Boxicity of Circular Arc Graphs

A k-dimensional box is a Cartesian product R(1)x...xR(k) where each R(i) is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. That is, two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc graph is a graph that can be represented as the intersection graph of arcs on a circle. We show that if G is a circular arc graph which admits a circular arc representation in which no arc has length at least pi(alpha-1/alpha) for some alpha is an element of N(>= 2), then box(G) <= alpha (Here the arcs are considered with respect to a unit circle). From this result we show that if G has maximum degree Delta < [n(alpha-1)/2 alpha] for some alpha is an element of N(>= 2), then box(G) <= alpha. We also demonstrate a graph having box(G) > alpha but with Delta = n (alpha-1)/2 alpha + n/2 alpha(alpha+1) + (alpha+2). For a proper circular arc graph G, we show that if Delta < [n(alpha-1)/alpha] for some alpha is an element of N(>= 2), then box(G) <= alpha. Let r be the cardinality of the minimum overlap set, i.e. the minimum number of arcs passing through any point on the circle, with respect to some circular arc representation of G. We show that for any circular arc graph G, box(G) <= r + 1 and this bound is tight. We show that if G admits a circular arc representation in which no family of k <= 3 arcs covers the circle, then box(G) <= 3 and if G admits a circular arc representation in which no family of k <= 4 arcs covers the circle, then box(G) <= 2. We also show that both these bounds are tight.

Ground-fault-arc suppression on series-and shunt-compensated lines

An extension of Rizk's analysis to cover any type of switching is presented for calculating the residual current and recovery voltage in a singlephase switched transmission system. Equations for the determination of the current and voltage are shown, and the method has been used for the analysis of a series- and shunt-compensated line.Three possible switching methods for the effective control of the recovery voltage and residual current are discussed: normal switching, switching at the ends of the line and switching of the series capacitors.

Minimization of the effects of harmonics and voltage dip caused by electric arc furnace

This study examines the thermal efficiency of the operation of arc furnace and the effects of harmonics and voltage dips of a factory located near Bangkok. It also attempts to find ways to improve the performance of the arc furnace operation and minimize the effects of both harmonics and voltage dips. A dynamic model of the arc furnace has been developed incorporating both electrical and thermal characteristics. The model can be used to identify potential areas for improvement of the furnace and its operation. Snapshots of waveforms and measurement of RMS values of voltage, current and power at the furnace, at other feeders and at the point of common coupling were recorded. Harmonic simulation program and electromagnetic transient simulation program were used in the study to model the effects of harmonics and voltage dips and to identify appropriate static and dynamic filters to minimize their effects within the factory. The effects of harmonics and voltage dips were identified in records taken at the point of common coupling of another factory supplied by another feeder of the same substation. Simulation studies were made to examine the results on the second feeder when dynamic filters were used in the factory which operated the arc furnace. The methodology used and the mitigation strategy identified in the study are applicable to general situation in a power distribution system where an arc furnace is a part of the load of a customer

Role of electrolyte additives on in-vitro electrochemical behavior of micro arc oxidized titania films on Cp Ti

The present work is aimed at studying the influence of electrolyte chemistry on the voltage-time (V-T) response characteristics, phase structure, surface morphology, film growth rate and corrosion properties of titania films fabricated by micro arc oxidation (MAO) on Cp Ti. The titania films were developed with a sodium phosphate based reference electrolyte comprising the additives such as sodium carbonate (Na2CO3), sodium nitrite (NaNO2) and urea (CO(NH2)(2)). The phase composition, surface morphology, elemental composition and thickness of the films were assessed by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) techniques. The corrosion characteristics of the fabricated films were studied under Kokubo simulated body fluid (SBF) condition by potentiodynamic polarization, long term potential and linear polarization resistance (LPR) measurements and electrochemical impedance spectroscopy (EIS) methods. In addition, the corrosion characteristics of the grown films were analyzed by EIS curve fitting and equivalent circuit modeling. Salt spray test (SST) as per ASTM B 117 standard was also conducted to verify the corrosion resistance of the grown films. The XRD results showed that the titania films were composed of both anatase and rutile phases at different proportions. Besides, the films grown in carbonate and nitrite containing electrolyte systems showed an enhanced growth of their rutile phase in the 1 0 1] direction which could be attributed to the modifications introduced in the growth process by the abundant oxygen available during the process. The SEM-EDX and elemental mapping results showed that the respective electrolyte borne elements were incorporated and distributed uniformly in all the films. Among all the grown films under study, the film developed in carbonate containing electrolyte system exhibited considerably improved corrosion resistance due to suitable modifications in its structural and morphological characteristics. The rate of anatase to rutile phase transformation and the rutile growth direction were strongly influenced by the abundant oxidizing species available during the film growth process. (C) 2012 Elsevier B. V. All rights reserved.