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Articles 1 - 17 of 17
Full-Text Articles in Physical Sciences and Mathematics
Holomorphic Basis For Families Of Subspaces Of A Banach Space, Milena Venkova, Christopher Boyd
Holomorphic Basis For Families Of Subspaces Of A Banach Space, Milena Venkova, Christopher Boyd
Articles
In this article we investigate the connection between a family of com-plemented subspaces of a Banach space having a holomorphic basis, and being holomorphically complemented.
Pricing European And American Options In The Heston Model With Accelerated Explicit Finite Differencing Methods, Conall O'Sullivan, Stephen O'Sullivan
Pricing European And American Options In The Heston Model With Accelerated Explicit Finite Differencing Methods, Conall O'Sullivan, Stephen O'Sullivan
Articles
No abstract provided.
On The Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev
On The Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev
Articles
We develop the direct scattering problem for quadratic bundles associated to Hermitian symmetric spaces. We adapt the dressing method for quadratic bundles which allows us to find special solutions to multicomponent derivative Schrodinger equation for instance. The latter is an infinite dimensional Hamiltonian system possessing infinite number of integrals of motion. We demonstrate how one can derive them by block diagonalization of the corresponding Lax pair.
Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev
Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev
Conference papers
We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)\times U(n)). We discuss the spectral properties of scattering operator, develop the direct scattering problem associated with it and stress on the effect of reduction on these. By applying a modification of Zakharov-Shabat's dressing procedure we demonstrate how one can obtain reflectionless potentials. That way one is able to generate soliton solutions to the nonlinear evolution equations belonging to the integrable hierarchy associated with quadratic bundles under study.
Mathematical Self-Efficacy: Addressing The Declining Interest In Engineering Careers, Eileen Goold
Mathematical Self-Efficacy: Addressing The Declining Interest In Engineering Careers, Eileen Goold
Conference Papers
This paper presents the findings of a study investigating whether there is a relationship between students’ experiences with school mathematics and their choice of engineering as a career. The study was inspired by the observation that there is a lacuna in the scholarly literature concerning the nature of mathematics’ role, if any, as a significant cause of the declining number of students entering professional engineering courses. The population of interest in this study comprises professional engineers practising in Ireland. Engineers’ experiences of school mathematics, factors that contributed to their engagement with school mathematics and the impact of their feelings about …
Particle Trajectories In Extreme Stokes Waves Over Inifinte Depth, Tony Lyons
Particle Trajectories In Extreme Stokes Waves Over Inifinte Depth, Tony Lyons
Articles
We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of the particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid being zero there.
Mathematical Modelling At Secondary School: The Macsi-Clongowes Wood College Experience, J.P.F. Charpin, S. O'Hara, Dana Mackey
Mathematical Modelling At Secondary School: The Macsi-Clongowes Wood College Experience, J.P.F. Charpin, S. O'Hara, Dana Mackey
Articles
In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students. Participants developed simple mathematical models for everyday life problems with an open-ended answer. The format and content of the workshop are described and feedback from both students and participating teachers is provided. For nearly all participants, this workshop was an enjoyable experience which showed mathematics and other STEM components in a very positive way.
Weyl-Titchmarsh Type Formula For Periodic Schrodinger Operator With Wigner-Von Neumann Potential, Sergey Simonov, Pavel Kurasov
Weyl-Titchmarsh Type Formula For Periodic Schrodinger Operator With Wigner-Von Neumann Potential, Sergey Simonov, Pavel Kurasov
Articles
Schroedinger operator on the half-line with periodic background potential perturbed by a certain potential of Wigner-von Neumann type is considered. The asymptotics of generalized eigenvectors for the values of the spectral parameter from the upper half-plane and on the absolutely continuous spectrum is established. Weyl-Titchmarsh type formula for this operator is proven.
Spectral Multiplicity Of Selfadjoint Schrodinger Operators On Star-Graphs With Standard Interface Conditions, Sergey Simonov, Harald Woracek
Spectral Multiplicity Of Selfadjoint Schrodinger Operators On Star-Graphs With Standard Interface Conditions, Sergey Simonov, Harald Woracek
Articles
We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of Theorem of I.S. Kac.
Eigenfunction Expansions Associated With The One-Dimensional Schrödinger Operator, Daphne Gilbert
Eigenfunction Expansions Associated With The One-Dimensional Schrödinger Operator, Daphne Gilbert
Articles
We consider the form of eigenfunction expansions associated with the time-independent Schrödinger operator on the line, under the assumption that the limit point case holds at both of the infinite endpoints. It is well known that in this situation the multiplicity of the operator may be one or two, depending on properties of the potential function. Moreover, for values of the spectral parameter in the upper half complex plane, there exist Weyl solutions associated with the restrictions of the operator to the negative and positive half-lines respectively, together with corresponding Titchmarsh-Weyl functions.
