Neighborhood Champions in Regular Graphs

For a vertex x in a graph G we define Ψ1(x) to be the number of edges in the closed neighborhood of x. Vertex x∗ is a neighborhood champion if Ψ1(x∗)\u3eΨ1(x) for all x≠x∗. We also refer to such an x∗ as a unique champion. For d≥4 let n0(1,d) be the smallest number such that for every n≥n0(1,d) there exists a n vertex d-regular graph with a unique champion. Our main result is that n0(1,d) satisfies d+3≤n0(1,d)≤3d+1. We also observe that there can be no unique champion vertex when d=3

The role of surface conditions in nucleate boiling

Nucleation from a single cavity has been stuied indicating that cavity gemtry is aportant in two ways. The mouth diameter determines the superheat nmeded to initiate boiling and its shape determines its stability one boiling has begun. Contact angle is shown to be important in bubble nucleation primarity thrugh its effect on cavity stability. Contact angle measurements made on "clean" and paraffin coated stainIess steel murftces with water shcw that the contact angle varies between 20 and 110* for tenperatures from 20[degree] to 170[degree] C. On the basis of single cavity nucleation theory, it is proposed to characterie the gross nucleation properties of a given surface for all fnds under all conditions with a single group having the dmnions of length. Finally, it is shown experimentally that this characterization is adequate by boiling water, methmnol and ethanol different copper surfaces finished with 3/0 emry, and showing that the number of active centers per unit area is a function of this variable alone.Office of Naval Research DSR Projec

Vertex-magic Labeling of Trees and Forests

A vertex-magic total labeling of a graph G(V,E) is a one-to-one map λ from E ∪ V onto the integers {1, 2, . . . , |E| + |V|} such that λ(x) + Σ λ(xy) where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite different from the conjectured behavior of edge-magic total labelings of these graphs. We pay special attention to the case of so-called galaxies, forests in which every component tree is a star

Closed-Neighborhood Anti-Sperner Graphs

For a simple graph G let NG[u] denote the closed-neighborhood of vertex u ∈ V (G). Then G is closed-neighborhood anti-Sperner (CNAS) if for every u there is a v ∈ V (G)\{u} with NG [u] ⊆ NG [v] and a graph H is closed-neighborhood distinct (CND) if every closed-neighborhood is distinct, i.e., if NH[u] ≠ NH[v] when u ≠ v, for all u and v ∈ V (H). In this paper we are mainly concerned with constructing CNAS graphs. We construct a family of connected CNAS graphs with n vertices for each fixed n ≥ 2. We list all connected CNAS graphs with ≤ 6 vertices, and find the smallest connected CNAS graph that lies outside these families. We indicate how some CNAS graphs can be constructed from a related type of graph, called a NAS graph. Finally, we present an algorithm to construct all CNAS graphs on a fixed number of vertices from labelled CND graphs on fewer vertices

Double Arrays, Triple Arrays and Balanced Grids

Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids

Agreement in Walking Speed Measured Using Four Different Outcome Measures: 6-Meter Walk Test, 10-Meter Walk Test, 2-Minute Walk Test, and 6-Minute Walk Test

Background: Walking speed is considered the sixth vital sign because it is a valid, reliable, and sensitive measure for assessing functional status in various populations. Purpose: The current study assessed agreement in walking speed using the 6-meter walk test, (6MWT) 10-meter walk test (10MWT), 2-minute walk test (2minWT), and 6-minute walk test (6minWT). We also determined differences in walking speed. Methods: Seventy-three healthy adults (44 females, 29 males; mean [SD] age=31.36 [10.33] years) participated. Lafayette Electronic timing devices measured walking speed for the 6MWT and 10MWT. Measuring wheels and stopwatches measured walking distance and speed for the 2minWT and 6minWT. Participants completed 1 trial, and all tests were administered simultaneously. Results: The intraclass correlation coefficient (2, 4) for the different measures of walking speed was excellent at 0.90 (95% confidence intervals, 0.86-0.93). The correlation was 0.95 between 6MWT and 10MWT, 0.94 between 2minWT and 6minWT, 0.67 between 6MWT and 2minWT, 0.63 between 10MWT and 2minWT, and 0.59 between 10MWT and 6minWT (all p \u3c 0.05). No differences in walking speed were found between the four walking tests. Conclusion: Administration of any of the four walking tests provided reliable measurement of walking speed

Protease Inhibitor Resistance Is Uncommon in HIV-1 Subtype C Infected Patients on Failing Second-Line Lopinavir/r-Containing Antiretroviral Therapy in South Africa

Limited data exist on HIV-1 drug resistance patterns in South Africa following second-line protease-inhibitor containing regimen failure. This study examined drug resistance patterns emerging in 75 HIV-1 infected adults experiencing virologic failure on a second-line regimen containing 2 NRTI and lopinavir/ritonavir. Ninety six percent of patients (n = 72) were infected with HIV-1 subtype C, two patients were infected with HIV-1 subtype D and one with HIV-1 subtype A1. Thirty nine percent (n = 29) of patients had no resistance mutations in protease or reverse transcriptase suggesting that medication non-adherence was a major factor contributing to failure. Major lopinavir resistance mutations were infrequent (5 of 75; 7%), indicating that drug resistance is not the main barrier to future viral suppression

Totally Magic Graphs

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , v+e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and the labels of the endpoints of the edge is constant. In this paper we examine graphs possessing a labeling that is simultaneously vertex magic and edge magic. Such graphs appear to be rare