An upper bound for Cubicity in terms of Boxicity

An axis-parallel b-dimensional box is a Cartesian product R-1 x R-2 x ... x R-b where each R-i (for 1 <= i <= b) is a closed interval of the form [a(i), b(i)] on the real line. The boxicity of any graph G, box(G) is the minimum positive integer b such that G can be represented as the intersection graph of axis-parallel b-dimensional boxes. A b-dimensional cube is a Cartesian product R-1 x R-2 x ... x R-b, where each R-i (for 1 <= i <= b) is a closed interval of the form [a(i), a(i) + 1] on the real line. When the boxes are restricted to be axis-parallel cubes in b-dimension, the minimum dimension b required to represent the graph is called the cubicity of the graph (denoted by cub(G)). In this paper we prove that cub(G) <= inverted right perpendicularlog(2) ninverted left perpendicular box(G), where n is the number of vertices in the graph. We also show that this upper bound is tight.Some immediate consequences of the above result are listed below: 1. Planar graphs have cubicity at most 3inverted right perpendicularlog(2) ninvereted left perpendicular.2. Outer planar graphs have cubicity at most 2inverted right perpendicularlog(2) ninverted left perpendicular.3. Any graph of treewidth tw has cubicity at most (tw + 2) inverted right perpendicularlog(2) ninverted left perpendicular. Thus, chordal graphs have cubicity at most (omega + 1) inverted right erpendicularlog(2) ninverted left perpendicular and circular arc graphs have cubicity at most (2 omega + 1)inverted right perpendicularlog(2) ninverted left perpendicular, where omega is the clique number.

Light scattering studies on solutions of chlorinated rubber

Measurements have been made of the depolarisation factors \sigma u ,\sigma v ,\sigma h, and the intensity of scattering in the horizontal transverse direction, in the case of solutions of four different samples of chlorinated rubber in carbon tetrachloride. The size, shape and molecular weight of the micelles have been deduced by the application of the light scattering theories of Gans, Vrklajan and Katalinic and Debye. The extent to which the degradation of the rubber molecule occurs on chlorination has also been assessed.

Studies on the Tracking and Erosion Resistance of RTV Silicone Rubber Nanocomposite

One of the problems associated with outdoor polymeric insulators is tracking and erosion of the weathershed which can directly influence the reliability of the power system. Flame retardants are added to the base material to enhance its tracking and erosion resistance. Hydroxide fillers are regarded as the best flame retardants. This paper deals with studies related to nano - sized magnesium dihydroxide (MDH) and micron-sized Alumina Trihydrate (ATH) fillers as flame retardants in RTV silicone rubber. Tracking and erosion resistance studies were carried out on MDH and ATH silicone rubber composites using an inclined plane tracking and erosion (IPT) resistance tester. The MDH filled (5% by wt) composites performed much better than ATH composites in terms of eroded mass, depth of erosion, width and length of erosion. The eroded mass of MDH composite is 49.8 % that of ATH composite which can be attributed to high surface area and higher thermal stability of MDH nanofillers.

Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.)

A trial was undertaken to evaluate the effect of microwaves on seed mortality of three weed species. Seeds of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.) were buried at six depths (0, 2.5, 5, 10, 20 and 40 cm) in coarse sand maintained at one of two moisture levels, oven dry or wet (field capacity), and then subjected to one of five microwave radiation durations of (0, 2, 4, 8 and 16 min). Significant interactions between soil moisture level, microwave radiation duration, seed burial depth and species were detected for mortality of seeds of all three species. Maximum seed mortality of rubber vine (88%), parthenium (67%) and bellyache bush (94%) occurred in wet soil irradiated for 16 min. Maximum seed mortality of rubber vine and bellyache bush seeds occurred in seeds buried at 2.5 cm depth whereas that of parthenium occurred in seeds buried at 10 cm depth. Maximum soil temperatures of 114.1 and 87.5°C in dry and wet soil respectively occurred at 2.5 cm depth following 16 min irradiation. Irrespective of the greater soil temperatures recorded in dry soil, irradiating seeds in wet soil generally increased seed mortality 2.9-fold compared with dry soil. Moisture content of wet soil averaged 5.7% compared with 0.1% for dry soil. Results suggest that microwave radiation has the potential to kill seeds located in the soil seed bank. However, many factors, including weed species susceptibility, determine the effectiveness of microwave radiation on buried seeds. Microwave radiation may be an alternative to conventional methods at rapidly depleting soil seed banks in the field, particularly in relatively wet soils that contain long lived weed seeds.

