22,079 research outputs found
Fractal functions on the real projective plane
Formerly the geometry was based on shapes, but since the last centuries this
founding mathematical science deals with transformations, projections and
mappings. Projective geometry identifies a line with a single point, like the
perspective on the horizon line and, due to this fact, it requires a
restructuring of the real mathematical and numerical analysis. In particular,
the problem of interpolating data must be refocused. In this paper we define a
linear structure along with a metric on a projective space, and prove that the
space thus constructed is complete. Then we consider an iterated function
system giving rise to a fractal interpolation function of a set of data.Comment: 25 pages, 18 figure
Rank-based linkage I: triplet comparisons and oriented simplicial complexes
Rank-based linkage is a new tool for summarizing a collection of objects
according to their relationships. These objects are not mapped to vectors, and
``similarity'' between objects need be neither numerical nor symmetrical. All
an object needs to do is rank nearby objects by similarity to itself, using a
Comparator which is transitive, but need not be consistent with any metric on
the whole set. Call this a ranking system on . Rank-based linkage is applied
to the -nearest neighbor digraph derived from a ranking system. Computations
occur on a 2-dimensional abstract oriented simplicial complex whose faces are
among the points, edges, and triangles of the line graph of the undirected
-nearest neighbor graph on . In steps it builds an
edge-weighted linkage graph where
is called the in-sway between objects and . Take to be
the links whose in-sway is at least , and partition into components of
the graph , for varying . Rank-based linkage is a
functor from a category of out-ordered digraphs to a category of partitioned
sets, with the practical consequence that augmenting the set of objects in a
rank-respectful way gives a fresh clustering which does not ``rip apart`` the
previous one. The same holds for single linkage clustering in the metric space
context, but not for typical optimization-based methods. Open combinatorial
problems are presented in the last section.Comment: 37 pages, 12 figure
An exploration of the language within Ofsted reports and their influence on primary school performance in mathematics: a mixed methods critical discourse analysis
This thesis contributes to the understanding of the language of Ofsted reports, their similarity to one another and associations between different terms used within ‘areas for improvement’ sections and subsequent outcomes for pupils. The research responds to concerns from serving headteachers that Ofsted reports are overly similar, do not capture the unique story of their school, and are unhelpful for improvement. In seeking to answer ‘how similar are
Ofsted reports’ the study uses two tools, a plagiarism detection software (Turnitin) and a discourse analysis tool (NVivo) to identify trends within and across a large corpus of reports.
The approach is based on critical discourse analysis (Van Dijk, 2009; Fairclough, 1989) but shaped in the form of practitioner enquiry seeking power in the form of impact on pupils and practitioners, rather than a more traditional, sociological application of the method.
The research found that in 2017, primary school section 5 Ofsted reports had more than half of their content exactly duplicated within other primary school inspection reports published that same year. Discourse analysis showed the quality assurance process overrode variables such as inspector designation, gender, or team size, leading to three distinct patterns of duplication: block duplication, self-referencing, and template writing. The most unique part of a report was found to be the ‘area for improvement’ section, which was tracked to externally verified outcomes for pupils using terms linked to ‘mathematics’. Those
required to improve mathematics in their areas for improvement improved progress and attainment in mathematics significantly more than national rates. These findings indicate that there was a positive correlation between the inspection reporting process and a beneficial impact on pupil outcomes in mathematics, and that the significant similarity of one report to another had no bearing on the usefulness of the report for school improvement purposes
within this corpus
A family of total Lagrangian Petrov-Galerkin Cosserat rod finite element formulations
The standard in rod finite element formulations is the Bubnov-Galerkin
projection method, where the test functions arise from a consistent variation
of the ansatz functions. This approach becomes increasingly complex when highly
nonlinear ansatz functions are chosen to approximate the rod's centerline and
cross-section orientations. Using a Petrov-Galerkin projection method, we
propose a whole family of rod finite element formulations where the nodal
generalized virtual displacements and generalized velocities are interpolated
instead of using the consistent variations and time derivatives of the ansatz
functions. This approach leads to a significant simplification of the
expressions in the discrete virtual work functionals. In addition, independent
strategies can be chosen for interpolating the nodal centerline points and
cross-section orientations. We discuss three objective interpolation strategies
and give an in-depth analysis concerning locking and convergence behavior for
the whole family of rod finite element formulations.Comment: arXiv admin note: text overlap with arXiv:2301.0559
Soliton Gas: Theory, Numerics and Experiments
The concept of soliton gas was introduced in 1971 by V. Zakharov as an
infinite collection of weakly interacting solitons in the framework of
Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted
soliton gas, solitons with random parameters are almost non-overlapping. More
recently, the concept has been extended to dense gases in which solitons
