A Note on the Cops and Robber Game on Graphs Embedded in Non-Orientable Surfaces

We consider the two-player, complete information game of Cops and Robber played on undirected, finite, reflexive graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and the robber are on the same vertex. The minimum number of cops needed to catch the robber on a graph is called the cop number of that graph. Let c(g) be the supremum over all cop numbers of graphs embeddable in a closed orientable surface of genus g, and likewise ${\tilde c(g)}$ for non-orientable surfaces. It is known (Andreae, 1986) that, for a fixed surface, the maximum over all cop numbers of graphs embeddable in this surface is finite. More precisely, Quilliot (1985) showed that c(g) ≤ 2g + 3, and Schröder (2001) sharpened this to ${c(g)\le \frac32g + 3}$ . In his paper, Andreae gave the bound ${\tilde c(g) \in O(g)}$ with a weak constant, and posed the question whether a stronger bound can be obtained. Nowakowski & Schröder (1997) obtained ${\tilde c(g) \le 2g+1}$ . In this short note, we show ${\tilde c(g) \leq c(g-1)}$ , for any g ≥ 1. As a corollary, using Schröder’s results, we obtain the following: the maximum cop number of graphs embeddable in the projective plane is 3, the maximum cop number of graphs embeddable in the Klein Bottle is at most 4, ${\tilde c(3) \le 5}$ , and ${\tilde c(g) \le \frac32g + 3/2}$ for all other g.     

Moran's genetics model via electric networks

Using the electric approach, we derive exact and asymptotic closed form formulas for hitting times in symmetric cases of the Moran's genetics model.     

Network management in a fast packet environment

StrataCom specializes in Asynchronous Transfer Mode (ATM) technology — a method of rapid wide-area distribution of all forms of traffic in cell format. This article will look at how StrataCom approaches network management for ATM switches.     

Information guided noise reduction for Monte Carlo integration of oscillatory functions

A simple procedure for decreasing the statistical error associated with Monte Carlo integration of oscillatory functions is presented. The method uses available information about the integral of a similar oscillatory function to correlate the estimates of the positive and negative components of the integral. Numerical tests show that information guided noise reduction (IGNoR) leads to substantial decrease of the statistical error, allowing meaningful results to be obtained with a fraction of the cost required to attain similar precision from the raw Monte Carlo estimate.     

Optimization of separations of alkyl-substituted phenolate anions by capillary zone electrophoresis

Anions of alkylphenols have very similar electrophoretic mobilities in CZE owing to their very small differences in size and the narrow range of their pK_a values. By studying electrophoretic mobility as a function both of pH and of the amount of acetonitrile in the electrolyte solution, optimum separation conditions were determined. It was possible to separate a group of methyl-substituted phenols, including several positional isomers. Mixtures containing n-propyl and isopropyl phenols and 1°, 2°, and 3° butylphenols could be resolved.     

A network-related nuclear power plant model with an intelligent branch-and-bound solution approach

This paper presents a network model with discrete requirements for a nuclear power plant. The model determines the batch size and timing for nuclear unit refueling and how much energy should be produced by nuclear and non-nuclear units for each time period to satisfy forecasted demand with minimum total operating costs over the planning horizon. Efficient modeling and solution strategies are developed which constitute a merger of operations research and artificial intelligence. A branch-and-bound solution approach is combined with a pattern recognition component, involving non-parametric discrimination analyses, to select branching variables and directions. By coupling this approach with network optimization techniques to exploit the underlying network structure of the problem, substantial improvements are obtained both in solution quality and solution efficiency.This research was supported in part by the Center for Business Decision Analysis, the Hugh Roy Cullen Centennial Chair in Business Administration, and the Office of Naval Research under contract N00014-87-K-0190. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. CENTER FOR BUSINESS DECISION ANALYSIS Darwin Klingman, Director The University of Texas at Austin Austin, TX 78712, U.S.A.     

Shock Tube Measurements of the Rate Constant of the Reaction NCN + O2

The rate constant of the comparably slow bimolecular NCN radical reaction NCN + O₂ has been measured for the first time under combustion relevant conditions using the shock tube method. The thermal decomposition of cyanogen azide (NCN₃) served as a clean high‐temperature source of NCN radicals. NCN concentration–time profiles have been detected by narrow‐bandwidth laser absorption at cm^?1. The experiments behind incident shock waves have been performed with up to 17% O₂ in the reaction gas mixture. At such high O₂ mole fractions, it was necessary to take O₂ relaxation into account that caused a gradual decrease of the temperature during the experiment. Moreover, following fast decomposition of NCN₃ and collision‐induced intersystem crossing of the initially formed singlet NCN to its triplet ground state, an unexpected and slow additional formation of triplet NCN has been observed on a 100‐μs timescale. This delayed NCN formation was attributed to a fast recombination of ¹NCN with O₂ forming a ³NCNOO adduct acting as a reservoir species for NCN. Rate constant data for the reaction NCN + O₂ have been measured at temperatures between 1674 and 2308 K. They are best represented by the Arrhenius expression . No pressure dependence has been observed at pressures between 216 and 706 mbar.