Acyclic Edge Coloring of Graphs with Maximum Degree 4

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). It was conjectured by Alon, Sudakov, and Zaks that for any simple and finite graph G, a'(G) <= Delta+2, where Delta=Delta(G) denotes the maximum degree of G. We prove the conjecture for connected graphs with Delta(G)<= 4, with the additional restriction that m <= 2n-1, where n is the number of vertices and m is the number of edges in G. Note that for any graph G, m <= 2n, when Delta(G)<= 4. It follows that for any graph G if Delta(G)<= 4, then a'(G) <= 7.

Lawyers linked to litigation funding face court censure: Bolitho v Banksia Securities Limited (No.4) [2014] VSC 582

In Bolitho v Banksia Securities Limited (No 4) [2014] VSC 582 the Supreme Court of Victoria concluded that the proper administration of justice, including the appearance of justice, required that the lawyers representing the plaintiff in the group proceeding should be restrained from continuing to act for the plaintiff. This Victorian case illustrates how courts are likely to respond when lawyers attempt to circumvent the prohibition on contingency fees through litigation funding in which they have a financial interest.

Microsomal 11-Alpha-hydroxylation of progesterone in Aspergillius ochraceus: Part I: Characterization of the hydroxylase system

Microsomes (105,000xg sediment) prepared from induced cells of A.ochraceus was found to hydroxylate progesterone to 11-Alpha-hydroxyprogesterone (11a-OHP) in high yields (85-�90% in 30 min.) in the presence of NADPH and O2. The pH optimum for the hydroxylase was found to be 7.7. However, for the isolation of active microsomes grinding of the mycelium should be carried out at pH 8.3. Metyrapone, carbon monoxide, SKF-525A, p-CMB and N-methyl maleimide inhibited the hydroxylase activity indicating the involvement of cytochrome P-450 system. The inhibition of the hydroxylase by cytochrome Image and the presence of high levels of NADPH-cytochrome Image reductase in induced microsomes suggest that the reductase could be one of the components in the hydroxylase system.

Two- and three-dimensional lead-1H-imidazole-4,5-dicarboxylates

Reaction of lead nitrate and 1H-imidazole-4,5-dicarboxylic acid under hydrothermal conditions carried out at different temperatures and pH yields a hybrid Compound Pb-2(1H-imidazole-4,5-dicarboxylate)2, 1, and a three-dimensional coordination polymer Pb(1H-imidazole-4,5-dicarboxylate), It. The two-dimensional double-layered compound, 1, with two-dimensional inorganic connectivities and one-dimensional organic connectivity is novel since hybrid compounds formed by 1H-imidazole-4,5-dicarboxylic acid are uncommon. The lead atoms in I have holodirectional geometry, while those in II show hemidirectionality. In both I and II, 1H-imidazole-4,5-dicarboxylic acid acts as a multi-dentate ligand with both the carboxylic groups and the amine group taking part in coordination. (C) 2009 Elsevier B.V. All rights reserved.

Recovery of intravenously infused chromium EDTA and lithium sulphate in the urine of cattle and their use as markers to measure urine volume

A series of metabolism experiments investigated the recovery of continuous-, intravenously infused chromium complexed with ethylenediamine tetra-acetic acid (CrEDTA) and lithium sulphate in the urine of cattle with a view to using the markers to estimate urine and metabolite output in grazing cattle. The recovery of Cr in urine from these infusions was similar (90%) in metabolism trials when cattle consumed three very contrasting diets: high-grain formulated pellet, lucerne hay (Medicago sativa) or low-quality native grass hay (predominantly Heteropogon contortus). By contrast, Li recovery in urine averaged 46.3 +/- 0.40% and 72.6 +/- 0.43% for native pasture and lucerne hays, respectively, but was not constant across days. There was negligible transfer of Cr from CrEDTA in blood serum to the rumen or faeces, whereas appreciable quantities of infused Li were found in both. The ratio of urine volume estimated by spot samples and marker dilution of Cr, to urine volume measured gravimetrically, was 1.05. In grazing studies using rumen-fistulated (RF) steers grazing seven different tropical and temperate grass and legume pastures, the ratio of concentrations of purine derivatives (PD) to Cr in spot samples of urine was shown to vary diurnally in the range of 49% to 157% of the average 24 h value. This finding indicated the need for regular sampling of urine to achieve an accurate average value for the PD: Cr ratio in urine for use in estimating urinary PD excretion and hence microbial protein production in the rumen. It was concluded that continuous, intravenous infusion of CrEDTA resulted in a constant recovery of Cr in the urine of cattle across diets and, provided an intensive sampling regime was followed to account for diurnal variation, it would be suitable as a marker to estimate urine volume and urinary output of PD in grazing cattle.