strongly and continuously interact. The notion of soliton gas is inherently
associated with integrable wave systems described by nonlinear partial
differential equations like the KdV equation or the one-dimensional nonlinear
Schr\"odinger equation that can be solved using the inverse scattering
transform. Over the last few years, the field of soliton gases has received a
rapidly growing interest from both the theoretical and experimental points of
view. In particular, it has been realized that the soliton gas dynamics
underlies some fundamental nonlinear wave phenomena such as spontaneous
modulation instability and the formation of rogue waves. The recently
discovered deep connections of soliton gas theory with generalized
hydrodynamics have broadened the field and opened new fundamental questions
related to the soliton gas statistics and thermodynamics. We review the main
recent theoretical and experimental results in the field of soliton gas. The
key conceptual tools of the field, such as the inverse scattering transform,
the thermodynamic limit of finite-gap potentials and the Generalized Gibbs
Ensembles are introduced and various open questions and future challenges are
discussed.Comment: 35 pages, 8 figure
The place where curses are manufactured : four poets of the Vietnam War
The Vietnam War was unique among American wars. To pinpoint its uniqueness, it was necessary to look for a non-American voice that would enable me to articulate its distinctiveness and explore the American character as observed by an Asian. Takeshi Kaiko proved to be most helpful. From his novel, Into a Black Sun, I was able to establish a working pair of 'bookends' from which to approach the poetry of Walter McDonald, Bruce Weigl, Basil T. Paquet and Steve Mason. Chapter One is devoted to those seemingly mismatched 'bookends,' Walt Whitman and General William C. Westmoreland, and their respective anthropocentric and technocentric visions of progress and the peculiarly American concept of the "open road" as they manifest themselves in Vietnam. In Chapter, Two, I analyze the war poems of Walter McDonald. As a pilot, writing primarily about flying, his poetry manifests General Westmoreland's technocentric vision of the 'road' as determined by and manifest through technology. Chapter Three focuses on the poems of Bruce Weigl. The poems analyzed portray the literal and metaphorical descent from the technocentric, 'numbed' distance of aerial warfare to the world of ground warfare, and the initiation of a 'fucking new guy,' who discovers the contours of the self's interior through a set of experiences that lead from from aerial insertion into the jungle to the degradation of burning human
feces. Chapter Four, devoted to the thirteen poems of Basil T. Paquet, focuses on the continuation of the descent begun in Chapter Two. In his capacity as a medic, Paquet's entire body of poems details his quotidian tasks which entail tending the maimed, the mortally wounded and the dead. The final chapter deals with Steve Mason's JohnnY's Song, and his depiction of the plight of Vietnam veterans back in "The World" who are still trapped inside the interior landscape of their individual "ghettoes" of the soul created by their war-time experiences
Implementing Health Impact Assessment as a Required Component of Government Policymaking: A Multi-Level Exploration of the Determinants of Healthy Public Policy
It is widely understood that the public policies of ‘non-health’ government sectors have greater impacts on population health than those of the traditional healthcare realm. Health Impact Assessment (HIA) is a decision support tool that identifies and promotes the health benefits of policies while also mitigating their unintended negative consequences. Despite numerous calls to do so, the Ontario government has yet to implement HIA as a required component of policy development. This dissertation therefore sought to identify the contexts and factors that may both enable and impede HIA use at the sub-national (i.e., provincial, territorial, or state) government level.
The three integrated articles of this dissertation provide insights into specific aspects of the policy process as they relate to HIA. Chapter one details a case study of purposive information-seeking among public servants within Ontario’s Ministry of Education (MOE). Situated within Ontario’s Ministry of Health (MOH), chapter two presents a case study of policy collaboration between health and ‘non-health’ ministries. Finally, chapter three details a framework analysis of the political factors supporting health impact tool use in two sub-national jurisdictions – namely, Québec and South Australia.
MOE respondents (N=9) identified four components of policymaking ‘due diligence’, including evidence retrieval, consultation and collaboration, referencing, and risk analysis. As prospective HIA users, they also confirmed that information is not routinely sought to mitigate the potential negative health impacts of education-based policies. MOH respondents (N=8) identified the bureaucratic hierarchy as the brokering mechanism for inter-ministerial policy development. As prospective HIA stewards, they also confirmed that the ministry does not proactively flag the potential negative health impacts of non-health sector policies. Finally, ‘lessons learned’ from case articles specific to Québec (n=12) and South Australia (n=17) identified the political factors supporting tool use at different stages of the policy cycle, including agenda setting (‘policy elites’ and ‘political culture’), implementation (‘jurisdiction’), and sustained implementation (‘institutional power’).
This work provides important insights into ‘real life’ policymaking. By highlighting existing facilitators of and barriers to HIA use, the findings offer a useful starting point from which proponents may tailor context-specific strategies to sustainably implement HIA at the sub-national government level
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