Cubicity of Interval Graphs and the Claw Number

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product l(1) x l(2) x ... x l(b), where each l(i) is a closed interval of unit length on the real line. The cub/city of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line-i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number psi(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least log(2) psi(G)]. In this article, we show that for an interval graph G log(2) psi(G)-]<= cub(G)<=log(2) psi(G)]+2. It is not clear whether the upper bound of log(2) psi(G)]+2 is tight: till now we are unable to find any interval graph with cub(G)> (log(2)psi(G)]. We also show that for an interval graph G, cub(G) <= log(2) alpha], where alpha is the independence number of G. Therefore, in the special case of psi(G)=alpha, cub(G) is exactly log(2) alpha(2)]. The concept of cubicity can be generalized by considering boxes instead of cubes. A b-dimensional box is a Cartesian product l(1) x l(2) x ... x l(b), where each I is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k-dimensional boxes. It is clear that box(G)<= cub(G). From the above result, it follows that for any graph G, cub(G) <= box(G)log(2) alpha]. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323-333, 2010

Directional solidification of aluminum-nickel eutectic alloys using electroslag remelting

Attempts were made to produce directionally solidified, specifically grain aligned Al-6 wt pct Ni eutectic alloy using a laboratory scale ESR unit. For this purpose sand cast alloy electrodes were electroslag remelted under different mold conditions. The grain structure of the ingots obtained from these meltings showed that insulated silica molds gave the best vertical alignment of grains along the length of the ingot. The NiAl3 fibers within the grains tended to fan out and there was only a preferred alignment of fibers along the growth direction under the conditions of our experiments. The ESR parameters most suitable for vertical alignment of eutectic grains have been identified. In some electroslag remelting trials ingots were grown on a seed ingot. This resulted in a fewer vertical grains compared to the case when no seed ingot was used. The sand cast specimen of the eutectic exhibited a maximum tensile strength of around 88.2 MN/m2 (9.0 kg/mm2) whereas conventional ESR using water cooled mold gave strength value of 98.0 MN/m2 (10 kg/mm2). The directionally solidified ESR material showed longitudinal tensile strength as high as 213.7 MN/m2 (21.8 kg/mm2) which could be further increased to 220.6 MN/m2 (22.5 kg/mm2) by using the seed ingot. The average growth rate was varied between 5 to 25 mm/min during electroslag remelting in this study. The flow stresses, tangent modulus and ultimate tensile strength of directionally solidified eutectic increased with increasing growth rates.

Monologeista dialogiksi : Keskustelua koulusta käytävien ohipuhumisten muuttamisesta neuvotteluksi sosiaalisen konstruktionismin hengessä.

From monologues to dialogue. A discussion about changing the fragmented character of the debate concerning schools to one of negotiation, in the spirit of social constructionism. The starting point for the study is the assumption that the interested parties concerning schools such as teachers, students, public servants within school administration or politics construct the idea of the school in disparate ways. It looks as if the representatives of the various interested parties perceive the school in distinctive ways or with particular emphases. Additionally, there are not many discussion forums where these different interested parties have an equal right to speak and be heard. It seems that the lack of dialogue characterizes the debate about school. At the centre of the study are negotiations concerning schools, and the conditions that promote changing the fragmented character of this school debate in a more promising and collectively responsible process of negotiation. The aims of the study are to find both an empirical and theoretical basis for more equal ways to negotiate about school, and to increase cultural self reflection. Social constructionism plays a key role in aspiring to meet these research aims. The research questions are (1) How do the informants of the study construct the idea of school in their texts, and (2) What kind of prospects does social constructionism bring to the negotiations about school. The research informants construct the idea of school in their texts in several ways. To sum up: school is constructed as a place for learning, a place for building the future, a place where ethical education is lived out, a place for social education and Bildung, and a place where the students well-being is ensured. The previously presented assumption that the interested parties of a school construct the idea of a school in disparate ways or with various emphases seems to have support in the informants texts. Based on that, a condition can be put forward: different perspectives should have an equal opportunity to be heard in negotiations about school. It would also be helpful if there was a chance for different perspectives to be documented and/or in some way, visualized. This ensures that different constructions of school are within reach of all the participants. Additionally, while making the process of negotiation transparent, this documentation becomes an important medium for self reflection. On one hand it visualizes the complexity of the school. On the other hand it protects the school and education from serving as the spokesman of any single truth that is presented as objective or universal. Social constructionism seems to offer a stable theoretical basis for changing the fragmented character of the school debate in one of negotiation. More equal and collectively responsible school negotiation presumes that certain aspects or conditions drawn from postmodernism and social constructionism have been studied. In the study, six conditions are presented that can be seen as mediums for changing the fragmented character of the school debate into one of more equal negotiation. Keywords: social constructionism, Kenneth J. Gergen, school negotiation, education policy, dialogue.