Structure of a peptide oxazolone: 2-(1'-benzyloxycarbonylamino-1'-methylethyl)-4,4-dimethyl-5-oxazolone

C16H20N204, monoclinic, P21, a = 6.270 (1),b= 11.119(3),c= ll.640(4)A, fl= 100.7 (2)°,Dm = 1-27 (flotation), Dc = 1-26 Mg m -3, Z = 2. The structure has been refined to a final R value of 0.041 for 1584 independent counter-measured reflections. The oxazolone ring in the molecule is nearly planar. The exocyclic O atom is 0.065 A out of the plane defined by the other four atoms in the ring belonging to the lactone group. The difference in length between the two adjacent C-O bonds in the ring is small, but significant. The crystal structure is stabilized by van der Waals interactions and a N--H... N hydrogen bond.

Structure of (4S)-2,4-dimethyl-1,2-dihydropyrazino[2,1-b]quinazoline-3(4H),6-dione

C13HI3N302, orthorhombic, P2~2121, a = 17.443 (5), b = 11.650 (4), c = 5.784 (1)/~, Z = 4, d m = 1.456, d c = 1.429 Mg m -3, F(000) = 512, g(Cu Ka) = 0.843 mm-L The R index is 0.040 for 1358 significant reflections. The structure is stabilized by C-H...O interactions. The N-methylated eis peptide group which forms part of a six-membered ring is non-planar. The torsion angle about the peptide bond is -6.1 (4) ° and the peptide bond length is 1.337 (3) A.

1-Benzoyl-3-methyl-2,6-diphenyl-4-piperidone

In the title moleclue, C25H23NO2, the 4-piperidone ring adopts a boat conformation. The molecular conformation is stabilized by an intramolecular C-H center dot center dot center dot O hydrogen bond. In the crystal, molecules are connected through weak intermolecular C-H center dot center dot center dot O hydrogen bonds.

Structure of 4-Hydroxymonophenylbutazone

4-Butyl-4-hydroxy-l-phenyl-3,5-pyrazolidinedione, ClaH16N20 a, Mr=248.3, monoclinic, P21/n, a = 22.357 (5), b = 5.014 (2), c = 11.350 (4)/~,, //=91.88(3) °, V=1272(1)A 3, Z=4, D,,=1.296(3), D x = 1.297 Mg m -3, 2(Cu Ka) = 1.5418/~, a = 0.777 mm -~, F(000) = 528, T= 293 K. Final R - 0.059 for 1668 observed reflections. The hetero nitrogen which carries the six-membered ring is planar in the structure while the other unsubstituted one is pyramidal. The five- and six-membered rings are almost coplanar. The crystal is made up of infinite columns of hydrogen-bonded molecules.

Impacts of grazing management options on pasture and animal productivity in a Heteropogon contortus (black speargrass) pasture in central Queensland. 4. Animal production.

