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     

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.     

A numerical method for reconstructing the coefficient in a wave equation

We present a numerical method for reconstructing the coefficient in a wave equation from a single measurement of partial Dirichlet boundary data. The original inverse problem is converted to a nonlinear integral differential equation, which is solved by an iterative method. At each iteration, one linear second‐order elliptic problem is solved to update the reconstruction of the coefficient, then the reconstructed coefficient is used to solve the forward problem to obtain the new data for the next iteration. The initial guess of the iterative method is provided by an approximate model. This model extends the approximate globally convergent method proposed by Beilina and Klibanov, which has been well developed for the determination of the coefficient in a special wave equation. Numerical experiments are presented to demonstrate the stability and robustness of the proposed method with noisy data.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 289–307, 2015     

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.     

Thermal conductivity of the PbGeO<Subscript>3</Subscript> and PbGe<Subscript>3</Subscript>O<Subscript>7</Subscript> glasses

This paper reports on a study of the thermal conductivity of the PbGeO₃ and PbGe₃O₇ glasses.     

A Solution‐Processed Air‐Stable Perylene Diimide Derivative for N‐type Organic Thin Film Transistors

For future all‐soluble organic thin film transistor (OTFT) applications, a new soluble n‐type air‐stable perylene diimide derivative semiconductor material with (trifluoromethyl)benzyl groups (TC–PDI–F) is synthesized. The film is formed by spin‐coating in air and optimized for OTFT fabrications. The transistor characteristics and air‐stability of the TC–PDI–F OTFTs is measured to investigate the feasibility of using solution‐processed TC–PDI–F for future OTFT applications. For all‐solution OTFT process applications, the transistor characteristics are demonstrated by using TC–PDI–F as an n‐type semiconductor material and liquid‐phase‐deposited SiO₂ (LPD–SiO₂) as a gate dielectric material. All processes (except material synthesis and electrode deposition) and electrical measurements are conducted in air.     

Cycloaddition Reactions of 7‐Benzylidenecycloocta‐1,3,5‐triene with Ethenetetracarbonitrile and 4‐Phenyl‐3H‐1,2,4‐triazole‐3,5(4H)‐dione

An (E)/(Z) mixture (3 : 2) of 7‐benzylidenecycloocta‐1,3,5‐triene ( 5 ) is obtained when 1‐benzylcycloocta‐1,3,5,7‐tetraene ( 7 ), prepared by an improved procedure, is treated with t‐BuOK in THF. Alternatively, a ca. 9 : 1 mixture (E)/(Z)‐ 5 can be prepared in a Wittig reaction involving benzaldehyde and cycloocta‐2,4,6‐trien‐1‐ylidenetriphenylphoshorane ( 9 ). Treatment of (E)/(Z)‐ 5 88 : 12 with ethenetetracarbonitrile (TCNE) gave a complex mixture of products, from which seven mono‐adducts and two bis‐adducts were isolated (Sect. 2.2.1). Of the mono‐adducts, four are π4+π2 adducts: two ((E)‐ and (Z)‐isomers) are derived from valence tautomers of the two isomers of (E)/(Z)‐ 5 , while it is tentatively suggested that the other two (again (E)‐ and (Z)‐isomers) are formed from the intermediacy of a pentadienyl zwitterion (Sect. 2.3). The remaining three mono‐adducts, two of which are epimers, are π8+π2 adducts. It is suggested that they are derived from the intermediacy of homotropylium zwitterions (Sect. 2.3). For the two bis‐adducts, it is postulated that they are derived from an initial π2+π2 cycloaddition involving the homotropylium zwitterions followed by π4+π2 cycloaddition to the valence tautomer of each of the π2+π2 cycloadducts. With 4‐phenyl‐3H‐1,2,4‐triazole‐3,5(4H)‐dione ( 6 ), (E)/(Z)‐ 5 91 : 9 yielded two π4+π2 cycloadducts ((E)‐ and (Z)‐isomers) as well as two epimeric π8+π2 cycloadducts (Sect. 2.2.2). The intermediacy of pentadienyl (tentative suggestion) and homotropylium zwitterions accounts for the formation of the products (Sect. 2.3).     

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.     

Influence of structural features on the self‐assembly of short ionic oligopeptides

We investigated the self‐aggregation of 12 short ionic oligopeptides constituted by 4–7 amino acid residues to establish useful structure–property relationships that might be exploited in the biomedical field by using the concept of molecular Lego. We show that the critical aggregation concentration (CAC) of tetrapeptides decreases with increasing hydrophobicity of neutral residues. Additionally, the dependence of the CAC of isomeric oligopeptides on the distribution of amino acid residues confirms the high tendency to self‐organization of molecules with alternating ionic and neutral residues. Indeed, atomic force microscopy (AFM) images recorded on oligopeptide solutions above the CAC show the presence of either fibrillar or spherical aggregates depending on oligopeptide structure and concentration, steric hindrance, solution pH, and time. The potential of the investigated oligopeptides in tissue engineering applications is supported by their in vitro cytocompatibility. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 889–897, 2010