Nordhaus–Gaddum problems for power domination

A power dominating set of a graph G is a set S of vertices that can observe the entire graph under the rules that (1) the closed neighborhood of every vertex in S is observed, and (2) if a vertex and all but one of its neighbors are observed, then the remaining neighbor is observed; the second rule is applied iteratively. The power domination number of G, denoted by gamma p(G), is the minimum number of vertices in a power dominating set. A Nordhaus-Gaddum problem for power domination is to determine a tight lower or upper bound on gamma p(G) + gamma p(G) or gamma p(G).gamma p(G), where G denotes the complement of G. The upper and lower Nordhaus-Gaddum bounds over all graphs for the power domination number follow from known bounds on the domination number and examples. In this note we improve the upper sum bound for the power domination number substantially for graphs having the property that both the graph and its complement are connected. For these graphs, our bound is tight and is also significantly better than the corresponding bound for the domination number. We also improve the product upper bound for the power domination number for graphs with certain properties

Zero forcing and power domination for graph products

The power domination number arose from the monitoring of electrical networks, and methods for its determination have the associated application. The zero forcing number arose in the study of maximum nullity among symmetric matrices described by a graph (and also in control of quantum systems and in graph search algorithms). There has been considerable effort devoted to the determination of the power domination number, the zero forcing number, and maximum nullity for specific families of graphs. In this paper we exploit the natural relationship between power domination and zero forcing to obtain results for the power domination number of tensor products and the zero forcing number of lexicographic products of graphs. In addition, we establish a general lower bound for the power domination number of a graph based on the maximum nullity of the matrices described by the graph. We also establish results for the zero forcing number and maximum nullity of tensor products and Cartesian products of certain graphs

Burnout and Substance Use in Collegiate Athletic Trainers

CONTEXT: The Smith Cognitive-Affective Model of Athletic Burnout suggests that athletic trainers (ATs) suffering from burnout may engage in substance use as a coping behavior. Increases in self-reported burnout symptoms are often associated with increases in heavy episodic drinking and tobacco use among various health care providers. However, this relationship has not been examined thoroughly. OBJECTIVE: To investigate the prevalence of substance use in ATs and identify relationships between symptoms of burnout and substance use among ATs. DESIGN: Cross-sectional study. SETTING: Web-based survey. PATIENTS OR OTHER PARTICIPANTS: A total of 783 certified ATs working full time in the collegiate or university setting were sampled for this study. Graduate assistant and other part-time ATs were excluded. The survey was distributed via the National Athletic Trainers\u27 Association membership directory e-mail broadcast service. MAIN OUTCOME MEASURE(S): A 100-item online questionnaire consisting of items from previously used scales was used for this study. The survey included the Maslach Burnout Inventory and questions on substance use from the Monitoring the Future study. Multiple regression analyses were performed to analyze the survey data. All independent (Maslach Burnout Inventory subscales) and dependent (use of alcohol, tobacco, and marijuana) variables were mapped to the Smith Cognitive-Affective Model of Athletic Burnout to determine which dimensions of burnout altered the odds of self-reported substance use. RESULTS: Almost half (46.3%) of participants admitted to at least 1 binge-drinking episode. However, the use of cigarettes, smokeless tobacco, marijuana, and energy drinks during the previous month was less pronounced in the sample. Emotional exhaustion (B = .008, P = .023) and personal accomplishment (B = -.016, P = .02) were significantly correlated with binge drinking. Emotional exhaustion (Exp[B] = 1.017, P \u3c .001) was also significantly positively correlated with energy-drink consumption. CONCLUSIONS: Some ATs engaged in heavy episodic drinking. Emotional exhaustion and a decreased sense of personal accomplishment were significantly correlated with this behavior

