Parallel cleaning of a network with brushes

AbstractWe consider the process of cleaning a network where at each time step, all vertices that have at least as many brushes as incident, contaminated edges, send brushes down these edges and remove them from the network. An added condition is that, because of the contamination model used, the final configuration must be the initial configuration of another cleaning of the network. We find the minimum number of brushes required for trees, cycles, complete bipartite networks; and for all networks when all edges must be cleaned on each step. Finally, we give bounds on the number of brushes required for complete networks

Game Brush Number

We study a two-person game based on the well-studied brushing process on graphs. Players Min and Max alternately place brushes on the vertices of a graph. When a vertex accumulates at least as many brushes as its degree, it sends one brush to each neighbor and is removed from the graph; this may in turn induce the removal of other vertices. The game ends once all vertices have been removed. Min seeks to minimize the number of brushes played during the game, while Max seeks to maximize it. When both players play optimally, the length of the game is the game brush number of the graph $G$, denoted $b_g(G)$. By considering strategies for both players and modelling the evolution of the game with differential equations, we provide an asymptotic value for the game brush number of the complete graph; namely, we show that $b_g(K_n) = (1+o(1))n^2/e$. Using a fractional version of the game, we couple the game brush numbers of complete graphs and the binomial random graph $\mathcal{G}(n,p)$. It is shown that for $pn \gg \ln n$ asymptotically almost surely $b_g(\mathcal{G}(n,p)) = (1 + o(1))p b_g(K_n) = (1 + o(1))pn^2/e$. Finally, we study the relationship between the game brush number and the (original) brush number.Comment: 20 pages, 3 figure

Graphite core condition monitoring through intelligent analysis of fuel grab load trace data

As a graphite core ages, there is an increased requirement to monitor the distortions within the core to permit safe continued operation of the station. In addition to existing monitoring and inspection, new methods of providing information relating to the core are being investigated

Investigations of the potential performance characteristics of selected contact lubricants for applications in miniature slip-ring capsules of the type used in ST 124 M stabilized inertial guidance platforms Final technical report, 27 Mar. 1968 - 30 Apr. 1970

Performance characteristics of liquid and solid lubricants for contacts of miniature slip-ring capsule

Evaluation of the Efficacy of a Conventional Bristle Brush and Cross-action Brush in Routine Oral Hygiene Practice: A Comparative Study

Background: Toothbrush filament configuration can vary to a large extent with a considerable emphasis on the design and texture of bristle of a toothbrush in order to enhance effective removal of plaque. Aims: The aim of the study was to compare the plaque removing efficiency of two branded toothbrushes with different brush head design and bristle arrangement in routine oral hygiene practice. Materials and methods: The study was randomized single blind, involving 100 healthy individuals, 50 samples in each group. At the time of initial examination the subjects randomly picked toothbrushes (Oral B fresh-clean and Oral B crossaction) and common toothpaste by lottery method along with the printed instructions to use the assigned brush for next 28 days. Plaque and gingival indices were recorded at appointed time every 0, 7th, 14th, 21st and 28th day. Finally, the resultswere subjected to student’s unpaired ‘t test’. Results: Plaque and gingival scores showed a significant decrease in all parameters at all time intervals. Plaque and gingival scores were found to be significantly reduced in 3rd and 4th week time interval with respect to both the brushes though the cross-action brush showed better result with mean reduction of gingival index score from 1.812 at baseline to 1.5733 at 4th week as compared to fresh-clean brush which showed mean reduction of gingival index score from 1.4161 at baseline to 1.4016 at 4th week. Conclusion: Among the two toothbrushes it was Oral-B crossaction toothbrush which showed the maximum reduction in plaque and gingival index scores followed by Oral-B fresh-clean toothbrush. It can be concluded that the arrangement of bristles plays a convincing role in reduction of plaque besides the manual dexterity of an individual

RESONANT ELECTROMAGNETIC PROCESSES AT UNSTABLE OPERATION OF SLIDING CURRENT COLLECTOR UNITS OF TURBOGENERATOR

The article is devoted to study of the resonance electromagnetic oscillations arising during unstable operation of the sliding current collection unit of turbo-generators. Mathematical modeling of these processes is carried out. It has been established that it is these processes that are the main cause of increased sparking and “ring fire” or “breakdown of commutation” on contact rings