Mass Transfer From A Vertical Flat Plate Due To A Constant Upward Flow, David Mcdonnell, Brendan Redmond, Lawrence J. Crane
Mass Transfer From A Vertical Flat Plate Due To A Constant Upward Flow, David Mcdonnell, Brendan Redmond, Lawrence J. Crane
Articles
This paper examines the mass transfer from a vertical flat surface of a soluble material due to a constant upward flow. The mass transfer rate due to this upward flow is calculated and used to obtain the distance along the surface at which the boundary layer separates. For relatively large velocities no separation will occur and the solution approaches that of forced convection on a horizontal surface.
Mass Transfer From A Vertical Flat Plate Due To Natural Convection With A Constant Counterflow, David Mcdonnell, Brendan Redmond, Lawrence J. Crane
Mass Transfer From A Vertical Flat Plate Due To Natural Convection With A Constant Counterflow, David Mcdonnell, Brendan Redmond, Lawrence J. Crane
Articles
This paper first examines the mass transfer from a vertical flat surface of a soluble material due to natural convection. A perturbation term is then introduced into the stream function to model the introduction of a constant counterflow. The effect this counterflow has on both the overall mass transfer and the overall velocity profile is studied in detail.
Bayesian Model Selection For Exponential Random Graph Models, Alberto Caimo, Nial Friel
Bayesian Model Selection For Exponential Random Graph Models, Alberto Caimo, Nial Friel
Articles
Exponential random graph models are a class of widely used exponential family models for social networks. The topological structure of an observed network is modelled by the relative prevalence of a set of local sub-graph configurations termed network statistics. One of the key tasks in the application of these models is which network statistics to include in the model. This can be thought of as statistical model selection problem. This is a very challenging problem---the posterior distribution for each model is often termed ``doubly intractable'' since computation of the likelihood is rarely available, but also, the evidence of the posterior …
Endomorphisms Of Abelian Groups With Small Algebraic Entropy, D. Dikranjan, Ketao Gong, P. Zanardo
Endomorphisms Of Abelian Groups With Small Algebraic Entropy, D. Dikranjan, Ketao Gong, P. Zanardo
Articles
We study the endomorphisms ϕ of abelian groups G having a “small” algebraic entropy h (where “small” usually means ). Using essentially elementary tools from linear algebra, we show that this study can be carried out in the group , where an automorphism ϕ with must have all eigenvalues in the open circle of radius 2, centered at 0 and ϕ must leave invariant a lattice in , i.e., be essentially an automorphism of . In particular, all eigenvalues of an automorphism ϕ with must be roots of unity. This is a particular case of a more general fact known …
Extreme Wave Events In Ireland: 14 680 Bp–2012, Laura Cooke, John M. Dudley, Frédéric Dias
Extreme Wave Events In Ireland: 14 680 Bp–2012, Laura Cooke, John M. Dudley, Frédéric Dias
Articles
The island of Ireland is battered by waves from all sides, most ferociously on the west coast as the first port of call for waves travelling across the Atlantic Ocean. However, when discussing ocean events relevant to the nation of Ire- land, one must actually consider its significantly larger designated continental shelf, which is one of the largest seabed territories in Europe. With this expanded definition, it is not surprising that Ireland has been subject to many oceanic events which could be designated as “extreme”; in this paper we present what we believe to be the first catalogue of such …
G-Strands And Peakon Collisions On Diff(R), Darryl Holm, Rossen Ivanov
G-Strands And Peakon Collisions On Diff(R), Darryl Holm, Rossen Ivanov
Articles
A G-strand is a map g : R x R --> G for a Lie group G that follows from Hamilton's principle for a certain class of G-invariant Lagrangians. Some G-strands on finite-dimensional groups satisfy 1+1 space-time evolutionary equations that admit soliton solutions as completely integrable Hamiltonian systems. For example, the SO(3)-strand equations may be regarded physically as integrable dynamics for solitons on a continuous spin chain. Previous work has shown that G-strands for diffeomorphisms on the real line possess solutions with singular support (e.g. peakons). This paper studies collisions of such singular solutions of G-strands when G = Diff( …
On The Persistence Properties Of The Cross-Coupled Camassa-Holm System, David Henry, Darryl Holm, Rossen Ivanov
On The Persistence Properties Of The Cross-Coupled Camassa-Holm System, David Henry, Darryl Holm, Rossen Ivanov
Articles
In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the persistence of compact support for the momenta. For solutions of the system itself, the answer is more convoluted, and we determine when the compactness of the support is lost, replaced instead by an exponential decay rate.