515 resultados para Smale’s Conjecture


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This chapter presents an historical narrative on the recent evolution of information and communications technology (ICT) that has been, and is, utilized for purposes of learning. In other words, it presents an account of the development of e-learning supported through the Web and other similar virtual environments. It does not attempt to present a definitive account; as such an exercise is fraught with assumptions, contextual bias, and probable conjecture. The concern here is more with contextualizing the role of inquiry in learning and the evolving digital tools that enable interfaces that promote and support it. In tracking this evolution, both multi-disciplinary and trans-disciplinary research has been pursued. Key historical developments are identified as well as interpretations of the key drivers of e-learning over time and into what might be better described as digital learning. Innovations in the development of digital tools are described as dynamic and emergent, evolving as a consequence of multiple, sometimes hidden drivers of change. But conflating advancements in learning technologies with e-learning seems to be pervasive. As is the push for the “open” agenda – a growing number of initiatives and movements dominated by themes associated with access, intellectual property, public benefit, sharing and technical interoperability. Openness is also explored in this chapter, however, more in terms of what it means when associated with inquiry. By investigating opportunities for the stimulation and support of questioning online – in particular, why-questioning – this chapter is focused on “opening” content – not just for access but for inquiry and deeper learning.

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There is little conjecture that quality teaching is essential to student achievement and well-being. Whilst much has been written about the importance of quality teaching, including the link to pre-service teacher education, to date there has been little investigation into specific pedagogical practices that can enhance quality teaching dimensions within a pre-service teacher education programme. This paper reports on a small-scale qualitative research study, undertaken in an Australian university, which linked the fields of quality teaching, pre-service teacher education and values education. The study followed the journey of five pre-service teacher education students as they undertook their second field experience unit where the focus was centred on the values-based pedagogy of Philosophy in the Classroom. The research findings, collected via interviews, demonstrated that an explicit values-based pedagogy can have a positive impact on the development of quality teaching dimensions. This new knowledge has potential for further research into examining the ways quality teaching dimensions are gained and practised by pre-service teacher education students and these findings and recommendations are discussed in this paper.

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In a standard overlapping generations growth model, with a fixed amount of land and endogenous fertility, the competitive economy converges to a steady state with a zero population growth rate and positive consumption per capita. The Malthusian hypothesis is interpreted as a positive statement about the relationship between population growth and consumption per-capita, when production exhibits diminishing returns to labor and there is a fixed amount of land essential for production. Even when individuals care only about the number of their children and not about their children's welfare, the equilibrium is such that they eventually would choose to have only one child for each adult. Hence, if Malthus's "positive check' on population is the result of the response of optimizing agents to competitively determined prices, Malthus's pessimistic conjecture is not necessarily true, even though his other assumptions hold. -from Authors

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Background: Knowledge of the human biosciences is fundamental to the development of competent nurse practitioners (Smales, 2010) with the requisite knowledge and skills, necessary for high quality patient care and good patient outcomes (Logan and Angel, 2011). Many of these students study bioscience units which cover topics in anatomy, physiology, pathophysiology and microbiology. Studies of science recall in general and medical education, report up to 33% loss of knowledge in the first year which declines to 50% in the subsequent year (Custers, 2010). Objectives: The objectives were to test the recall of bioscience knowledge by nursing students and to ascertain their perceptions of the testing. Questions explored: What would the results be for multiple choice questions in fundamental microbiology and gastrointestinal anatomy and physiology (A&P) undertaken by nursing students 4, 9 and 16 months after their first bioscience exam on these topics? Would pre-warning the students of a microbiology quiz and not a gastrointestinal A&P quiz affect the findings? How would the students respond to the testing when surveyed? Recall results: The nursing students performed better in the final exam on gastrointestinal A&P than on fundamental microbiology. There was an approximate 20% loss in knowledge of gastrointestinal A&P after 4 months and this did not change significantly over the next 12 months. Although there was an improved performance in microbiology quizzes after 4 months, there was no significant difference in results over the next 12 months. Survey results: More than 50% of students thought the testing helped them focus for the lectures and made them aware they had some pre-knowledge of the lecture topics. Discussion: Although there was a loss of knowledge of gastrointestinal A&P, it appears that warning the students about the microbiology quiz may have helped their recall. The majority of students valued the testing as a useful learning exercise. References: Custers, E. J. F. M. (2010). Long-term retention of basic science knowledge: a review study. Advances in Health Science Education, 15, 109-128. Smales, K. (2010). Learning and applying biosciences to clinical practice in nursing. Nursing Standard, 24(33), 35-39. Logan, P.A., & Angel, L. (2011). Nursing as a scientific undertaking and the intersection with science in undergraduate studies: implications for nursing management. Journal of Nursing Management, 19(3), 407-417.

