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Displaying Results 1  25 of 618 on page 1 of 25
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Mark
``I don't like Maths as a subject but I like doing it'': a methodology for understanding mathematical identity
(2019)
Howard, Fionnán; Nic Mhuirí, Siún; O'Reilly, Maurice
``I don't like Maths as a subject but I like doing it'': a methodology for understanding mathematical identity
(2019)
Howard, Fionnán; Nic Mhuirí, Siún; O'Reilly, Maurice
Abstract:
This paper presents a thematic analysis methodology which uses a hybrid coding process to understand how science and engineering students in higher level education relate to mathematics. This process utilises and builds on previous research on mathematical identity amongst student teachers by using deductive coding while continuing to be grounded in the new data through inductive coding. Many authors have written on both or either of these methods. Most treat it was a simple choice between one or the other. Few have addressed best practice in integrating these approaches
http://doras.dcu.ie/25276/
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$h$Vectors of Generalized Associahedra and Noncrossing Partitions
(2006)
Watt, Colum; Brady, Thomas; Athanasiadis, Christos A; McCammond, Jon
$h$Vectors of Generalized Associahedra and Noncrossing Partitions
(2006)
Watt, Colum; Brady, Thomas; Athanasiadis, Christos A; McCammond, Jon
Abstract:
A uniform proof is given that the entries of the $h$vector of the cluster complex $\Delta (\Phi)$, associated by S. Fomin and A. Zelevinsky to a finite root system $\Phi$, count elements of the lattice $\mathbf{L}$ of noncrossing partitions of corresponding type by rank. Similar interpretations for the $h$vector of the positive part of $\Delta (\Phi)$ are provided. The proof utilizes the appearance of the complex $\Delta (\Phi)$ in the context of the lattice $\mathbf{L}$ in recent work of two of the authors, as well as an explicit shelling of $\Delta (\Phi)$.
https://arrow.dit.ie/scschmatart/147
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A bifurcation problem arising from chemical engineering
(1986)
Coghlan, Neil
A bifurcation problem arising from chemical engineering
(1986)
Coghlan, Neil
http://doras.dcu.ie/18417/
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Mark
A blended learning teaching approach aimed at improving postprimary students’ conceptual understanding of mathematics – a focus on algebra supported by digital pencasts
(2016)
Gallagher, Jason
A blended learning teaching approach aimed at improving postprimary students’ conceptual understanding of mathematics – a focus on algebra supported by digital pencasts
(2016)
Gallagher, Jason
Abstract:
This research project investigated whether students’ conceptual understanding of algebra was improved with a taught intervention supported by digital pencasts. The motivation for this project was inspired by observing students’ difficulties when learning algebra in the author’s own classroom. Digital pencasts were used as a support tool throughout this investigation. Digital pencasting is the process of viewing webbased hand written notes with accompanying audio. The teaching intervention focused on the elements of Niemi’s (1996) framework for measuring conceptual understanding within the two separate groups; an adult education group and a transition year group. A statistically significant improvement was observed in the transition years’ conceptual understanding of algebra whereas there was no statistically significant improvement observable in the adult education group. The completion of this project unveiled the dearth of research currently available on digital pencasting. This...
http://hdl.handle.net/10344/5234
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A branching process approach to the identification of influential nodes in complex networks
(2019)
Cassidy, Ailbhe
A branching process approach to the identification of influential nodes in complex networks
(2019)
Cassidy, Ailbhe
Abstract:
We live in a world surrounded by networks. They are ubiquitous. Be it social media networks linking us to our friends, transportation networks interconnecting locations around the globe, or the metabolic network breaking down food in our bodies. The study of networks is an interdisciplinary field spanning from fields of mathematics, psychology, sociology, biology, computer science, physics, and many other areas. The field of Network Science has greatly profited from the contributions of such diverse scientific communities. However, there are still remaining challenges that are open for further research and discussion. The identification of influential nodes in a network is a constant challenge faced by researchers. Regardless of the specific field of study the solution to this problem is constantly in demand. In this thesis, we present a new measure for the identification of influential nodes in complex networks. It is based on a mathematical model which uses a branching process app...
