Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Effect of bone graft type on fusion rates following endoscopic anterior scoliosis correction

Bone graft is generally considered fundamental in achieving solid fusion in scoliosis correction and pseudarthrosis following instrumentation may predispose to implant failure. In endoscopic anterior-instrumented scoliosis surgery, autologous rib or iliac crest graft has been utilised traditionally but both techniques increase operative duration and cause donor site morbidity. Allograft bone and bone- morphogenetic-protein alternatives may improve fusion rates but this remains controversial. This study's objective was to compare two-year postoperative fusion rates in a series of patients who underwent endoscopic anterior instrumentation for thoracic scoliosis utilising various bone graft types. Significantly better rates of fusion occurred in endoscopic anterior instrumented scoliosis correction using femoral allograft compared to autologous rib-heads and iliac crest graft. This may be partly explained by the difficulty obtaining sufficient quantities of autologous graft. Lower fusion rates in the autologous graft group appeared to predispose to rod fracture although the clinical consequence of implant failure is uncertain.

Sound radiation characteristics of a box-type structure

The finite element and boundary element methods are employed in this study to investigate the sound radiation characteristics of a box-type structure. It has been shown [T.R. Lin, J. Pan, Vibration characteristics of a box-type structure, Journal of Vibration and Acoustics, Transactions of ASME 131 (2009) 031004-1–031004-9] that modes of natural vibration of a box-type structure can be classified into six groups according to the symmetry properties of the three panel pairs forming the box. In this paper, we demonstrate that such properties also reveal information about sound radiation effectiveness of each group of modes. The changes of radiation efficiencies and directivity patterns with the wavenumber ratio (the ratio between the acoustic and the plate bending wavenumbers) are examined for typical modes from each group. Similar characteristics of modal radiation efficiencies between a box structure and a corresponding simply supported panel are observed. The change of sound radiation patterns as a function of the wavenumber ratio is also illustrated. It is found that the sound radiation directivity of each box mode can be correlated to that of elementary sound sources (monopole, dipole, etc.) at frequencies well below the critical frequency of the plates of the box. The sound radiation pattern on the box surface also closely related to the vibration amplitude distribution of the box structure at frequencies above the critical frequency. In the medium frequency range, the radiated sound field is dominated by the edge vibration pattern of the box. The radiation efficiency of all box modes reaches a peak at frequencies above the critical frequency, and gradually approaches unity at higher frequencies.

Linking early design decisions across multiple disciplines

The early stages of the building design process are when the most far reaching decisions are made regarding the configuration of the proposed project. This paper examines methods of providing decision support to building designers across multiple disciplines during the early stage of design. The level of detail supported is at the massing study stage where the basic envelope of the project is being defined. The block outlines on the building envelope are sliced into floors. Within a floor the only spatial divisions supported are the “user” space and the building core. The building core includes vertical transportation systems, emergency egress and vertical duct runs. The current focus of the project described in the paper is multi-storey mixed use office/residential buildings with car parking. This is a common type of building in redevelopment projects within and adjacent to the central business districts of major Australian cities. The key design parameters for system selection across the major systems in multi-storey building projects - architectural, structural, HVAC, vertical transportation, electrical distribution, fire protection, hydraulics and cost – are examined. These have been identified through literature research and discussions with building designers from various disciplines. This information is being encoded in decision support tools. The decision support tools communicate through a shared database to ensure that the relevant information is shared across all of the disciplines. An internal data model has been developed to support the very early design phase and the high level system descriptions required. A mapping to IFC 2x2 has also been defined to ensure that this early information is available at later stages of the design process.

Raman spectroscopic study of the mixed anion mineral Yecoraite Bi5Fe3O9(Te4+O3)(Te6+O4)2•9H2O

Tellurates are rare minerals as the tellurate anion is readily reduced to the tellurite ion. Often minerals with both tellurate and tellurite anions in the mineral are found. An example of such a mineral containing tellurate and tellurite is yecoraite. Raman spectroscopy has been used to study this mineral, the exact structure of which is unknown. Two Raman bands at 796 and 808 cm-1 are assigned to the ν1 (TeO4)2- symmetric and ν3 (TeO3)2- antisymmetric stretching modes and Raman bands at 699 cm-1 are attributed to the the ν3 (TeO4)2- antisymmetric stretching mode and the band at 690 cm-1 to the ν1 (TeO3)2- symmetric stretching mode. The intense band at 465 cm-1 with a shoulder at 470 cm-1 is assigned the (TeO4)2- and (TeO3)2- bending modes. Prominent Raman bands are observed at 2878, 2936, 3180 and 3400 cm-1. The band at 3936 cm-1 appears quite distinct and the observation of multiple bands indicates the water molecules in the yecoraite structure are not equivalent. The values for the OH stretching vibrations listed provide hydrogen bond distances of 2.625 Å (2878 cm-1), 2.636 Å (2936 cm-1), 2.697 Å (3180 cm-1) and 2.798 Å (3400 cm-1). This range of hydrogen bonding contributes to the stability of the mineral. A comparison of the Raman spectra of yecoraite with that of tellurate containing minerals kuranakhite, tlapallite and xocomecatlite is made.

The effect of bone graft type on fusion rates following anterior thoracoscopic scoliosis correction

Bone graft is generally considered fundamental in achieving solid fusion in scoliosis correction and pseudarthrosis following instrumentation may predispose to implant failure. In thoracoscopic anterior-instrumented scoliosis surgery, autologous rib or iliac crest graft has been utilised traditionally but both techniques increase operative duration and cause donor site morbidity. Allograft bone and bone morphogenetic protein (BMP) alternatives may improve fusion rates but this remains controversial. This study's objective was to compare two-year postoperative fusion rates in a series of patients who underwent thoracoscopic anterior instrumentation for thoracic scoliosis utilising various bone graft types.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.