rank. We generalize some basic results for the term rank to the t-term rank, including a formula for the maximum term rank over a nonempty class of (0,1)-matrices with the the same row sum and column sum vectors. We also show the surprising result that in such a class there exists a matrix which realizes all of the maximum terms ranks between 1 and t.Comment: 18 page

Popular Anger or Planned Pogrom? What Really Happened During Kristallnacht 78 Years Ago

Dr. Michael A. Meyer, Adolph S. Ochs Professor Emeritus, Hebrew-Union College-Jewish Institute of Religion, Cincinnati, historian, author.https://digitalcommons.fairfield.edu/bennettcenter-posters/1337/thumbnail.jp

Temperature and brain death determination: need for updated criteria

For an excellent review on the diagnosis of brain death, the interested reader is directed to the review of <a href="/journals/index.php/ni/article/view/ni.2010.e2" target="_blank">Machado</a> appearing in this journal; the author reviews all aspects of brain death and cites nine different references where the minimum temperature for brain death exams appear to have been at least 32°C. Given the new data listed above, it is clearly time for a reconsideration of the how we approach the exam for diagnosis of brain death – normal or near normal temperatures of 36°C and above are very reasonable starting points

Cyclic Matching Sequencibility of Graphs

We define the cyclic matching sequencibility of a graph to be the largest integer $d$ such that there exists a cyclic ordering of its edges so that every $d$ consecutive edges in the cyclic ordering form a matching. We show that the cyclic matching sequencibility of $K_{2m}$ and $K_{2m+1}$ equal $m-1$

Polarization observables in the longitudinal basis for pseudo-scalar meson photoproduction using a density matrix approach

The complete expression for the intensity in pseudo-scalar meson photoproduction with a polarized beam, target, and recoil baryon is derived using a density matrix approach that offers great economy of notation. A Cartesian basis with spins for all particles quantized along a single direction, the longitudinal beam direction, is used for consistency and clarity in interpretation. A single spin-quantization axis for all particles enables the amplitudes to be written in a manifestly covariant fashion with simple relations to those of the well-known CGLN formalism. Possible sign discrepancies between theoretical amplitude-level expressions and experimentally measurable intensity profiles are dealt with carefully. Our motivation is to provide a coherent framework for coupled-channel partial-wave analysis of several meson photoproduction reactions, incorporating recently published and forthcoming polarization data from Jefferson Lab.Comment: 11 pages, 2 figure

An Improbable Solution to the Underluminosity of 2M1207B: A Hot Protoplanet Collision Afterglow

We introduce an alternative hypothesis to explain the very low luminosity of the cool (L-type) companion to the ~25 M_Jup ~8 Myr-old brown dwarf 2M1207A. Recently, Mohanty et al. (2007) found that effective temperature estimates for 2M1207B (1600 +- 100 K) are grossly inconsistent with its lying on the same isochrone as the primary, being a factor of ~10 underluminous at all bands between I (0.8 um) and L' (3.6 um). Mohanty et al. explain this discrepency by suggesting that 2M1207B is an 8 M_Jup object surrounded by an edge-on disk comprised of large dust grains producing 2.5^m of achromatic extinction. We offer an alternative explanation: the apparent flux reflects the actual source luminosity. Given the temperature, we infer a small radius (~49,000 km), and for a range of plausible densities, we estimate a mass < M_Jup. We suggest that 2M1207B is a hot protoplanet collision afterglow and show that the radiative timescale for such an object is >~1% the age of the system. If our hypothesis is correct, the surface gravity of 2M1207B should be an order of magnitude lower than predicted by Mohanty et al. (2007).Comment: ApJ Letters, in press (11 pages