Strongly regular graphs with non-trivial automorphisms

The possible existence of 16 parameter sets for strongly regular graphs with 100 or less vertices is still unknown. In this paper, we outline a method to search for strongly regular graphs by assuming a non-trivial automorphism of prime order. Among these unknown parameter sets, we eliminated many possible automorphisms, but some small prime orders still remain. We also found 6 new strongly regular graphs with parameters (49,18,7,6).     

Reviving Pólya's “Look Back” in a Singapore school

This study is based on the stance that Pólya's “Look Back,” though understudied, remains relevant to Mathematics curricula that place emphasis on problem solving. Although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare. In our project, we focus on a redesign of a teacher development programme that is targeted to help teachers realize Pólya's original vision of Look Back in the classroom. We report the cases of two teachers who have participated in the teacher development programme: their thinking about Look Back (through interview records) and their interpretation of Look Back in their classroom practice (through video records). By bringing these two spheres of data together, we discuss their degree of ‘buy-in’ to Look Back in the overall problem solving enterprise.     

In vitro and in vivo studies of androst‐4‐ene‐3,6,17‐trione in horses by gas chromatography–mass spectrometry

This paper describes the application of gas chromatography–mass spectrometry (GC‐MS) for in vitro and in vivo studies of 6‐OXO in horses, with a special aim to identify the most appropriate target metabolite to be monitored for controlling the administration of 6‐OXO in racehorses. In vitro studies of 6‐OXO were performed using horse liver microsomes. The major biotransformation observed was reduction of one keto group at the C3 or C6 positions. Three in vitro metabolites, namely 6α‐hydroxyandrost‐4‐ene‐3,17‐dione (M1), 3α‐hydroxyandrost‐4‐ene‐6,17‐dione (M2a) and 3β‐hydroxyandrost‐4‐ene‐6,17‐dione (M2b) were identified. For the in vivo studies, two thoroughbred geldings were each administered orally with 500 mg of androst‐4‐ene‐3,6,17‐trione (5 capsules of 6‐OXO_®) by stomach tubing. The results revealed that 6‐OXO was extensively metabolized. The three in vitro metabolites (M1, M2a and M2b) identified earlier were all detected in post‐administration urine samples. In addition, seven other urinary metabolites, derived from a further reduction of either one of the remaining keto groups or one of the remaining keto groups and the olefin group, were identified. These metabolites included 6α,17β‐dihydroxyandrost‐4‐en‐3‐one (M3a), 6,17‐dihydroxyandrost‐4‐en‐3‐one (M3b and M3c), 3β,6β‐dihydroxyandrost‐4‐en‐17‐one (M4a), 3,6‐dihydroxyandrost‐4‐en‐17‐one (M4b), 3,6‐dihydroxyandrostan‐17‐one (M5) and 3,17‐dihydroxyandrostan‐6‐one (M6). The longest detection time observed in urine was up to 46 h for the M6 metabolite. For blood samples, the peak 6‐OXO plasma concentration was observed 1 h post administration. Plasma 6‐OXO decreased rapidly and was not detectable 12 h post administration. Copyright © 2009 John Wiley & Sons, Ltd.     

Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model

We consider a reaction-diffusion-advection equation arising from a biological model of migrating species. The qualitative properties of the globally attracting solution are studied and in some cases the limiting profile is determined. In particular, a conjecture of Cantrell, Cosner and Lou on concentration phenomena is resolved under mild conditions. Applications to a related parabolic competition system are also discussed.     

Equilibrium conditions for CO2 hydrate in porous medium

Experimental phase equilibrium conditions data for carbon dioxide (CO₂) hydrate in porous medium with the presence of sodium chloride (NaCl) solution were investigated in this study. The experimental data were generated using graphic-method in presence of solutions contained (0, 0.2, 0.4, 0.6, and 0.8) mol/L NaCl. The results indicated the increase of NaCl concentration caused the enhancement in the equilibrium pressure of CO₂ hydrate as the pore size and the temperature were kept the same. Effects of NaCl solutions on CO₂ hydrate equilibrium conditions could be neglected when the temperature is lower than ice point. An improved model was used to predict CO₂ hydrate equilibrium conditions, and the predictions showed good agreement with experimental measurements.     

Optimum convective heat transfer coefficient for diode-pumped laser slabs

It is important for laser designers to study the characteristics of heat transfer from the laser crystal slab to the coolant in high-power DPSS laser operations. We have simulated and obtained the optimum heat transfer coefficient and coolant flow rate for our cavity design, in which the circulating coolant is maintained at a constant temperature. It has been determined that the coolant temperature and the convective heat transfer coefficient (h) are important parameters in the thermal analysis. The coefficient h is affected by the coolant flow rate, the physical properties of the laser slab and the coolant and the pumping cavity geometry. Using analytical heat transfer equation, for cooling water temperature of 300 K, the optimum flow rate for our cavity geometry is found to be 390 cm³/s, corresponding to h=5 W/cm² K.     

Piezoelectric PMN-PT fibre hydrophone for ultrasonic transducer calibration

A newly developed ceramic fibre hydrophone with an active element as small as 0.25 mm in diameter is described in this work. Lead magnesium niobate-lead titanate (PMN-PT) ceramic fibre with a nominal composition of 0.65Pb(Mg_1/3Nb_2/3)O₃-0.35PbTiO₃ was fabricated by an extrusion method. PMN-PT single crystals were ground to a powder form and then mixed with poly(acrylic) acid to form a homogenous slurry. The fibre was extruded by pressing the slurry through a spinneret and then sintering at 1250 °C for crystallization. The electrical characteristics of the PMN-PT fibre were evaluated by measuring the relative permittivity and the impedance spectrum. A piezoelectric PMN-PT fibre hydrophone was fabricated and its sensitivity, angular response, and spatial resolution were evaluated. The fibre hydrophone provides good spatial resolution, angular response and receiving sensitivity. PACS 43.58.+z; 77.84.Dy     

Spin-cluster effects and frustration in the uniaxial spin glass Fe2−xTi1+xO5

Transverse-field (TF) muon-spin-relaxation (μSR) and Mössbauer experiments on the uniaxial insulating spin glass Fe_2?xTi_1+xO₅ (x=0.25) have been performed near and below the spin-glass temperature (T _g). The effect of a transverse field on the spin-freezing process and spin-glass state has been investigated by measuring the field-and temperature-dependencies of the μSR parameters. Spin-cluster effects signaled by anomalous μ-spin relaxation have been observed in a temperature region just aboveT _g. An interpretation supported by recently developed theoretical models addressing non-linear relaxation in an intermediate Griffiths phase is offered.