Algorithms for Colouring Random k-colourable Graphs

The k-colouring problem is to colour a given k-colourable graph with k colours. This problem is known to be NP-hard even for fixed k greater than or equal to 3. The best known polynomial time approximation algorithms require n(delta) (for a positive constant delta depending on k) colours to colour an arbitrary k-colourable n-vertex graph. The situation is entirely different if we look at the average performance of an algorithm rather than its worst-case performance. It is well known that a k-colourable graph drawn from certain classes of distributions can be ii-coloured almost surely in polynomial time. In this paper, we present further results in this direction. We consider k-colourable graphs drawn from the random model in which each allowed edge is chosen independently with probability p(n) after initially partitioning the vertex set into ii colour classes. We present polynomial time algorithms of two different types. The first type of algorithm always runs in polynomial time and succeeds almost surely. Algorithms of this type have been proposed before, but our algorithms have provably exponentially small failure probabilities. The second type of algorithm always succeeds and has polynomial running time on average. Such algorithms are more useful and more difficult to obtain than the first type of algorithms. Our algorithms work as long as p(n) greater than or equal to n(-1+is an element of) where is an element of is a constant greater than 1/4.

Superconductivity in the 100–120 K region in oxides of the Tl-Ca-Ba-Cu-O system

Oxides with different cation ratios 2122, 2212, 2213 and 2223 in the Ti-Ca-Ba-Cu-O system exhibit onset of superconductivity in the 110–125 K range with zero-resistance in the 95–105 K range. Electron microscopic studies show dislocations, layered morphology and other interesting features. These oxides absorb electromagnetic radiation (9.11 GHz) in the superconducting phase.

Thermodynamic measurements of b.c.c. Cr-Mn solid solutions at 1373 K

Thermodynamics of Cr-Mn alloys have been studied by Eremenko et al (l) using a fused salt e.m.f.technique. Their results indicate positive deviations from ideality at 1023 K. Kaufman (2) has independently estimated negative enthaipy and excess entropy for the b.c.c. Cr-Mn alloys, such that at high temperatures, the entropy term predominates over the enthalpy term giving positive deviations from ideality. Recently the thermodynamic properties of the alloys have been measured by 3acob (3) using a Knudsen cell technique in the temperature range of 1200 to 1500 K. The results indicate mild negative deviations from ideality over the entire composition range. Because of the differences in the reported results and Mn being a volatile component in the alloys which leads to surface depletion under a dynamic set up, an isopiestic technique is used to measure the properties of the alloys.

Practical Proposals for Specifying k-Nearest Neighbours Weights Matrices

In this article we introduce and evaluate testing procedures for specifying the number k of nearest neighbours in the weights matrix of spatial econometric models. The spatial J-test is used for specification search. Two testing procedures are suggested: an increasing neighbours testing procedure and a decreasing neighbours testing procedure. Simulations show that the increasing neighbours testing procedures can be used in large samples to determine k. The decreasing neighbours testing procedure is found to have low power, and is not recommended for use in practice. An empirical example involving house price data is provided to show how to use the testing procedures with real data.

Activity–Composition Relations in the Nickel Oxide–Magnesium Oxide System at 1300 K by the Solid-State Galvanic Cell Technique

The activity of NiO in NiO-MgO rock salt solid solution has been measured at 1300 K by employing a solid-state galvanic cell: Pt,Ni+ NiO||(CaO)ZrO2||Ni + (Nix,Mgl-x)O, Pt. A high-density tube of Zr02-15 mol% CaO has been used as the solid electrolyte for the emf measurements. The activities of the component oxides in the rock salt solid solution exhibit negative deviation from ideality at the temperature of investigation. The solid solution obeys regular solution behavior at 1300 K. The value of the regular solution parameter is found to be -12000 ((l000) J mol-1. The composition dependence of ΔGEx obtained in this study agrees reasonably well with the calorimetric data reported in the literature for NiO-MgO solid solution.

A XANES study of the K-absorption edge of copper in some of its compounds and use of the same in the determination of bond length

XANES in the K-edge of copper in the systems CuO, Cu(OH)2, La2CuO4, Cu3AsO4 and CuOHF have been investigated and transitions have been assigned to the observed structures. The measurements have been used for calculating the first coordination bond distance in the above systems. It is observed that the values so determined agree fairly well with crystallographic values.