Lower-bound collapse load Of square footing

Based on a radial moment field and the square yield criterion, a lower-bound collapse load is developed for a square footing subjected to a generalized contact pressure distribution. The current lower-bound collapse load compares well with the available upper-bound solutions.

Phosphorus nutrition and tolerance of cotton to water stress: II. Water relations, free and bound water and leaf expansion rate

In previous experiments, increased leaf-Phosphorus (P) content with increasing P supply enhanced the individual leaf expansion and water content of fresh cotton leaves in a severely drying soil. In this paper, we report on the bulk water content of leaves and its components, free and bound water, along with other measures of plant water status, in expanding cotton leaves of various ages in a drying soil with different P concentrations. The bound water in living tissue is more likely to play a major role in tolerance to abiotic stresses by maintaining the structural integrity and/or cell wall extensibility of the leaves, whilst an increased amount of free water might be able to enhance solute accumulation, leading to better osmotic adjustment and tolerance to water stress, and maintenance of the volumes of sub-cellular compartments for expansive leaf growth. There were strong correlations between leaf-P%, leaf water (total, free and bound water) and leaf expansion rate (LER) under water stress conditions in a severely drying soil. Increased soil-P enhanced the uptake of P from a drying soil, leading to increased supply of osmotically active inorganic solutes to the cells in growing leaves. This appears to have led to the accumulation of free water and more bound water, ultimately leading to increased leaf expansion rates as compared to plants in low P soil under similar water stress conditions. The greater amount of bound and free water in the high-P plants was not necessarily associated with changes in cell turgor, and appears to have maintained the cell-wall properties and extensibility under water stressed conditions in soils that are nutritionally P-deficient.

Changes in the Activities of two membrane-bound enzymes during solar eclipse on February 16, 1980

ON Saturday February 16, 1980 total solar eclipse Occurred for a period of 2-3 min in a belt of 135 km during the eclipse from 14'17 to 17'00 hrs across peninsular India. The city of Bangalore, being just outside this belt, had witnessed 92% eclipse for about 2. 1/2 min at the peak period of 15.44 hr at which time a temperature drop of 2' C and a considerable dimness of the light were experienced. In view of the interest in our laboratory on biochemical adaptation under conditions of environmental stress, we designed an experiment to study the possible changes in enzyme activities during the solar eclipse on February 16, 1980.

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem o limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (xi(gamma)) is determined. On account of interference, the magnitude of xi(gamma) is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.

Interactions between butterfly pea (Clitoria ternatea) and rubber vine (Cryptostegia grandiflora)

The arutors studied the impact of a forage legume, butterfly pea, on rubber vine at the early establishment phase under seven planting combinations at three nitrogen fertiliser levels. In pure stands, both species increased their shoot and root dry weight yield in response to nitrogen but rubber vine exhibited the greater response. In mixed stands, rubber vine and butterfly pea did not compete with each other at any nitrogen level. An over-yielding response resulted in all mixture combinations in terms of shoot and root yields. Total shoot and root mass of mixed stands significantly out-yielded their highest yielding pure stands by 8% and 27% respectively, suggesting that butterfly pea not only failed to reduce shoot and root growth of rubber vine, but actually improved its growth performance. Consequently, the introduction of butterfly pea to suppress rubber vine is not warranted.

Structures of mannose-6-phosphate isomerase from Salmonella typhimurium bound to metal atoms and substrate: implications for catalytic mechanism

Mannose-6-phosphate isomerase (MPI) catalyzes the inter-conversion of mannose 6-phosphate and fructose 6-phosphate. X-ray crystal structures of MPI from Salmonella typhimurium in the apo form (with no metal bound) and in the holo form (with bound Zn2+) and two other structures with yttrium bound at an inhibitory site and complexed with Zn2+ and fructose 6-phosphate (F6P) were determined in order to gain insights into the structure and the isomerization mechanism. Isomerization involves acid/base catalysis with proton transfer between the C1 and C2 atoms of the substrate. His99, Lys132, His131 and Asp270 are close to the substrate and are likely to be the residues involved in proton transfer. The interactions observed at the active site suggest that the ring-opening step is probably catalyzed by His99 and Asp270. An active-site loop consisting of residues 130-133 undergoes conformational changes upon substrate binding. Zn2+ binding induces structural order in the loop consisting of residues 50-54. The metal atom appears to play a role in substrate binding and is probably also important for maintaining the architecture of the active site. Isomerization probably follows the previously suggested cis-enediol mechanism.