http://hdl.handle.net/10344/8495
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A Combined NNLO LatticeContinuum Determination of Lr10
(2014)
GARRON, NICOLAS
A Combined NNLO LatticeContinuum Determination of Lr10
(2014)
GARRON, NICOLAS
http://hdl.handle.net/2262/69180
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A Dirichlet problem for a coupled system of two singularly perturbed convectiondiffusion ordinary differential equations
(2003)
Bellew, Seamus
A Dirichlet problem for a coupled system of two singularly perturbed convectiondiffusion ordinary differential equations
(2003)
Bellew, Seamus
Abstract:
A Dirichlet problem for a system of two singularly perturbed convectiondiffusion ordinary differential equations is examined where th e two singular perturbation parameters can be of a different order. A finite difference numerical method whose solutions converge pointwise independently of the singular perturbation parameters is constructed. A full theoretical analysis is provided which shows that the numerical method is robust. This is done over a piecewise uniform fitted mesh involving two transition points. The first differential equation has only one dependent variable while the second equation has two dependent variables. The solution to the first differential equation is present in the second differential equation and th is introduces coupling which is examined in this thesis. The solution of the first differential equation is decomposed into regular and singular components. The numerical solution is decomposed in an analogous manner. The convergence of the numerical method...
http://doras.dcu.ie/17413/
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A Hamiltonian Approach to WaveCurrent Interactions in TwoLayer Fluids
(2015)
Constantin, Adrian; Ivanov, Rossen
A Hamiltonian Approach to WaveCurrent Interactions in TwoLayer Fluids
(2015)
Constantin, Adrian; Ivanov, Rossen
Abstract:
We provide a Hamiltonian formulation for the governing equations describing the twodimensional nonlinear interaction between coupled surfacewaves, internalwaves, and an underlying current with piecewise constant vorticity, in a twolayered fluid overlying a flat bed. This Hamiltonian structure is a starting point for the derivation of simpler models, which can be obtained systematically by expanding the Hamiltonian in dimensionless parameters. These enable an indepth study of the coupling between the surface and internal waves, and how both these wave systems interact with the background current.
https://arrow.dit.ie/scschmatart/191
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A lens on two classrooms: implications for research on teaching
(2019)
Nic Mhuirí, Siún
A lens on two classrooms: implications for research on teaching
(2019)
Nic Mhuirí, Siún
Abstract:
This paper uses the Teaching for Robust Understanding framework (Schoenfeld, 2013) as an analytic lens on episodes of mathematics teaching from two different countries. This lens highlights differences in teaching approaches across the two settings and draws attention to the need for further interrogation of how culture, curriculum and values inform teaching practices. It also has implications for research practices as it shows that the theoretical frameworks and methodological tools that are used in research are not value free or culturally neutral.
http://doras.dcu.ie/24195/
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A mathematical model for measles epidemics in Ireland
(1988)
Comiskey, Catherine M.
A mathematical model for measles epidemics in Ireland
(1988)
Comiskey, Catherine M.
Abstract:
The aim of this work is to establish a matnematical model for measles epidemics and to predict levels of vaccination coverage require! in Ireland in order to eradicate tne disease The emphasis througnout has oeen to derive the parameters of the model using data collected in Ireland. To achieve this a nonlinear differential equation model first oroposed by Anderson R M. and May R.M. has been adopted and adjusted to meet our application. In Chapter 1 we introduce the concept of mathematically modelling the dynamics of an infectious disease and we also propose a simple constant parameter model We then move on in Chapter 2 to discuss what is known as ”the force of the infection". This is then calculated for Ireland by testing over 100 blood samples for measles antibodies. In Chapter 3 we estimated the Irish interepidemic period using Hopf's bifurcation theorem. In Chapter 4 we move on to the more detailed model with age dependence. We also estimate the age dependent survival...
http://doras.dcu.ie/19193/
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A metric space approach to the information capacity of spike trains
(2010)
HOUGHTON, CONOR JAMES; GILLESPIE, JAMES
A metric space approach to the information capacity of spike trains
(2010)
HOUGHTON, CONOR JAMES; GILLESPIE, JAMES
Abstract:
Classical information theory can be either discrete or continuous, corresponding to discrete or continuous random variables. However, although spike times in a spike train are described by continuous variables, the information content is usually calculated using discrete information theory. This is because the number of spikes, and hence, the number of variables, varies from spike train to spike train, making the continuous theory difficult to apply.It is possible to avoid this problem by using a metric space approach to spike trains. A metric gives a distance between different spike trains. The continuous version of information theory is then rephrased in terms of metric quantities and used to estimate the information capacity of spike trains. This method works by matching the distribution of distances between responses to the same stimulus to a distribution: the distribution is the length distribution for a vector of Gaussian variables. This defines a noise dimension for the s...
http://hdl.handle.net/2262/40197
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A model equation for the optical tunnelling problem using parabolic cylinder functions
(1989)
Brazel, Neal
A model equation for the optical tunnelling problem using parabolic cylinder functions
(1989)
Brazel, Neal
Abstract:
The fundamental purpose of this thesis is to estimate the exponentially small imaginary part of the eigenvalue of a second order ordinary differential equation subject to certain stated boundary conditions. This problem is modelled on a partial differential equation which arises when examining wave losses m bent fibre optic waveguides. In Chapter 1 we provide an overview of the thesis and introduce the area of mathematics known as exponential asymptotics. In Chapter 2 we investigate the physical background to the problem of energy losses due to optical tunnelling in fibre optic waveguides. We then derive the partial differential equation upon which we base our model. In Chapter 3 we commence by manipulating the partial differential equation into a more convenient form. We then outline the model problem we shall consider and obtain a preliminary estimate for the eigenvalue of this problem. In Chapter 4 we introduce the special function known as the parabolic cylinder function and de...