Tree mortality, fire scar formation and regeneration 8 years after low-intensity fire in managed Pinus sylvestris stands

Fire is an important driver of the boreal forest ecosystem, and a useful tool for the restoration of degraded forests. However, we lack knowledge on the ecological processes initiated by prescribed fires, and whether they bring about the desired restoration effects. The purpose of this study was to investigate the impacts of low-intensity experimental prescribed fires on four ecological processes in young commercial Scots pine (Pinus sylvestris) stands eight years after the burning. The processes of interest were tree mortality, dead wood creation, regeneration and fire scar formation. These were inventoried in twelve study plots, which were 30 m x 30 m in size. The plots belonged to two different stand age classes: 30-35 years or 45 years old at the time of burning. The study was partly a follow-up of study plots researched by Sidoroff et al. (2007) one year after burning in 2003. Tree mortality increased from 183 stems ha-1 in 2003 to 259 stems ha-1 in 2010, corresponding to 15 % and 21 % of stem number respectively. Most mortality was experienced in the stands of the younger age class, in smaller diameter classes and among species other than Scots pine. By 2010, the average mortality of Scots pine per plot was 18%, but varied greatly ranging from 0% to 63% of stem number. Delayed mortality, i.e. mortality that occurred between 2 and 8 years after fire, seemed to become more important with increasing diameter. The input of dead wood also varied greatly between plots, from none to 72 m3 ha-1, averaging at 12 m3 ha-1. The amount of fire scarred trees per plot ranged from none to 20 %. Four out of twelve plots (43 %) did not have any fire scars. Scars were on average small: 95% of scars were less than 4 cm in width, and 75% less than 40 cm in length. Owing to the light nature of the fire, the remaining overstorey and thick organic layer, regeneration was poor overall. The abundance of pine and other seedlings indicated a viable seed source existed, but the seedlings failed to establish under dense canopy. The number of saplings ranged from 0 to 12 333 stems ha-1. The results of this study indicate that a low intensity fire does not necessarily initiate the ecological processes of tree mortality, dead wood creation and regeneration in the desired scale. Fire scars, which form the basis of fire dating in fire history studies, did not form in all cases.

Sequence Independent Recombination Triple Helices: A Molecular Dynamics Study

Recent experimental studies have shown that the Rec-A mediated homologous recombination reaction involves a triple helical intermediate, in which the third strand base forms hydrogen bonds with both the bases in the major groove of the Watson-Crick duplex. Such 'mixed' hydrogen bonds allow formation of sequence independent triplexes. DNA triple helices involving 'mixed' hydrogen bonds have been studied, using model building, molecular mechanics (MM) and molecular dynamics (MD). Models were built for a tripler comprising all four possible triplets viz., G.C*C, C.G*G, A.T*T and T.A*A. To check the stability of all the 'mixed' hydrogen bonds in such triplexes and the conformational preferences of such tripler structures, MD studies were carried out starting from two structures with 30 degrees and 36 degrees twist between the basepairs. It was observed that though the two triplexes converged towards a similar structure, the various hydrogen bonds between the WC duplex and the third strand showed differential stabilities. An MD simulation with restrained hydrogen bonds showed that the resulting structure was stable and remained close to the starting structure. These studies help us in defining stable hydrogen bond geometries involving the third strand and the WC duplex. It was observed that in the C.G*G triplets the N7 atom of the second strand is always involved in hydrogen bonding. In the G.C*C triplets, either N3 or O2 in the third strand cytosine can interchangeably act as a hydrogen bond acceptor.

(+/-)-cis-Dichloro[P-(isopropylamino)-dinaphtho[2,1-d:1',2'-f][1,3,2]dioxaphosphepine](triethylphosphine)platinum(II) dichloromethane solvate

In the racemic title compound, [PtCl2(C23H20NO2P)-(C6H15P)].CH2Cl2, the platinum(II) ion, which has approximately square-planar coordination geometry, is coordinated to two different monophosphorus ligands in a cis arrangement along with two chloride ions. A significant shortening of the P-N bond [1.604(7) Angstrom] relative to that in phosphinoamines and their complexes was observed.

