scholarly journals On the Domination Number of a Random Graph

10.37236/1581 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Ben Wieland ◽  
Anant P. Godbole
Keyword(s):  
Chromatic Number ◽  
Random Graph ◽  
Moment Method ◽  
High Probability ◽  
Domination Number ◽  
Infinite Graph ◽  
Cantelli Lemma ◽  
Second Moment ◽  
Second Moment Method ◽  
The Second Moment Method

In this paper, we show that the domination number $D$ of a random graph enjoys as sharp a concentration as does its chromatic number $\chi$. We first prove this fact for the sequence of graphs $\{G(n,p_n\},\; n\to\infty$, where a two point concentration is obtained with high probability for $p_n=p$ (fixed) or for a sequence $p_n$ that approaches zero sufficiently slowly. We then consider the infinite graph $G({\bf Z}^+, p)$, where $p$ is fixed, and prove a three point concentration for the domination number with probability one. The main results are proved using the second moment method together with the Borel Cantelli lemma.

Photochemical Studies. XVI. Second Moment Analysis of the Electron Spin Resonance Spectra of Radicals Formed by Ultraviolet Irradiation of 9-Phenylacridine and of Acridine

1973 ◽  
Vol 51 (21) ◽  
pp. 3508-3513 ◽  
Author(s):  
Azélio Castellano ◽  
Jean-Pierre Catteau ◽  
Alain Lablache-Combier ◽  
Guy Allan
Keyword(s):  
Electron Spin Resonance ◽  
Moment Method ◽  
Membered Ring ◽  
Second Moment ◽  
Second Moments ◽  
Deuterated Analog ◽  
Spin Resonance ◽  
Second Moment Method ◽  
The Second Moment Method ◽  
Spin Densities

The irradiation of 9-phenylacridine in methanol, ethanol, or ether leads to the formation of the 9-phenylacridinyl radical. In methanol-d4, the radical formed is the singly deuterated analog. The structure of these radicals, which exhibit a hyperfine structure in their e.s.r. spectra measured at 233 °K, is supported by simulation of the spectra using calculated spin densities. The agreement between the experimental and theoretical second moment values of the deuterated radical indicates that the parameters previously chosen for the calculation of the theoretical second moments of pyridinyl-type radicals derived from six-membered ring azaaromatics are suitable and that the second moment method can be used in studies of radicals of this type. We conclude that acridine irradiated in methanol-d4 leads to the formation of the singly deuterated acridinyl radical.

Spanning Subgraphs of Random Graphs

2000 ◽  
Vol 9 (2) ◽  
pp. 125-148 ◽  
Author(s):  
OLIVER RIORDAN
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Moment Method ◽  
Subgraph Isomorphic ◽  
Square Grid ◽  
Spanning Subgraphs ◽  
Spanning Subgraph ◽  
Fixed Probability ◽  
Second Moment Method ◽  
The Second Moment Method

Let Gp be a random graph on 2d vertices where edges are selected independently with a fixed probability p > ¼, and let H be the d-dimensional hypercube Qd. We answer a question of Bollobás by showing that, as d → ∞, Gp almost surely has a spanning subgraph isomorphic to H. In fact we prove a stronger result which implies that the number of d-cubes in G ∈ [Gscr ](n, M) is asymptotically normally distributed for M in a certain range. The result proved can be applied to many other graphs, also improving previous results for the lattice, that is, the 2-dimensional square grid. The proof uses the second moment method – writing X for the number of subgraphs of G isomorphic to H, where G is a suitable random graph, we expand the variance of X as a sum over all subgraphs of H itself. As the subgraphs of H may be quite complicated, most of the work is in estimating the various terms of this sum.

Simulation Research of Charged Particle Discrimination Methods

2014 ◽  
Vol 568-570 ◽  
pp. 146-151
Author(s):  
Jin Tao Zhu ◽  
Guo Fu Liu ◽  
Jun Yang ◽  
Lei Zhang
Keyword(s):  
Moment Method ◽  
Integration Method ◽  
Discrimination Performance ◽  
Good Discrimination ◽  
Simulation Research ◽  
Second Moment ◽  
Discrimination Methods ◽  
Second Moment Method ◽  
The Second Moment Method ◽  
Charge Integration

A simple model was used to simulate the current pulse induced by charged particles with Si detector. With simulated current shapes of three element groups, H/D/T (6MeV), He-3/He-4 (15MeV) and Li-6/Li-7 (35MeV), three methods of pulse shape analysis (PSA), i.e. the m2-m3 method, the integration method and the second moment method, were compared and analyzed. Their discrimination performance and noise resisting property are investigated. The results show that the charge integration method and the m2-m3 method both have good discrimination performance and noise resisting property. While neither the discrimination performance nor the noise resisting property of the second moment method is satisfactory.

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