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Brisbane, the capital of Queensland, in South-East Queensland is situated on the Brisbane River, one of the largest rivers (and floodplains) on the east coast of Australia. The river defines the city and gives it its name. The river has been a natural place to accommodate some population growth for the city with high-density development that capitalises on the natural amenity, cycleways and a string of parks and the flatter land. The major floods of 2011 and the scare of 2013, has seen a more malevolent quality of the river and shift of thinking on its role within the city. The floods have made council, for the first time, acquire prime development sites near the river, with proposals for high density development and made them parks, at great cost. The pressure for population growth in Brisbane remains. 140,000 new dwellings are required by 2031. Brownfield sites are less plentiful and there is interest to rethink of some of the other strategic locations in the city away from the river on higher ground and steeper slopes. Some of these places are currently open spaces. Victoria Park Golf Course sits on a high ridge line and a very strategic part of the city just north of the city centre is one of the few remaining golf courses close to the centre of an Australian capital city. While it is a public course and a valuable community asset, it has been compromised by the recently completed northern busway with two bus stations constructed on its edges. It is bounded on the west and north-east by two major community facilities, the Queensland University of Technology (QUT) to the west and RBW Hospital at its northern end. In a city in need of urban consolidation, perhaps it is time to review the future of the golf course. This question has been investigated as a conjecture in the Master of Architecture program at the QUT. The project has been to re-imagine Victoria Park as a new city parkland and a place that makes an urban connection from the QUT to the hospital. This new urban precinct is be a medium to high-density transit oriented development that capitalises on the bus way stations and the proximity of the university and hospital. The precinct will frame/define/interact with the new major urban park for the city. A key question being addressed is how the design can embody and define principles of a subtropical urbanism. Students are identifying the appropriate street and block structure, density and built form to be accommodated on blocks that define and activate a rich sequence of streets and public spaces. The paper will present a critical overview of the project work that provides a lens to how future professionals may respond to these issue that will be the focus of their professional lives.

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Unlike US and Continental European jurisdictions, Australian monetary policy announcements are not followed promptly by projections materials or comprehensive summaries that explain the decision process. This information is disclosed 2 weeks later when the explanatory minutes of the Reserve Bank board meeting are released. This paper is the first study to exploit the features of the Australian monetary policy environment in order to examine the differential impact of monetary policy announcements and explanatory statements on the Australian interest rate futures market. We find that both monetary policy announcements and explanatory minutes releases have a significant impact on the implied yield and volatility of Australian interest rate futures contracts. When the differential impact of these announcements is examined using the full sample, no statistically significant difference is found. However, when the sample is partitioned based on stable periods and the Global Financial Crisis, a differential impact is evident. Further, contrary to the findings of Kim and Nguyen (2008), Lu et al. (2009), and Smales (2012a), the response along the yield curve, is found to be indifferent between the short and medium terms.

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In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

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Two beetle-type scanning tunneling microscopes are described. Both designs have the thermal stability of the Besocke beetle and the simplicity of the Wilms beetle. Moreover, sample holders were designed that also allow both semiconductor wafers and metal single crystals to be studied. The coarse approach is a linear motion of the beetle towards the sample using inertial slip–stick motion. Ten wires are required to control the position of the beetle and scanner and measure the tunneling current. The two beetles were built with different sized piezolegs, and the vibrational properties of both beetles were studied in detail. It was found, in agreement with previous work, that the beetle bending mode is the lowest principal eigenmode. However, in contrast to previous vibrational studies of beetle-type scanning tunneling microscopes, we found that the beetles did not have the “rattling” modes that are thought to arise from the beetle sliding or rocking between surface asperities on the raceway. The mass of our beetles is 3–4 times larger than the mass of beetles where rattling modes have been observed. We conjecture that the mass of our beetles is above a “critical beetle mass.” This is defined to be the beetle mass that attenuates the rattling modes by elastically deforming the contact region to the extent that the rattling modes cannot be identified as distinct modes in cross-coupling measurements.

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Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

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The aim of this study was to asses results obtained from a range of commonly performed lower extremity “open and closed” chain kinetic tests used for predicting foot function and correlate these test findings to data obtained from the Zebris WinFDM-T system®. When performed correctly these tests are thought to be indicators of lower extremity function. Podiatrists frequently perform examinations of joint and muscle structures to understand biomechanical function; however the relationship between these routine tests and forces generated during the gait cycle are not always well understood. This can introduce a degree of variability in clinical interpretation which creates conjecture regarding the value of these tests.

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An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). It was conjectured by Alon, Sudakov, and Zaks that for any simple and finite graph G, a'(G) <= Delta+2, where Delta=Delta(G) denotes the maximum degree of G. We prove the conjecture for connected graphs with Delta(G)<= 4, with the additional restriction that m <= 2n-1, where n is the number of vertices and m is the number of edges in G. Note that for any graph G, m <= 2n, when Delta(G)<= 4. It follows that for any graph G if Delta(G)<= 4, then a'(G) <= 7.

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It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

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Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has an odd cycle as a component, or (2) n>2 and Kn+1 is a component of G. In this paper we prove that if a graph G has none of some three graphs (K1,3;K5−e and H) as an induced subgraph and if Δ(G)greater-or-equal, slanted6 and d(G)<Δ(G), then χ(G)<Δ(G). Also we give examples to show that the hypothesis Δ(G)greater-or-equal, slanted6 can not be non-trivially relaxed and the graph K5−e can not be removed from the hypothesis. Moreover, for a graph G with none of K1,3;K5−e and H as an induced subgraph, we verify Borodin and Kostochka's conjecture that if for a graph G,Δ(G)greater-or-equal, slanted9 and d(G)<Δ(G), then χ(G)<Δ(G).

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Sonography is an important clinical tool in diagnosing appendicitis in children as it can obviate both exposure to potentially harmful ionising radiation from computed tomography scans and the need for unnecessary appendicectomies. This review examines the diagnostic accuracy of ultrasound in the identification of acute appendicitis, with a particular focus on the the utility of secondary sonographic signs as an adjunct or corollary to traditionally examined criteria. These secondary signs can be important in cases where the appendix cannot be identified with ultrasound and a more meaningful finding may be made by incorporating the presence or absence of secondary sonographic signs. There is evidence that integrating these secondary signs into the final ultrasound diagnosis can improve the utility of ultrasound in cases where appendicitis is expected, though there remains some conjecture about whether they play a more important role in negative or positive prediction in the absence of an identifiable appendix.

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This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.