Approximation algorithm for maximum independent set in planar traingle-free graphs

The maximum independent set problem is NP-complete even when restricted to planar graphs, cubic planar graphs or triangle free graphs. The problem of finding an absolute approximation still remains NP-complete. Various polynomial time approximation algorithms, that guarantee a fixed worst case ratio between the independent set size obtained to the maximum independent set size, in planar graphs have been proposed. We present in this paper a simple and efficient, O(|V|) algorithm that guarantees a ratio 1/2, for planar triangle free graphs. The algorithm differs completely from other approaches, in that, it collects groups of independent vertices at a time. Certain bounds we obtain in this paper relate to some interesting questions in the theory of extremal graphs.

Reaction of Hexachlorocyclotriphosphazene with Sodium p-Cresoxide

The reaction of hexachlorocyclotriphosphazene (N3P3Cl6) with sodium p-cresoxide proceeds by a predominantly nongeminal pathway. The presence of geminal isomers at the bis- and tris-stages of substitution in tiny quantities (< 5%) has also been observed. All the chloro(p-cresoxy)cyclotriphosphazenes and their dimethylamino derivatives have been characterized by 1H-, 13C{1H}-, and 31P{1H}-NMR spectroscopy. The reaction of N3P3Cl6 with sodium phenoxide has been reinvestigated. The relative yields of the products at various stages of substitution and their isomeric compositions are almost the same for both phenoxy and p-cresoxy systems. Possible mechanisms to explain the observed isomeric compositions are discussed. A through-space interaction involving oxygen-2p and phosphorus-3d orbitals is invoked to explain the greater yield of the cis isomer of N3P3Cl4(OAr)2 than that of its trans isomer.

Computer model for vedavati ground water basin. Part 1. Well field model

It is shown that a leaky aquifer model can be used for well field analysis in hard rock areas, treating the upper weathered and clayey layers as a composite unconfined aquitard overlying a deeper fractured aquifer. Two long-duration pump test studies are reported in granitic and schist regions in the Vedavati river basin. The validity of simplifications in the analytical solution is verified by finite difference computations.

Reaction of thiophosphoryl fluoride with sulphur trioxide

Thiophosphoryl fluoride is observed to undergo a facile reaction with sulphur trioxide forming phosphoryl fluoride, sulphur dioxide and elemental sulphur in quantitative yields. In the presence of excess of sulphur trioxide, however, the elemental sulphur released combines with it to form sulphur sesquioxide which subsequently decomposes and gives off sulphur dioxide. Similar observations are made with oleum.

Spinup or spindown of a rotating electrically conducting fluid in a magnetic field

The hydromagnetic spinup or spindown of an incompressible, rotating, electrically conducting fluid over an infinite insulated disk with an applied magnetic field is studied when the impulsive motion is imparted either to the fluid or to the disk. The nonlinear partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. It is found that the spinup (or spindown) time due to impulsive motion of the disk is much shorter than the spinup (or spindown) time due to the impulsive motion of the distant fluid. The spinup (or spindown) time for the hydromagnetic case is comparatively smaller than the corresponding nonmagnetic case. Spindown is not merely a mirror reflection of spinup. Physics of Fluids is copyrighted by The American Institute of Physics.

Rural energy consumption patterns - A field study

This paper is a condensed version of the final report of a detailed field study of rural energy consumption patterns in six villages located west of Bangalore in the dry belt of Karnataka State in India. The study was carried out in two phases; first, a pilot study of four villages and second, the detailed study of six villages, the populations of which varied from around 350 to about 950. The pilot survey ended in late 1976, and most of the data was collected for the main project in 1977. Processing of the collected data was completed in 1980. The aim was to carry out a census survey, rather than a sample study. Hence, considerable effort was expended in production of both a suitable questionnaire, ensuring that all respondents were contacted, and devising methods which would accurately reflect the actual energy use in various energy-utilising activities. In the end, 560 households out of 578 (97%) were surveyed. The following ranking was found for the various energy sources in order of average percentage contribution to the annual total energy requirement: firewood, 81A·6%; human energy, 7A·7%; animal energy, 2A·7%; kerosene, 2A·1%; electricity, 0A·6% and all other sources (rice husks, agro-wastes, coal and diesel fuel), 5A·3%. In other words commercial fuels made only a small contribution to the overall energy use. It should be noted that dung cakes are not burned in this region. The average energy use pattern, sector by sector, again on a percentage basis, was as follows: domestic, 88A·3%; industry, 4A·7%; agriculture, 4A·3%; lighting, 2A·2% and transport, 0A·5%. The total annual per capita energy consumption was 12A·6 A± 1A·2 GJ, giving an average annual household consumption of around 78A·6 GJ.

