Modeling study on transport organization methods choice of highway rapid passenger transport in China

Some new types of mathematical model among four key techno - economic indexes of highway rapid passenger through transportation were established based on the principles of transportation economics. According to the research on the feasible solutions to the associated parameters which were then compared to the actual value, found some limitation in the existing transport organization method. In order to conquer that, two new types of transport organization method, namely CD (Collecting and Distributing) Method and Relay Method were brought forward. What’s more, a further research was down to estimate their characteristics, such as feasibilities, operation flows, applicability fields, etc. This analysis proves the two methods can offset the shortage of rapid passenger through transportation. To ensure highway rapid passenger transport develop harmoniously, a three-stage development targets was suggested to fuse different organization methods.

Group metacognition during mathematical problem solving

Although various studies have shown that groups are more productive than individuals in complex mathematical problem solving, not all groups work together cooperatively. This review highlights that addressing organisational and cognitive factors to help scaffold group mathematical problem solving is necessary but not sufficient. Successful group problem solving also needs to incorporate metacognitive factors in order for groups to reflect on the organisational and cognitive factors influencing their group mathematical problem solving.

New parameters for daytime wandering

This study aimed to describe wandering using new parameters and to evaluate parameters as a function of cognitive impairment and mobility. Forty-four wanderers in long-term care settings were videotaped 12 times. Rate and duration of wandering episodes were plotted and used to derive parameters from values above and below case medians, proportion of hours wandering, and time of day. Participants wandered during 47% of observations; on average, the hourly rate was 4.3 episodes, the peak hourly rate was 18 episodes, and the peak hourly duration was 19.9 minutes. Mini-Mental State Examination (MMSE) scores was negatively correlated with overall duration and number of observations during which duration exceeded 15 minutes per hour, was positively correlated with number of observations without wandering, and was not significantly correlated with rate-related parameters. Mobility correlated positively with rate and duration parameters. Interaction of MMSE score and mobility was the strongest predictor of wandering duration. Parameters derived from repeated measures provide a new view of daytime wandering and insight into relationships between MMSE score and mobility status with specific parameters of wandering.

Promoting interdisciplinarity through mathematical modelling

This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems— one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean

Phase-type distributions represent the time to absorption for a finite state Markov chain in continuous time, generalising the exponential distribution and providing a flexible and useful modelling tool. We present a new reversible jump Markov chain Monte Carlo scheme for performing a fully Bayesian analysis of the popular Coxian subclass of phase-type models; the convenient Coxian representation involves fewer parameters than a more general phase-type model. The key novelty of our approach is that we model covariate dependence in the mean whilst using the Coxian phase-type model as a very general residual distribution. Such incorporation of covariates into the model has not previously been attempted in the Bayesian literature. A further novelty is that we also propose a reversible jump scheme for investigating structural changes to the model brought about by the introduction of Erlang phases. Our approach addresses more questions of inference than previous Bayesian treatments of this model and is automatic in nature. We analyse an example dataset comprising lengths of hospital stays of a sample of patients collected from two Australian hospitals to produce a model for a patient's expected length of stay which incorporates the effects of several covariates. This leads to interesting conclusions about what contributes to length of hospital stay with implications for hospital planning. We compare our results with an alternative classical analysis of these data.

Effect of inaccuracies in anthropometric data and linked-segment inverse dynamic modeling on kinetics of gait in persons with partial foot amputation

The accuracy of data derived from linked-segment models depends on how well the system has been represented. Previous investigations describing the gait of persons with partial foot amputation did not account for the unique anthropometry of the residuum or the inclusion of a prosthesis and footwear in the model and, as such, are likely to have underestimated the magnitude of the peak joint moments and powers. This investigation determined the effect of inaccuracies in the anthropometric input data on the kinetics of gait. Toward this end, a geometric model was developed and validated to estimate body segment parameters of various intact and partial feet. These data were then incorporated into customized linked-segment models, and the kinetic data were compared with that obtained from conventional models. Results indicate that accurate modeling increased the magnitude of the peak hip and knee joint moments and powers during terminal swing. Conventional inverse dynamic models are sufficiently accurate for research questions relating to stance phase. More accurate models that account for the anthropometry of the residuum, prosthesis, and footwear better reflect the work of the hip extensors and knee flexors to decelerate the limb during terminal swing phase.