http://doras.dcu.ie/18354/
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A modified depth function for outlier detection in multivariate data with applications
(2020)
Abedin, Md Jaynal
A modified depth function for outlier detection in multivariate data with applications
(2020)
Abedin, Md Jaynal
Abstract:
Data Science is the new and exciting interdisciplinary response that has emerged as a consequence of the staggering amounts of data generated in many new forms from digital images to audio to text. It is an interdisciplinary field involving Statistics, Computer Science and Mathematics. It involves the study of data, how they are collected, stored, accessed, visualised, modelled and ultimately used to inform decision making by turning data into intelligence. Despite this ’data revolution’ and the development of Data Science as a consequence, the aim of any data analysis is still the same, to make inference about unknown population parameters using sample statistics. One fundamental challenge in inference is the identification of outliers. Such oddities, or atypical observations, could be indicative of poor data management or biased sampling. In this situation the presence of such outliers are considered a negative aspect and efforts are needed to account for them (e.g. correct dat...
http://hdl.handle.net/10379/16188
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A modified mathematical model for HIV transmission, AIDS and intervention strategies in Ireland
(1995)
Dunne, Mary T.
A modified mathematical model for HIV transmission, AIDS and intervention strategies in Ireland
(1995)
Dunne, Mary T.
Abstract:
The aim of this project was to modify transmission models previously developed to describe HIV transmission in Ireland through more precise estimates of parameters delineating sexual and needle sharing behaviour and AIDS related mortality, with a view to examining the extent of spread from IVDUs to the general heterosexual population. To provide predictions on HIV transmission and AIDS cases up to the year 2010 and to examine the sensitivity of the predictions to changes in the key parameters under different assumptions on intervention strategies. Essential data of relevance to HIV transmission were acquired (through the cooperation of the Department of Health, the AIDS Resource Centre, the Drug Treatment Centre, the Ana Liffey Drug Project, and St James’s Hospital, Dublin) and analysed. The parameters obtained from the descriptive and survival analyses were used in a refined deterministic model of HIV transmission which was solved numerically. An attempt at a solution using pertur...
http://doras.dcu.ie/18558/
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A note about waves in dissipative and dispersive solids
(2016)
Destrade, Michel; Saccomandi, Giuseppe
A note about waves in dissipative and dispersive solids
(2016)
Destrade, Michel; Saccomandi, Giuseppe
Abstract:
We study shear waves propagating in a special viscoelastic model proposed first by Fosdick and Yu in 1996. We deduce an asymptotic approximation which reduces the full balance equations to a system of evolution equations which are a vectorial generalization of the Modified KDVBurger equation. In such a way we show that the model takes into account not only dissipative effects but also dispersive effects.
Not peer reviewed
http://hdl.handle.net/10379/5733
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A note on clean abelian groups
(2007)
Goldsmith, Brendan; Vamos, P.
A note on clean abelian groups
(2007)
Goldsmith, Brendan; Vamos, P.
Abstract:
Nicholson defined a ring to be clean if every element is the sum of a unit and an idempotent. A module is clean if its endomorphism algebra is clean. We show that torsioncomplete Abelian pgroups are clean and characterize the clean groups among the class of totally projective pgroups. An example is given of a clean pgroup which is neither totally projective nor torsion complete
https://arrow.dit.ie/scschmatart/24
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A note on coslender groups
(1988)
Dimitric, R.; Goldsmith, Brendan
A note on coslender groups
(1988)
Dimitric, R.; Goldsmith, Brendan
Abstract:
The notion of a coslender group has been introduced previously by the first author. This work continues the investigation of such groups, defines coslender part of a group, proves embeddability results, gives a characterization of finite rank coslender grops, and proves a result on smooth ascending chains of coslender groups with a conjecture that every countable coslender torsion free group is a smooth ascending union of finite rank coslender pure subgroups.
https://arrow.dit.ie/scschmatart/20
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A note on element centralizers in finite Coxeter groups
(2017)
Konvalinka, Matjaž; Pfeiffer, Götz; Röver, Claas E.
A note on element centralizers in finite Coxeter groups
(2017)
Konvalinka, Matjaž; Pfeiffer, Götz; Röver, Claas E.
