A class of transformed Markov processes

This paper considers some properties of a class of transformed Markov processes. The analogy with Whittle's relaxed Markov process is pointed out. Some applications of the transformed Markov processes to queueing networks are described     

Teacher preparation for a problem-solving curriculum in Singapore

Problem solving is at the heart of the Singapore Mathematics curriculum. However, it remains a challenge for teachers to realise this curricular goal in practice. Here, we review the efforts of Singapore mathematics teacher educators in incorporating problem-solving (teaching) competency in teacher education and PD programmes. We discuss conceptual and practical issues, actions taken and changes made in building teachers?? capacity to enact a problem-solving curriculum in a school-based design experiment project. In the project, teachers learnt problem solving, observed and then carried out lessons, using the ??Mathematics Practical????akin to the science practical??as key to instruction and assessment.     

Bubble particle heterocoagulation under turbulent conditions

An analytical model that enables the calculation of the flotation rate constant of particles as a function of particle size with, as input parameters, measurable particle, bubble, and hydrodynamic quantities has been derived. This model includes the frequency of collisions between particles and bubbles as well as their efficiencies of collision, attachment, and stability. The generalized Sutherland equation collision model and the modified Dobby-Finch attachment model developed previously for potential flow conditions were used to calculate the efficiencies of particle-bubble collision and attachment, respectively. The bubble-particle stability efficiency model includes the various forces acting between the bubble and the attached particle, and we demonstrate that it depends mainly on the relative magnitude of particle contact angle and turbulent dissipation energy. The flotation rate constants calculated with these models produced the characteristic shape of the flotation rate constant versus particle size curve, with a maximum appearing at intermediate particle size. The low flotation rate constants of fine and coarse particles result from their low efficiency of collision and low efficiencies of attachment and stability with gas bubbles, respectively. The flotation rate constants calculated with these models were compared with the experimental flotation rate constants of methylated quartz particles with diameters between 8 and 80 micro m interacting with gas bubbles under turbulent conditions in a Rushton flotation cell. Agreement between theory and experiment is satisfactory.     

Field ion microscope observations of surface rearrangement and oxide formation at clean rhenium surfaces heated in oxygen

The interaction between oxygen and clean, well-ordered rhenium surfaces has been investigated in the field ion microscope over a wide range of temperatures. The surface structure of vacuum annealed specimens was extensively modified by the presence of adsorbed oxygen. At partial monolayer coverages, surface metal atom rearrangement was inhibited, particularly at {112?2}, but at coverages near saturation, facets were produced at {101?0} at a lower temperature than on the clean surface, resulting in the exposure of an increased proportion of closepacked surface structures and suggesting a change in the rearrangement mechanism at high coverages. The production of facets at the major poles was temperature and coverage dependent as a result of the varying influence of adsorbed oxygen on surface free energy. A decrease in oxygen coverage was observed at 1200–1300 K on near-saturated surfaces, which may be associated with the formation of volatile ReO₃ from regions where oxygen concentration exceeds a critical value. There was little evidence of the production of a discrete surface oxide phase formed on specimens heated in the presence of gas phase oxygen, but a reduction in specimen radius as a result of volatile oxide formation was observed at pressures greater than 10^?4 Torr and temperatures above 1400 K. It is concluded that the final structure of rhenium surfaces heated in oxygen is dependent upon the rate of oxide formation, the effective oxygen coverage during oxidation, and the extent of surface rearrangement.     

Syntheses and crystal structures of binuclear ruthenium complexes bearing 1,8′-bis(diphenylphosphinomethyl)naphthalene