Purification of Antibodies Specific to a Dinucleotide Using the Hapten Bound to Deae Cellulose as an Affinity Column

The dinucleotide dpTpA held electrostatically on DEAE cellulose was used as an affinity column for the purification of dpTpA specific antibodies. Chromatography of the y-globulin fraction from dpTpA specific antisera on this column resulted in the retention of dpTpA specific antibodies which were later eluted along with the bound dpTpA using 1M NaC1. Dextran coated charcoal was the method of choice for the dissociation and removal of dpTpA bound to the antibodies. This method may extend itself to the purification of antibodies specific for other oligonucleotides.

Utilisation of local ingredients in commercial pig feeds

The long-term competitiveness of the both the Vietnamese feed and pig production industries are constrained and under pressure whilst the industry is dependent on the use of imported feed ingredients in diets for animal production. These cost pressures are a result of import taxes, transport costs, currency fluctuations and feed supply limitations. By undertaking studies on available resources which are currently under-utilised and with potential as local feeds, we can prove their suitability for use as feedstuffs in pig diets and as replacements for imported feed ingredients. In undertaking this process we can lower feeding costs for pig production in Vietnam by the use of local feeds which are cheaper, generate new industries in Vietnam harvesting or processing these feeds and increase the incomes of Vietnamese workers who are involved in producing these by-products. Our project has shown that rubber seed, when processed correctly to lower the hydrogen cyanide content, is a safe and suitable protein meal feedstuff for use in pig diets with the potential to replace significant quantities of imported soybean and fishmeal in Vietnamese pig diets as long as diets are balanced for any amino acid shortfalls. Our peanut studies have shown that use of binders can help alleviate pig production problems with aflatoxin content in peanut meals. Further work is needed to characterise the fate of the bound aflatoxin to see if there is any meat residue risk. Cassava residue is a resultant by-product from starch extraction in both large and small cassava processing factories. Sub-samples from these two mill types were collected and evaluated for residue HCN. Analyses has shown that the processing and sun drying results in a product with relatively consistent low HCN content. Chemical analyses also reveal that significant residual starch also remains in this by-product. Digestibility studies and pig performance feeding studies have shown that cassava residue can be included in diets at 30% with no adverse effect, although the higher fibre content of this product means that strategically, cassava residue is more suitably used in finisher and sow diets. Research has examined the digestible energy content of a number of sunflower meal types available in Australia and identified major differences in their energy value based on processing, additionally, amino acid analysis has shown a significantly lower lysine content than previous reported. We also examined the digestible energy content of a number of Australian stylo forage legume harvest batches and identified the differences in their energy value based on age/harvest time of the forage legume. Analysis results of various stylo cuts showed that the early cut stylo has a higher starch content and lower fibre fraction content than observed in late and recut stylo which were allowed to grow longer. As a result the faecal digestible energy content was higher for the early cut stylo than for the subsequent cut stylo material which had been allowed to become woody. The results have shown that feeding of stylo meal does provide some nutritive value to the pig with increased energy and nitrogen supply, with a portion of the nitrogen presented which the pig is able to retain. Based on nutrient and fibre content stylo could have a useful role in sow feeding and satiety under non-stall housing situations. With increasing Vietnamese investment in rubber production seen with larger areas under plantations the amounts of rubber seed available for animal feeding will grow significantly over the next 15 years and the importance of the by-product ie rubber seed meal as a protein source in diets for Vietnamese pigs.

An investigation of bond formation in the weakly bound first excited 1Σ and lowest 3Σ states of HeH+

The role of the electronic kinetic energy and its Cartesian components is examined during the formation of the first excited 1�£ and the lowest 3�£ states of HeH+ employing wavefunctions of multi-configuration type with basis orbitals in elliptic coordinates. Results show that the bond formation in these states is preceded primarily by a charge transfer from H to He+ rather than by polarisation of the H-orbital by He+

Improvement On Brooks Chromatic Bound For A Class Of Graphs

Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has an odd cycle as a component, or (2) n>2 and Kn+1 is a component of G. In this paper we prove that if a graph G has none of some three graphs (K1,3;K5−e and H) as an induced subgraph and if Δ(G)greater-or-equal, slanted6 and d(G)<Δ(G), then χ(G)<Δ(G). Also we give examples to show that the hypothesis Δ(G)greater-or-equal, slanted6 can not be non-trivially relaxed and the graph K5−e can not be removed from the hypothesis. Moreover, for a graph G with none of K1,3;K5−e and H as an induced subgraph, we verify Borodin and Kostochka's conjecture that if for a graph G,Δ(G)greater-or-equal, slanted9 and d(G)<Δ(G), then χ(G)<Δ(G).