Portfolio Vol. IV N 4

Wager, Dick. Collective Bargaining. Prose. 3-5. Raymond, Toby. Lochinvar Rides Again. Poetry. 6. Wyman, John. Lily of the Alley. Prose. 8-9. Benson, Virginia. Lost Cause. Prose. 10. Collins, Peg. The Curtain Falls. Prose. 11. Dorsey, Ann. Jack. Picture. 12. Sulke, Jim. Old Pete. Picture. 12. Myers, Sue. Jerry. Picture. 12. Rosenthal, Joan. Canadian Farmhouse. Picture. 13. Deeds, Ed. Mirror Lake. Picture. 13. Peters, Doris. Trees. Picture. 13. Seagrave, Leslie. Chinese Coins. Poetry. 14. White, Molly. Thoughts in the Rain. Poetry. 14. Smith, Duke. Keeping the Records Straight. Prose. 15. Stocker, Ed. Joe. Prose. 16-17. Saunders, John. Seven Year\u27s Luck. Prose. 19-22

Portfolio Vol. IV N 3

Benson, Virginia. Rejected. Prose. 3. Phillips, Alison. Lure in April. Poetry. 6. Shields, Margaret. Wedding Morning. Prose. 7. Willett, Thelma. Ex Libris: G.K.W. Poetry. 8. Benson, Virginia. High Note. Poetry. 8. Maxwell, Bob. Discovery. Poetry. 8. Eschman, Karl. The Case for Modern Music. Prose. 8-9. Wyman, John. Dissonance. Prose. 10-11. Hart, Dorothy. The Origin of Memorial Day. Prose. 12. Reed, Roger. Notes on the Drama. Prose. 13. Parker, Mab. Black Girl. Picture. 14. Mather, William. The Pasquin. Prose. 15. Hammer, John. Over the Green Grass. Prose. 16. Maxwell, Bob. Genesis... Poetry. 19. Maxwell, Bob. We Three. Poetry. 19. Stransky, Ed. Concerning The Well-Known \u27Butch.\u27 Prose. 20. Seagrave, Leslie. Memory. Prose. 21

Portfolio Vol. V N 1

Dippery, Franklin M. Unnamed. Prose. 2. Shields, Margaret. The Dance . Prose. 4. Raymond, Toby. Tundra . Prose. 7. Pruyn, Scott. Lest We Forget . Poem. 9. Tolan, Maurice. Pronounced \u27Mejico\u27 . Picture. 10. Phillips, Alison. Pronounced Mejico . Prose. 10. Benson, Virginia. Matter of Opinion . Poem. 12. Benson, Virginia. Cloud Shadows . Poem. 12. Benson, Virginia. Autumn Organist . Poem. 12. Sherman, Hoyt Leon. Orchard . Picture. 12. Nussbaum, Ervin. The End of John Brown . Picture. 13. Brannon, Pat. Revolution . Poem. 13. Anonymous, Pat. A Dream . Poem. 13. Anonymous, Pat. Her . Poem. 13. Seagrave, Leslie. Tibetan Rug . Prose. 14. Benson, Virginia. Cronin-The Keys of the Kingdom . Prose. 15. Benson, Virginia. Koestler-Darkness at Noon . Prose. 15. Jones, Charles. Mr. Doakes Almost Goes to Washington . Prose. 16. Collins, Peggy. Thespiana . Prose. 18. Smith, Duke. Keeping the Records Straight . Prose. 19

Probing the Protostellar Envelope around L1157: the Dust and Gas Connection

We present observations of the Class 0 protostar L1157-mm using the Combined Array for Research in Millimeter-wave Astronomy (CARMA) in 3 mm dust continuum and N2H+ line emission. In the N2H+ line, we detect a large-scale envelope extended over a linear size of ~20,000AU flattened in the direction perpendicular to the outflow. This N2H+ feature coincides with the outer envelope seen in the 8 micron extinction by Looney et al. Meanwhile, the dust continuum traces the compact, nearly spherical structure of the inner envelope, where N2H+ becomes depleted. This highly flattened N2H+ envelope also shows dynamical signatures consistent with gravitational infall in the inner region, but a slow, solid-body rotation at large scales. This flattened structure is not a rotationally supported circumstellar disk; instead, it resembles a prestellar core both morphologically and kinematically, representing the early phase of a Class 0 system. In this paper, we construct a simple model to interpret both the dust continuum and N2H+ emission and suggest a possible dynamical scenario for the overall properties of the envelope.Comment: Accepted for publication by the ApJ, 34 pages, 10 figures and 2 table