Treatment of [RuCl₂(η⁶-C₆H₆)]_x with bidentate phosphine ligand BDNA [1,8-bis(diphenylphosphinomethyl)naphthalene] in methanol at room temperature gave η⁶-benzene-ruthenium complexes Ru₂Cl₄(η⁶-C₆H₆)₂(μ-BDNA) (1). Complex 1 further reacted with AgBF₄ to form complex [Ru₂Cl₂(μ-Cl)(η⁶-C₆H₆)₂(μ-BDNA)](BF₄) (2). [RuCl₂(η⁶-C₆H₆)]_x reacted with BDNA in refluxing methanol and then the reaction solution was treated with AgBF₄ to generate complex [Ru₂Cl₂(η⁶-C₆H₆)₂(μ-BDNA)₂](BF₄)₂ (3). Their compositions and structures had been determined by elemental analyses, NMR spectra and single crystal X-ray diffractions. X-ray diffraction showed that complex 1 belonged to monoclinic crystal system, P2₁/c space group with Z = 4, a = 12.810 Å, b = 21.507 Å, c = 18.471 Å, β = 107.95°; complex 2 belonged monoclinic crystal system, P2₁/n space group with Z = 4, a = 14.498 Å, b = 15.644 Å, c = 20.788 Å, β = 103.404°, and complex 3 belonged to monoclinic crystal system, P2₁/n space group with Z = 2, a = 13.732 Å, b = 14.351 Å, c = 19.733 Å, β = 94.82°.     

Cobalt complexes in aqueous solutions as dioxygen carriers

This article provides a short survey on the thermodynamic and kinetic behaviour of cobalt complexes, which are able to bind molecular oxygen in aqueous solutions. The focus is on cobalt complexes with simple polyamines and with polynucleating ligands that share the same basic structure, in terms of them being elements of a sequence with increasing complexity. Ditopic polyazapolyoxalkanes and dicompartimental ligands containing a phenolic moiety are also considered. The aim is to elucidate the relation between the structure of the ligands and the behaviour of their cobalt complexes as donors and acceptors of dioxygen.     

Kinetic and equilibrium studies on the polyazamacrocycle neotetren: metal-complex formation and DNA interaction

The macrocyclic polyamine 2,5,8,11,14-pentaaza[15]-[15](2,9)[1,10]phenanthrolinophane (neotetren) is studied in its ability to coordinate Cu(ii) even at very low pH values and to interact, as a metal complex, with DNA. The kinetics and equilibria for 1 : 1 and 2 : 1 metal-ligand complexes formation are studied by the stopped-flow method and UV spectrophotometry. Differently protonated complexes are formed, with rate constants much lower than that of water exchange at copper(II) and other Cu(II)/amine systems, this behaviour being ascribed to ring effects and intra-molecular hydrogen bonds. Concerning the DNA/copper(II)-neotetren complexes interaction, analysis of data suggests an intercalative mode of binding. The kinetic results for both DNA/CuL and DNA/Cu(2)L systems agree with the sequence D + S <-->D,S <-->DS where the metal complexes (D) react with the DNA sites (S) leading to fast formation of an externally bound form (D,S) which is converted into an intercalated complex (DS). A very slow process is also detected and ascribed to a conformational change in the polynucleotide secondary structure where the metal centre plays a crucial role. Chromatographic experiments demonstrate that both the investigated Cu(II)/L complexes are able to cleave DNA, but only in the presence of hydrogen peroxide.     

Paclitaxel‐Loaded Stabilizer‐Free Poly(D,L‐lactide‐co‐glycolide) Nanoparticles Conjugated with Quantum Dots for Reversion of Anti‐Cancer Drug Resistance and Cancer Cellular Imaging

We prepared the PLGA‐loaded anti‐cancer drug and coated it with quantum dots to make it a dual‐function nanoparticles, and analyzed its potential use in cellular imaging and curing cancers. Two cancer cell lines, paclitaxel‐sensitive KB and paclitaxel‐resistant KB paclitaxel‐50 cervical carcinoma cells, were the relativistic models for analysis of the cytotoxicity of free paclitaxel and paclitaxel‐loaded PLGA conjugated with quantum‐dot nanoparticles. The paclitaxel‐loaded PLGA conjugated with quantum dots nanoparticles were significantly more cytotoxic than the free paclitaxel drug in paclitaxel‐resistant KB paclitaxel‐50 cells. This might have been because the cancer cells developed multi‐drug resistance (MDR), which hampered the action of free paclitaxel by pumping its molecules to extracellular areas. Addition of verapamil, a P‐glycoprotein inhibitor, reversed the MDR mechanism and significantly reduced KB paclitaxel‐50 cell viability. As a result, KB paclitaxel‐50 was highly associated with MDR on the cell membrane. The cytotoxicity results indicated that PLGA nanoparticles served as drug carriers and protected the drugs from MDR‐accelerated efflux. Combined quantum dots with PLGA nanoparticles allowed additional functionality for cellular imaging.     

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.