Comparative Nucleotide and Amino Acid Sequence Analysis of the Sequence-Specific RNA-Binding Rotavirus Nonstructural Protein NSP3

NSP3, an acidic nonstructural protein, encoded by gene 7 has been implicated as the key player in the assembly of the 11 viral plus-strand RNAs into the early replication intermediates during rotavirus morphogenesis. To date, the sequence or NSP3 from only three animal rotaviruses (SA11, SA114F, and bovine UK) has been determined and that from a human strain has not been reported. To determine the genetic diversity among gene 7 alleles from group A rotaviruses, the nucleotide sequence of the NSP3 gene from 13 strains belonging to nine different G serotypes, from both humans and animals, has been determined. Based on the amino acid sequence identity as well as phylogenetic analysis, NSP3 from group A rotaviruses falls into three evolutionarily related groups, i.e., the SA11 group, the Wa group, and the S2 group. The SA 11/SA114F gene appears to have a distant ancestral origin from that of the others and codes for a polypeptide of 315 amino acids (aa) in length. NSP3 from all other group A rotaviruses is only 313 aa in length because of a 2-amino-acid deletion near the carboxy-terminus, While the SA114F gene has the longest 3' untranslated region (UTR) of 132 nucleotides, that from other strains suffered deletions of varying lengths at two positions downstream of the translational termination codon. In spite of the divergence of the nucleotide (nt) sequence in the protein coding region, a stretch of about 80 nt in the 3' UTR is highly conserved in the NSP3 gene from all the strains. This conserved sequence in the 3' UTR might play an important role in the regulation of expression of the NSP3 gene. (C) 1995 Academic Press, Inc.

Metastable phase relations and europium(II) luminescence of barium hexa-aluminates prepared by gel to crystallite conversion

Wet chemical reaction of hydrated alumina gels, Al2O3.yH(2)O(80

Microstructure evolution during solidification of DRMMCs (discontinuously reinforced metal matrix composites): State of art

Distribution of particle reinforcements in cast composites is determined by the morphology of the solidification front. Interestingly, during solidification, the morphology of the interface is intrinsically affected by the presence of dispersed reinforcements. Thus the dispersoid distribution and length scale of matrix microstructure is a result of the interplay between these two. A proper combination of material and process parameters can be used to obtain composites with tailored microstructures. This requires the generation of a broad data base and optimization of the complete solidification process. The length scale of soldification microtructure has a large influence on the mechanical properties of the composites. This presentation addresses the concept of a particle distribution map which can help in predicting particle distribution under different solidification conditions Future research directions have also been indicated.

The influence of temperature gradient and lowering speed on the melt-solid interface shape of GaxIn1-xSb alloy crystals grown by vertical Bridgman technique

Radially homogeneous bulk alloys of GaxIn1-xSb in the range 0.7 < x < 0.8, have been grown by vertical Bridgman technique. The factors affecting the interface shape during the growth were optimised to achieve zero convexity. From a series of experiments, a critical ratio of the temperature gradient (G) of the furnace at the melting point of the melt composition to the ampoule lowering speed (v) was deduced for attaining the planarity of the melt-solid interface. The studies carried out on directional solidification of Ga0.77In0.23Sb mixed crystals employing planar melt-solid interface exhibited superior quality than those with nonplanar interfaces. The solutions to certain problems encountered during the synthesis and growth of the compound were discussed. (C) 1999 Elsevier Science B.V. All rights reserved.

Zero-point entropy in 'spin ice'

Common water ice (ice I-h) is an unusual solid-the oxygen atoms form a periodic structure but the hydrogen atoms are highly disordered due to there being two inequivalent O-H bond lengths'. Pauling showed that the presence of these two bond lengths leads to a macroscopic degeneracy of possible ground states(2,3), such that the system has finite entropy as the temperature tends towards zero. The dynamics associated with this degeneracy are experimentally inaccessible, however, as ice melts and the hydrogen dynamics cannot be studied independently of oxygen motion(4). An analogous system(5) in which this degeneracy can be studied is a magnet with the pyrochlore structure-termed 'spin ice'-where spin orientation plays a similar role to that of the hydrogen position in ice I-h. Here we present specific-heat data for one such system, Dy2Ti2O7, from which we infer a total spin entropy of 0.67Rln2. This is similar to the value, 0.71Rln2, determined for ice I-h, SO confirming the validity of the correspondence. We also find, through application of a magnetic field, behaviour not accessible in water ice-restoration of much of the ground-state entropy and new transitions involving transverse spin degrees of freedom.

Altruistic Wasps?

Polistes dominulus is one of the most common social wasps in Europe and is an invasive species in the United States. Its wide prevalence has made it one of the best-studied social wasps. In most social wasps, the female wasps live in a colony and organize themselves into a behavioral dominance hierarchy such that only the dominant alpha individual (the queen) reproduces while the rest function as apparently altruistic, sterile subordinates (workers), building the nest, foraging for food and pulp, and feeding and caring for the brood. Why should workers invest their time and energy helping to rear the queen's brood, rather than found their own nests and rear their own brood—something they are quite capable of? On page 874 of this issue, Leadbeater et al. (1) show that the subordinates indeed produce their own offspring and this raises interesting questions about the links between altruism, direct reproduction, and the evolution of social behavior.