Reaction product of lime and silica from rice husk ash

Rice husk ash (about 95% silica) with known physical and chemical characteristics has been reacted with lime and water. The setting process for a lime-excess and a lime-deficient mixture has been investigated. The product of the reaction has been shown to be a calcium silicate hydrate, C-S-H(I)+ by a combination of thermal analysis, XRD and electron microscopy. Formation of C-S-H(I) accounts for the strength of lime-rice husk ash cement.

Applications of the Vilsmeier reaction. 13. Vilsmeier approach to polycyclic aromatic hydrocarbons

The Synthesis of three typical polycyclic hydrocarbons (PAH) has been described, wherein the Vilsmeier reaction plays a major role. Vilsmeier reaction of the tetraloll gives the dihydronaphthaldehyde 2 which on cyclodehydration gives the dihydroarene 3. Ita dehydrogenation affords 3-methoxybenz[a]anthracene (4). Vilsmeier reaction on the dimethoxydihydronaphthalene 5 gives the versatile dimethoxydihydronaphthaldehyde 6 which has been converted to the dimethoxybenzo[c]fluorene 7 by direct cyclodehydration and the fulvene 10 by cyclodehydration of allylic alcohol 8 derived from 6 followed by dehydrogenation. The saturated alcohol 12 corresponding to 8 undergoes cyclodehydration to give the dimethoxyhexahydrobenzo[c]phenanthrene (13). Some of the advantages of the Vilsmeier approach to PAH have been pointed out.

Surface instability of a current-carrying plasma under the influence of a high-frequency electric-field

Surface instability of a collisionless semi-infinite current carrying plasma is studied. The semi-infinite plasma bounded by a plane surface is under the influence of a high frequency (hf) field. There are two classes of surface modes. One is a normal extension of zero high frequency field and the other due entirely to the presence ofhf field. As expected, with the increase in thehf field, the growth rates of the surface instabilities decrease. There are regions defined by the electron drift velocityu where the unstable surface and bulk regions overlap. The interesting result is that unlike the bulk plasma, there is a stable region on theu-axis flanked by two unstable regions. The width of this stable region increases with the increase in the field strength.

Microprocessor-Based Field-Oriented Control of A CSI-Fed Induction Motor Drive

This paper describes the method of field orientation of the stator current vector with respect to the stator, mutual, and rotor flux vectors, for the control of an induction motor fed from a current source inverter (CSI). A control scheme using this principle is described for orienting the stator current with respect to the rotor flux, as this gives natural decoupling between the current coordinates. A dedicated microcomputer system developed for implementing this scheme has been described. The experimental results are also presented.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

Photolysis of the dithiolactone 4-isopropylidene-3,3-dimethyl-1-thietan-2-thione; a Norrish type I reaction

The dithiolactone (1) upon excitation gives the dithione (2) in cyclohexane and other aprotic solvents and a 1 : 1 adduct in hydroxylic solvents from an n* excited singlet state via an -cleavage process.

Contributions to organic synthesis and reaction mechanisms

Development of new methods, leading to the first stereo-specific total synthesis of a steroid,viz equilenin, and of estrone and their derivatives and of several important synthones, useful for the preparation of physiologically active steroids, and the first conversion of an equilenane to estrane have been described. An account of the achievement of original syntheses of testosterone and its isomers and derivatives and degradation products, urinary steroids, terpenes and their important degradation products has been given. Mechanisms of Dieckmann cyclization, a novel dehydrogenation-addition reaction involving abietic acid and tetrachloro-o-benzoquinone, a rearrangement involving a substitution of cyclopentanone-2-carboxylic ester have been elucidated. An abnormaluv absorption exhibited by saturated 1,2-dicyano esters has been rationalized. Divergences in theord data of testosterone and 19-nortesto-sterone from their isomers have been explained by x-ray crystallographic studies of 8-isotestosterone, 8-iso-10-isotestosterone and 8-iso-10-iso-19-nortestosterone. A tentative explanation for the difference in their physiological activities has been suggested.