Abstract:
The normalizer NW(WJ) of a standard parabolic subgroup WJ of a finite Coxeter group W splits over the parabolic subgroup with complement NJ consisting of certain minimal length coset representatives of WJ in W. In this note we show that (with the exception of a small number of cases arising from a situation in Coxeter groups of type Dn) the centralizer CW(w) of an element w epsilon W is in a similar way a semidirect product of the centralizer of w in a suitable small parabolic subgroup WJ with complement isomorphic to the normalizer complement NJ. Then we use this result to give a new short proof of Solomon's Character Formula and discuss its connection to MacMahon's master theorem.
The second author wishes to acknowledge support from Science Foundation Ireland.
http://hdl.handle.net/10379/7011
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A note on elongations of Abelian Groups
(1975)
Goldsmith, Brendan
A note on elongations of Abelian Groups
(1975)
Goldsmith, Brendan
Abstract:
No abstract available.
https://arrow.dit.ie/scschmatart/2
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A note on gravityscalar fluctuations in holographic RG flow geometries
(2000)
FROLOV, SERGEY
A note on gravityscalar fluctuations in holographic RG flow geometries
(2000)
FROLOV, SERGEY
Abstract:
We study fivedimensional gravity models with nonvanishing background scalar fields which are dual to nonconformal boundary field theories. We develop a procedure to decouple the graviton fluctuations from the scalar ones and apply it to the simplest case of one scalar field. The quadratic action for the decoupled scalar fluctuations has a very simple form and can be used to compute twopoint functions. We perform this computation for the two examples of background RG flow recently considered by DeWolfe and Freedman and find physically reasonable results.
http://hdl.handle.net/2262/49072
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A Note on Hopfian and CoHopfian Abelian Groups
(2012)
Goldsmith, Brendan; Gong, Ketao
A Note on Hopfian and CoHopfian Abelian Groups
(2012)
Goldsmith, Brendan; Gong, Ketao
Abstract:
The notions of Hopfian and coHopfian groups have been of interest for some time. In this present work we exploit some unpublished ideas of Corner to answer questions relating to such groups. In particular, we extend an answer given by Corner to a problem of Beaumont and Pierce and show how the properties may be lifted from subgroups to the whole group in certain situations.
https://arrow.dit.ie/scschmatcon/9
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A note on products of infinite cyclic groups
(1981)
Goldsmith, Brendan
A note on products of infinite cyclic groups
(1981)
Goldsmith, Brendan
Abstract:
No abstract available
https://arrow.dit.ie/scschmatart/7
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A Numerical Method for a Nonlinear Singularly Perturbed Interior Layer Problem Using an Approximate Layer Location
(2014)
Quinn, Jason
A Numerical Method for a Nonlinear Singularly Perturbed Interior Layer Problem Using an Approximate Layer Location
(2014)
Quinn, Jason
Abstract:
A class of nonlinear singularly perturbed interior layer problems is examined in this paper. Solutions exhibit an interior layer at an a priori unknown location. A numerical method is presented that uses a piecewise uniform mesh refined around approximations to the first two terms of the asymptotic expansion of the interior layer location. The first term in the expansion is used exactly in the construction of the approximation which restricts the range of problem data considered. The method is shown to converge pointwise to the true solution with a first order convergence rate (overlooking a logarithmic factor) for sufficiently small values of the perturbation parameter. A numerical experiment is presented to demonstrate the convergence rate established.
https://arrow.dit.ie/scschmatart/180
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A Partial Order on the Orthogonal Group
(2002)
Watt, Colum; Brady, Thomas
A Partial Order on the Orthogonal Group
(2002)
Watt, Colum; Brady, Thomas
Abstract:
We define a natural partial order on the orthogonal group and completely describe the intervals in this partial order. The main technical ingredient is that an orthogonal transformation induces a unique orthogonal transformation on each subspace of the orthogonal complement of its fixed subspace.
https://arrow.dit.ie/scschmatart/152
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A point mass in an isotropic universe: existence, uniqueness, and basic properties
(1998)
Nolan, Brien C.
A point mass in an isotropic universe: existence, uniqueness, and basic properties
(1998)
Nolan, Brien C.
Abstract:
Criteria which a spacetime must satisfy to represent a point mass embedded in an open RobertsonWalker (RW) universe are given. It is shown that McVittie’s solution in the case k=0 satisfies these criteria, but does not in the case k=1. The existence of a solution for the case k=1 is proven and its representation in terms of an elliptic integral is given. The following properties of this and McVittie’s k=0 solution are studied; uniqueness, the behavior at future null infinity, the recovery of the RW and Schwarzschild limits, the compliance with energy conditions, and the occurrence of singularities. The existence of solutions representing more general spherical objects embedded in a RW universe is also proven.
http://doras.dcu.ie/15650/
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