Encouraging problem-solving disposition in a Singapore classroom

In this article, we share our learning experience as a Lesson Study team. The Research Lesson was on Figural Patterns taught in Year 7. In addition to helping students learn the skills of the topic, we wanted them to develop a problem-solving disposition. The management of these two objectives was a challenge to us. From the lesson observation and the students’ classwork, it turned out better than we expected.     

Role of polyethyleneimine in the purification of recombinant human tumour necrosis factor beta

The chromatographic behaviour of recombinant human tumour necrosis factor beta (rhTNF-β) (pI9.0) during cation-exchange chromatography at pH 7.5 is investigated. Without prior treatment of the Escherichia coli cell extract with polyethyleneimine (PEI), very little rhTNF-β was bound to the column. However, upon addition of 5% PEI (100 μl ml⁻¹) to the cell lysate, rhTNF-β was shown to bind to cation-exchange columns normally. TNF-β was readily precipitated from the clarified cell extract by 20% ammonium sulphate, but only ca. 25% of this precipitate could be re-solubilized for further purification. However, when 5% PEI was included in the solubilization buffer, the balance of the rhTNF-β could be recovered. It is proposed that charge interaction between rhTNF-β and nucleic acids in the cell extract is responsible for both of these anomalous phenomena, and that PEI (a cationic polyelectrolyte) was able to disrupt this interaction by displacing rhTNF-β from the charge complex.     

Total chromatic number of complete r-partite graphs

Rosenfeld (1971) proved that the Total Colouring Conjecture holds for balanced complete r-partite graphs. Bermond (1974) determined the exact total chromatic number of every balanced complete r-partite graph. Rosenfeld's result had been generalized recently to complete r-partite graphs by Yap (1989). The main result of this paper is to prove that the total chromatic number of every complete r-partite graph G of odd order is Δ (G) + 1. This result gives a partial generalization of Bermond's theorem.     

Incorporating operations research techniques to evaluate information systems impact on healthcare

Over the past 4 years, the Hospice Palliative Care Network Project, co-led by the Temmy Latner Centre for Palliative Care, Mount Sinai Hospital, and the Toronto Community Care Access Centre, has been working toward developing an innovative model of home palliative care coordination and service delivery. After a successful completion of stage one involving data collection of approximately 400 variables to a common Linux database repository, the current stage of the Project is to compare various modes of care delivery and disseminate the results to internal and external evaluation stakeholders. The Temmy Latner Centre's customized Panacea Information Management System (PIMS) had been linked to the Linux repository in order to customize reports to determine the optimal model of coordination and service delivery that could serve as a template for home palliative care delivery in Ontario. The objective of this paper is to outline the development and functionality of the PIMS and to evaluate its contribution in terms of improved data quality and health outcomes; in other words, to justify the information systems investment by demonstrating the relationship between this investment and improved health system delivery and effectiveness.     

Cobalt tris(mercaptoimidazolyl)borate complexes: synthetic studies and the structure of the first cobaltaboratrane

The paramagnetic complexes (TmtBu)CoX (X = Cl, Br, I) have been readily prepared and structurally characterized and provide a convenient entry into cobalt(II) tris(mercaptoimidazolyl)borate chemistry. A number of derivatives, including mononuclear triphenylphosphine adducts [(TmtBu)Co(PPh3)]X and dinuclear compounds [Co2(TmtBu)2X]Y, have been prepared in order to ascertain whether cobalt is a reliable surrogate for zinc in biological systems, particularly in sulfur-rich coordination environments. The structure of the first cobaltaboratrane is also reported.     

Modeling of hard disk drives for shock and vibration analysis – consideration of nonlinearities and discontinuities

This paper reviews recent advances (mostly after year 2000) in shock and vibration analysis of hard disk drives (HDD) considering the presence of nonlinearities and discontinuities. Components and dynamic phenomena in HDD where effects of mechanical nonlinearity and discontinuities are significant are discussed, e.g., head actuator suspension, dimple and slider, head–disk interface, fluid dynamic bearing, spinning disks, and load/unload dynamics. Ways to model these nonlinearities and discontinuities are reviewed in detail. Our research on modeling an entire HDD in operating mode subject to shock and vibration using a flexible multibody dynamics formulation is also presented. The numerical simulation of the shock response of a 1-in. form factor HDD is presented. A half-sinusoidal acceleration shock is applied at the base of the HDD. Response of the flying height for different shock amplitudes and duration times is simulated.     

The orthogonal convex skull problem

We give a combinatorial definition of the notion of a simple orthogonal polygon beingk-concave, wherek is a nonnegative integer. (A polygon is orthogonal if its edges are only horizontal or vertical.) Under this definition an orthogonal polygon which is 0-concave is convex, that is, it is a rectangle, and one that is 1-concave is orthoconvex in the usual sense, and vice versa. Then we consider the problem of computing an orthoconvex orthogonal polygon of maximal area contained in a simple orthogonal polygon. This is the orthogonal version of the potato peeling problem. AnO(n ²) algorithm is presented, which is a substantial improvement over theO(n ⁷) time algorithm for the general problem.The work of the first author was supported under a Natural Sciences and Engineering Research Council of Canada Grant No. A-5692 and the work of the second author was partially supported by NSF Grants Nos. DCR-84-01898 and DCR-84-01633.     

Synthesis and Structural Characterization of Bis(μ2-Iodo)-Bis(Diethyl Ether)-(N-N′-(Bis(2,6-Diisopropylphenyl)Pentane-2,4-Diketiminato)-Lithium-Chromium, a Cr(II) (β-Diketiminato) Complex with a Coordinated LiI Salt

Abstract  Addition of CrI₂ to the lithium salt of N-N′-bis(2,6-diisopropylphenyl)-2,4-diketiminate in diethylether yields a Cr(II) iodide complex with a coordinated, solvated LiI salt. This complex is the intermediate in the synthesis of a bridging iodide complex that is itself a precursor to a side-on bridging dinitrogen complex. This complex crystallizes in the P2₁/n space group with the crystal cell parameters a = 12.3160(19) ?, b = 21.067(3) ?, c = 15.837(3)?, β = 96.767°, V = 4080.6(11) ?³ and Z = 4. Graphical Abstract  Addition CrI2 to the lithium salt of N-N′-bis(2,6- diisopropylphenyl)-2,4-diketiminate in diethylether yields a Cr(II) iodide complex with a coordinated, solvated LiI salt. Herein we report the spectroscopic and structural characterization. An erratum to this article can be found at