High-Temperature (1023 K to 1273 K 750 degrees C to 1000 degrees C]) Plastic Deformation Behavior of B-Modified Ti-6Al-4V Alloys: Temperature and Strain Rate Effects

A minor addition of B to the Ti-6Al-4V alloy, by similar to 0.1 wt pct, reduces its as-cast prior beta grain size by an order of magnitude, whereas higher B content leads to the presence of in situ formed TiB needles in significant amounts. An experimental investigation into the role played by these microstructural modifications on the high-temperature deformation behavior of Ti-6Al-4V-xB alloys, with x varying between 0 wt pct and 0.55 wt pct, was conducted. Uniaxial compression tests were performed in the temperature range of 1023 K to 1273 K (750 degrees C to 1000 degrees C) and in the strain rate range of 10(-3) to 10(+1) s(-1). True stress-true strain responses of all alloys exhibit flow softening at lower strain rates and oscillations at higher strain rates. The flow softening is aided by the occurrence of dynamic recrystallization through lath globularization in high temperature (1173 K to 1273 K 900 degrees C to 1000 degrees C]) and a lower strain rate (10(-2) to 10(-3) s(-1)) regime. The grain size refinement with the B addition to Ti64, despite being marked, had no significant effect on this. Oscillations in the flow curve at a higher strain rate (10(0) to 10(+1) s(-1)), however, are associated with microstructural instabilities such as bending of laths, breaking of lath boundaries, generation of cavities, and breakage of TiB needles. The presence of TiB needles affected the instability regime. Microstructural evidence suggests that the matrix cavitation is aided by the easy fracture of TiB needles.

K -shell diagram and hypersatellite spectra of 4d transition elements

The K-shell diagram (K alpha(1,2) and K beta(1,3)) and hypersatellite (HS) (K-h alpha(1,2)) spectra of Y, Zr, Mo, and Pd have been measured with high energy-resolution using photoexcitation by 90 keV synchrotron radiation. Comparison of the measured and ab initio calculated HS spectra demonstrates the importance of quantum electrodynamical (QED) effects for the HS spectra. Phenomenological fits of the measured spectra by Voigt functions yield accurate values for the shift of the HS from the diagram lines, the splitting of the HS lines, and their intensity ratio. Good agreement with theory was found for all quantities except for the intensity ratio, which is dominated by the intermediacy of the coupling of the angular momenta. The observed deviations imply that our current understanding of the variation of the coupling scheme from LS to jj across the periodic table may require some revision.

Origin of nonmetallicity in PrBa2Cu3O7 from a study of Gd1−xPrxBa2Cu3O7 using soft x-ray absorption at the oxygen K-edge

We present the x-ray absorption data at the oxygen K-edge using total yield technique for Gd1−xPrxba2Cu3O7 (x= 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0). The data clearly to oxygen that the holes doped in the GdBa2Cu3O7 due to oxygen composition are not removed by Pr doping even for the x = 1.0 sample, suggesting that Pr is predominantly in the formally trivalent state. However, the data also clearly indicate the evidence of hybridization effects between the Pr3+ and the adjacent CuO2 layers. This is suggested to be responsible for the progressive suppression of Tc and the metallicity with Pr doping in these systems.

Phase relations in the system BiO1.5–SrO–CuO at 1123 K

Phase relations in the system Bi-Sr-Cu-O at 1123 K have been investigated using optical microscopy, electron-probe microanalysis (EPMA) and powder X-ray diffraction (XRD) of equilibrated samples. Differential thermal analysis (DTA) was used to confirm liquid formation for compositions rich in BiO1.5. Compositions along the three pseudo-binary sections and inside the pseudo-ternary triangle have been examined. The attainment of equilibrium was facilitated by the use of freshly prepared SrO as the starting material. The loss of Bi2O3 from the sample was minimized by double encapsulation. A complete phase diagram at 1123 K is presented. It differs significantly from versions of the phase diagram published recently.

Valokuvallistettu luonto : I. K. Inhan tuotanto luonnon merkityksellistäjänä

Photographized nature I. K. Inha s work as a signification of nature The dissertation examines, through the work of the Finnish photographer and writer I. K. Inha (formerly Konrad Into Nyström) (1865 1930), the different ways in which the signification of nature is achieved. The principal material consists of Inha s work from 1890 to 1925, from which a number of photographs and texts are considered and upon which the photographization of nature is contemplated. The dissertation addresses the issue of how nature is conceived and how the act of photographizing it can be defined. The methodical context of the study is composed of three thematic baskets that structure the material and which consist of narrations on Finnish national perception, nature conservation and understanding the world. In the first case nature is seen as the natural environment encompassing lakes, seashores, forests, and hills, which at the time were often perceived from a utilitarian viewpoint. By the photographization they generated a pictorial narrative that could be shared. The natural environment was thus turned into landscape by means of photography, following the global pictorial concepts picturesque and sublime, as well as the national canons that had been developed in literature and the visual arts. In the narrations concerning nature conservation, the photographization did not merely occur within the limits of presuppositions, but rather nature was given the opportunity to unfold itself. While the photograph was being established as a basis for supporting nature conservation or to highlight the destruction of nature at the hand of Man, an attempt was made to represent subjects that were difficult to convey in photographs, such as nature s power or the miracle of growth. The thesis suggests, that in the third case the concept of nature broke away from its strict interconnection with the natural environment and led to a contemplation of nature that is perceivable in a person. In this context the photograph and the photographization are interpreted as an attempt to understand a person and his or her very existence in the world, while this same existential wonder is seen as being embodied in Inha s portrait of a rune singer and in his photographs of forest interior and water. Further, the thesis asks whether photographing nature could be interpreted as an action similar to the idea of the phenomenological reduction as a means of bypassing the photographer s prevailing way of being.