Scaffolding students’ thinking in mathematical investigations

This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

Simulation and development of a mock circulation loop with variable compliance

Heart disease is attributed as the highest cause of death in the world. Although this could be alleviated by heart transplantation, there is a chronic shortage of donor hearts and so mechanical solutions are being considered. Currently, many Ventricular Assist Devices (VADs) are being developed worldwide in an effort to increase life expectancy and quality of life for end stage heart failure patients. Current pre-clinical testing methods for VADs involve laboratory testing using Mock Circulation Loops (MCLs), and in vivo testing in animal models. The research and development of highly accurate MCLs is vital to the continuous improvement of VAD performance. The first objective of this study was to develop and validate a mathematical model of a MCL. This model could then be used in the design and construction of a variable compliance chamber to improve the performance of an existing MCL as well as form the basis for a new miniaturised MCL. An extensive review of literature was carried out on MCLs and mathematical modelling of their function. A mathematical model of a MCL was then created in the MATLAB/SIMULINK environment. This model included variable features such as resistance, fluid inertia and volumes (resulting from the pipe lengths and diameters); compliance of Windkessel chambers, atria and ventricles; density of both fluid and compressed air applied to the system; gravitational effects on vertical columns of fluid; and accurately modelled actuators controlling the ventricle contraction. This model was then validated using the physical properties and pressure and flow traces produced from a previously developed MCL. A variable compliance chamber was designed to reproduce parameters determined by the mathematical model. The function of the variability was achieved by controlling the transmural pressure across a diaphragm to alter the compliance of the system. An initial prototype was tested in a previously developed MCL, and a variable level of arterial compliance was successfully produced; however, the complete range of compliance values required for accurate physiological representation was not able to be produced with this initial design. The mathematical model was then used to design a smaller physical mock circulation loop, with the tubing sizes adjusted to produce accurate pressure and flow traces whilst having an appropriate frequency response characteristic. The development of the mathematical model greatly assisted the general design of an in vitro cardiovascular device test rig, while the variable compliance chamber allowed simple and real-time manipulation of MCL compliance to allow accurate transition between a variety of physiological conditions. The newly developed MCL produced an accurate design of a mechanical representation of the human circulatory system for in vitro cardiovascular device testing and education purposes. The continued improvement of VAD test rigs is essential if VAD design is to improve, and hence improve quality of life and life expectancy for heart failure patients.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Same-sex intimate partner violence : exploring the parameters

Intimate partner violence (IPV) is not only a problem for heterosexual couples. Although research in the area is beset by methodological and definitional problems, studies generally demonstrate that IPV also affects those who identify as non-heterosexual; that is, those sexualities that are typically categorized as lesbian, gay, bisexual, transgender, or intersex (LGBTI). IPV appears to be at least as prevalent in LGBTI relationships as it is in heterosexual couples, and follows similar patterns (e.g. Australian Research Centre on Sex, Health and Society 2006; Donovan et al. 2006; Chan 2005; Craft and Serovich 2005; Burke et al. 2002; Jeffries and Ball 2008; Kelly and Warshafsky 1987; Letellier 1994; Turrell 2000; Ristock 2003; Vickers 1996). There is, however, little in the way of specific community or social services support available to either victims or perpetrators of violence in same-sex relationships (see Vickers 1996). In addition, there are important differences in the experience of IPV between LGBTI and non-LGBTI victims, and even among LGBTI individuals; for example, among transgender populations (Chan 2005), and those who are HIV sero-positive (Craft and Serovich 2005). These different experiences of IPV include the use of HIV and the threat of “outing” a partner as tools of control, as just two examples (Jeffries and Ball 2008; Salyer 1999; WA Government 2008b). Such differences impact on how LGBTI victims respond to the violence, including whether or not and how they seek help, what services they are able to avail themselves of, and how likely they are to remain with, or return to, their violent partners (Burke et al. 2002). This chapter explores the prevalent heteronormative discourses that surround IPV, both within the academic literature, and in general social and government discourses. It seeks to understand how same-sex IPV remains largely invisible, and suggests that these dominant discourses play a major role in maintaining this invisibility. In many respects, it builds on work by a number of scholars who have begun to interrogate the criminal justice and social discourses surrounding violent crime, primarily sexual violence, and who problematize these discourses (see for example Carmody 2003; Carmody and Carrington 2000; Marcus 1992). It will begin by outlining these dominant discourses, and then problematize these by identifying some of the important differences between LGBTI IPV and IPV in heterosexual relationships. In doing so, this chapter will suggest some possible reasons for the silence regarding IPV in LGBTI relationships, and the effects that this can have on victims. Although an equally important area of research, and another point at which the limitations of dominant social discourses surrounding IPV can be brought to light, this chapter will not examine violence experienced by heterosexual men at the hands of their intimate female partners. Instead, it will restrict itself to IPV perpetrated within same-sex relationships.

End-winding effect on shalft voltage in AC generators

This paper presents effects of end-winding on shaft voltage in AC generators. A variety of design parameters have been considered to calculate the parasitic capacitive couplings in the machine structure with Finite Elements simulations and mathematical calculations. End-winding capacitances have also been calculated to have a precise estimation of shaft voltage and its relationship with design parameters in AC generators.

Info-gap theory and robust design of surveillance for invasive species : the case study of Barrow Island

Surveillance for invasive non-indigenous species (NIS) is an integral part of a quarantine system. Estimating the efficiency of a surveillance strategy relies on many uncertain parameters estimated by experts, such as the efficiency of its components in face of the specific NIS, the ability of the NIS to inhabit different environments, and so on. Due to the importance of detecting an invasive NIS within a critical period of time, it is crucial that these uncertainties be accounted for in the design of the surveillance system. We formulate a detection model that takes into account, in addition to structured sampling for incursive NIS, incidental detection by untrained workers. We use info-gap theory for satisficing (not minimizing) the probability of detection, while at the same time maximizing the robustness to uncertainty. We demonstrate the trade-off between robustness to uncertainty, and an increase in the required probability of detection. An empirical example based on the detection of Pheidole megacephala on Barrow Island demonstrates the use of info-gap analysis to select a surveillance strategy.