Buffon's needle problem with a twist

Some simple variations of Buffon's well-known needle problem in probability are discussed, and an interesting observation connecting the corresponding results is then made

Overseas trained teachers: part of a problem or part of a solution?

Overseas trained teachers (OTTs) have grown in numbers during the past decade, particularly in London and the South East of England. In this recruitment explosion many OTTs have experienced difficulties. In professional literature as well as press coverage OTTs often become part of a deficit discourse. A small-scale pilot investigation of OTT experience has begun to suggest why OTTs have been successful as well as the principal challenges they have faced. An important factor in their success was felt to be the quality of support in school from others on the staff. Major challenges included the complexity of the primary curriculum. The argument that globalisation leads to brain-drain may be exaggerated. Suggestions for further research are made, which might indicate the positive benefits OTTs can bring to a school.

Full interference cancellation for two-path relay cooperative networks

This paper proposes the full interference cancellation (FIC) algorithm to cancel the inter-relay interference (IRI) in the two-path cooperative system. Arising from simultaneous data transmission from the source and relay nodes, IRI may significantly decrease the performance if it is not carefully handled. Compared to the existing partial interference cancellation (PIC) scheme, the FIC approach is more robust yet with less complexity. Numerical results are also given to verify the proposed scheme.

Multistep electrochemical reduction path of clusters [Os3(CO)10(α-diimine)]: comparison of electrochemical and photochemical Os-Os(α-diimine) bond cleavage

Electrochemical reduction of the triangular clusters [Os-3(CO)(10)(alpha-dimine)] (alpha-dimine = 2,2'-bipyridine (bpy), 2,2'-bipyrimidine (bpym)) and [Os-3(CO)(10)(mu-bpym) ReBr(CO)(3)] produces primarily the corresponding radical anions. Their stability is strongly determined by the pi acceptor ability of the reducible alpha-dimine ligand, which decreases in the order mu-bpym > bpym >> bpy. Along this series, increasing delocalisation of the odd electron density in the radical anion over the Os(alpha-dimine) chelate ring causes weakening of the axial (CO)(4)Os-Os(CO)(2)(alpha-dimine) bond and its facile cleavage for alpha-diimine = bpy. In contrast, the cluster radical anion is inherently stable for the bridging bpym ligand, the strongest pi-acceptor in the studied series. In the absence of the partial delocalisation of the unpaired electron over the Re( bpym) chelate bond, the Os-3-core of the radical anion remains intact only at low temperatures. Subsequent one-electron reduction of [Os-3(CO)(10)(bpym)](center dot-) at T = 223 K gives the open-triosmium core (= Os-3*) dianion, [Os-3*(CO)(10)(bpym)](2-). Its oxidation leads to the recovery of parent [Os-3(CO)(10)( bpym)]. At room temperature, [Os-3*( CO)(10)(bpym)](2-) is formed along a two-electron (ECE) reduction path. The chemical step (C) results in the formation of an open- core radical anion that is directly reducible at the cathodic potential of the parent cluster in the second electrochemical (E) step. In weakly coordinating tetrahydrofuran, [Os-3*(CO)(10)( bpym)](2-) rapidly attacks yet non- reduced parent cluster molecules, producing the relatively stable open- core dimer [Os-3*(CO)(10)(bpym)](2)(2-) featuring two open- triangle cluster moieties connected with an ( bpym) Os - Os( bpym) bond. In butyronitrile, [Os-3*( CO)(10)(bpym)](2-) is stabilised by the solvent and the dimer [Os-3*(CO)(10)(bpym)](2)(2-) is then mainly formed by reoxidation of the dianion on reverse potential scan. The more reactive cluster [Os-3(CO)(10)(bpy)] follows the same reduction path, as supported by spectroelectrochemical results and additional valuable evidence obtained from cyclic voltammetric scans. The ultimate process in the reduction mechanism is fragmentation of the cluster core triggered by the reduction of the dimer [Os-3*(CO)(10)(alpha- diimine)](2)(2-). The products formed are [Os-2(CO)(8)](2-) and {Os(CO)(2)(alpha- diimine)}(2). The latter dinuclear fragments constitute a linear polymeric chain [Os( CO)(2)(alpha-dimine)] n that is further reducible at the alpha-dimine ligands. For alpha-dimine = bpy, the charged polymer is capable of reducing carbon dioxide. The electrochemical opening of the triosmium core in the [Os-3( CO)(10)(alpha-dimine)] clusters exhibits several common features with their photochemistry. The same Os-alpha-dimine bond dissociates in both cases but the intimate mechanisms are different.

Worry and problem-solving skills and beliefs in primary school children

Objective. To examine the association between worry and problem-solving skills and beliefs (confidence and perceived control) in primary school children. Method. Children (8–11 years) were screened using the Penn State Worry Questionnaire for Children. High (N ¼ 27) and low (N ¼ 30) scorers completed measures of anxiety, problem-solving skills (generating alternative solutions to problems, planfulness, and effectiveness of solutions) and problem-solving beliefs(confidence and perceived control). Results. High and low worry groups differed significantly on measures of anxiety and problem-solving beliefs (confidence and control) but not on problem-solving skills. Conclusions. Consistent with findings with adults, worry in children was associated with cognitive distortions, not skills deficits. Interventions for worried children may benefit froma focus on increasing positive problem-solving beliefs.

A model for self-directed problem-based learning for renal therapeutics

Objective To introduce a new approach to problem-based learning (PBL) for self-directed learning in renal therapeutics. Design This 5-week course, designed for large student cohorts using minimal teaching resources, was based on a series of case studies and subsequent pharmaceutical care plans, followed by intensive and regular feedback from the instructor. Assessment Assessment of achievement of the learning outcomes was based on weekly-graded care plans and peer review assessment, allowing each student to judge the contributions of each group member and their own, along with a written case-study based examination. The pharmaceutical care plan template, designed using a “tick-box” system, significantly reduced staff time for feedback and scoring. Conclusion The proposed instructional model achieved the desired learning outcomes with appropriate student feedback, while promoting skills that are essential for the students' future careers as health care professionals.

On the principal eigenvalue of a Robin problem with a large parameter

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

The Prony fitting method for digital deconvolution problem

The Prony fitting theory is applied in this paper to solve the deconvolution problem. There are two cases in deconvolution in which unstable solution is easy to appear. They are: (1)the frequency band of known kernel is more narraw than that of the unknown kernel; (2) there exists noise. These two cases are studied thoroughly and the effectiveness of Prony fitting method is showed. Finally, this method is simulated in computer. The simulation results are compared with those obtained by using FFT method directly.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Interference cancellation in two-path successive relay system with network coding

This paper proposes a novel interference cancellation algorithm for the two-path successive relay system using network coding. The two-path successive relay scheme was proposed recently to achieve full date rate transmission with half-duplex relays. Due to the simultaneous data transmission at the relay and source nodes, the two-path relay suffers from the so-called inter-relay interference (IRI) which may significantly degrade the system performance. In this paper, we propose to use the network coding to remove the IRI such that the interference is first encoded with the network coding at the relay nodes and later removed at the destination. The network coding has low complexity and can well suppress the IRI. Numerical simulations show that the proposed algorithm has better performance than existing approaches.