Split rank of triangle and quadrilateral inequalities

A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. [2] and Cornu´ejols and Margot [13] showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Through a result by Cook et al. [12], it is known that one particular class of facet- defining triangle inequality does not have a finite split rank. In this paper, we show that all other facet-defining triangle and quadrilateral inequalities have finite split rank. The proof is constructive and given a facet-defining triangle or quadrilateral inequality we present an explicit sequence of split inequalities that can be used to generate it.mixed integer programs, split rank, group relaxations

Global microscopic calculations of ground-state spin and parity for odd-mass nuclei

Systematic calculations of ground-state spin and parity of odd-mass nuclei have been performed within the Hartree--Fock--BCS (HFBCS) approach and the Finite-Range Droplet Model for nuclei for which experimental data are available. The unpaired nucleon has been treated perturbatively, and axial and left-right reflection symmetries have been assumed. As for the HFBCS approach, three different Skyrme forces have been used in the particle-hole channel, whereas the particle-particle matrix elements have been approximated by a seniority force. The calculations have been done for the 621 nuclei for which the Nubase 2003 data set give assignments of spin and parity with strong arguments. The agreement of both spin and parity in the self-consistent model reaches about 80% for spherical nuclei, and about 40% for well-deformed nuclei regardless of the Skyrme force used. As for the macroscopic-microscopic approach, the agreement for spherical nuclei is about 90% and about 40% for well-deformed nuclei, with different sets of spherical and deformed nuclei found in each model.Comment: 5 pages, 4 figures (three in color), 1 table, to be submitted to Physical Review

The Hα\alpha surface brightness −- radius plane as a diagnostic tool for photoionized nebulae

The H$\alpha$ surface brightness $-$ radius ($S-r$) relation is a robust distance indicator for planetary nebulae (PNe), further enhanced by different populations of PNe having distinct loci in $S-r$ space. Other types of photoionized nebulae also plot in quite distinct regions in the $S-r$ plane, allowing its use as a diagnostic tool. In particular, the nova shells and massive star ejecta (MSE) plot on relatively tight loci illustrating their evolutionary sequences. For the MSE, there is potential to develop a distance indicator for these objects, based on their trend in $S-r$ space. As high-resolution, narrowband surveys of the nearest galaxies become more commonplace, the $S-r$ plane is a potentially useful diagnostic tool to help identify the various ionized nebulae in these systems.Comment: 4 pages, 2 figures. To appear in the proceedings of the 11th Pacific Rim Conference on Stellar Astrophysics: Physics and Chemistry of the Late Stages of Stellar Evolution, held in Hong Kong, Dec 201

The Effect of Organic Trenching on Grain Yields, Soil Moisture and Root Penetration on Claypan Soils in South Dakota

The impervious nature of claypan soils decreases the rate of water infiltration, air exchange, and root penetration. As a result, these soils are recognized as “problem soils” by farmers and research workers because of the associated tillage difficulties and low crop yields. Several methods or approaches have been devised in an attempt to overcome this inherent handicap to crop production. The methods presently used are most often centered around the planting of legumes in a crop rotation or the use of a subsoiler to mechanically break up the claypan. The purpose of this study was to measure the effect of holding open the mechanically fractured claypan with a wedge of organic matter

The Commander and Individual Behavior

One of the explanations that has been postulated to explain individual differences in human behavior is the role theory. In this article the author examines this theory and then, through several examples, illustrates how it applies to the decisions that must be made by the commanding officer