Steer liveweight gains were measured in an extensive grazing study conducted in a Heteropogon contortus (black speargrass) pasture in central Queensland between 1988 and 2001. Treatments included a range of stocking rates in native pastures, legume-oversown native pasture and animal diet supplement/spring-burning pastures. Seasonal rainfall throughout this study was below the long-term mean. Mean annual pasture utilisation ranged from 13 to 61%. Annual liveweight gains per head in native pasture were highly variable among years and ranged from a low of 43 kg/steer at 2 ha/steer to a high of 182 kg/steer at 8 ha/steer. Annual liveweight gains were consistently highest at light stocking and decreased with increasing stocking rate. Annual liveweight gain per hectare increased linearly with stocking rate. These stocking rate trends were also evident in legume-oversown pastures although both the intercept and slope of the regressions for legume-oversown pastures were higher than that for native pasture. The highest annual liveweight gain for legume-oversown pasture was 221 kg/steer at 4 ha/steer. After 13 years, annual liveweight gain per unit area occurred at the heaviest stocking rate despite deleterious changes in the pasture. Across all years, the annual liveweight advantage for legume-oversown pastures was 37 kg/steer. Compared with native pasture, changes in annual liveweight gain with burning were variable. It was concluded that cattle productivity is sustainable when stocking rates are maintained at 4 ha/steer or lighter (equivalent to a utilisation rate around 30%). Although steer liveweight gain occurred at all stocking rates and economic returns were highest at heaviest stocking rates, stocking rates heavier than 4 ha/steer are unsustainable because of their long-term impact on pasture productivity.

Osseointegrated total knee replacement connected to a lower limb prosthesis: 4 cases

Background and purpose — Osseointegrated implants are an alternative for prosthetic attachment in individuals with amputation who are unable to wear a socket. However, the load transmitted through the osseointegrated fixation to the residual tibia and knee joint can be unbearable for those with transtibial amputation and knee arthritis. We report on the feasibility of combining total knee replacement (TKR) with an osseointegrated implant for prosthetic attachment. Patients and methods — We retrospectively reviewed all 4 cases (aged 38–77 years) of transtibial amputations managed with osseointegration and TKR in 2012–2014. The below-the-knee prosthesis was connected to the tibial base plate of a TKR, enabling the tibial residuum and knee joint to act as weight-sharing structures. A 2-stage procedure involved connecting a standard hinged TKR to custom-made implants and creation of a skin-implant interface. Clinical outcomes were assessed at baseline and after 1–3 years of follow-up using standard measures of health-related quality of life, ambulation, and activity level including the questionnaire for transfemoral amputees (Q-TFA) and the 6-minute walk test. Results — There were no major complications, and there was 1 case of superficial infection. All patients showed improved clinical outcomes, with a Q-TFA improvement range of 29–52 and a 6-minute walk test improvement range of 37–84 meters. Interpretation — It is possible to combine TKR with osseointegrated implants.

Superconformal transformations of theN = 2,D = 4, SSYM

We obtain the superconformal transformation laws for theN=2,D=4 SSYM. The transformations involve Yang-Mills fields and the corresponding field strength tensor is not constrained to be self antidual. We explicitly demonstrate the closure of the superconformal algebra.

Structure of ethyl 1,2,2-tricyano 3-(4-nitrophenyl)-cyclopropane-1-carboxylate

C15HIoN404, monoclinic, P2~/c, a = 10.694(8), b = 11.743 (8), c - 12.658 (8) A, fl = 113.10 (7) °, V = 1462.1 A 3, Z = 4, O m = 1 "38, O c = 1.408 g cm -3, t,t(MoKa, ~, = 0.7107 ]~) = 0.99 cm -i, F(000) = 640. The structure was solved by direct methods and refined to an R value of 0.054 using 1398 intensity measurements. The relative magnitudes of interaction of the substituents and the extent to which a ring can accommodate interactions with substituents are discussed.

Culture Condition Dependent Changes Of 4-Thiouridine In The Transfer-Rna Of Azotobacter-Vinelandii

4..T~iouridine, a thionucleoside present in the transfer RNA of the free living, nitrogen-fixing ?actenu~ Azotobacter »inelandii shows a culture condition dependent change. When thebacterium IS grown Intheabsen~e ofanyfixed nit~ogen thetRNA contains 4-thiouridine to theextent of 45% of the total sulphur Incorporated. This gets reduced to 5%when the bacterium is grown in the presen~e of.e~ces~ ofamm~nium salt.Instead, a new thionucleoside which appears to be a derivative of 4-thloundlne IS found In the tRNA to the extent of 28%of the total sulphur incorporated.