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Articles 241 - 270 of 356
Full-Text Articles in Mathematics
Schrödinger Operators With Δ'Interactions And The Krein–Stieltjes String, Aleksey Kostenko, M. M. Malamud
Schrödinger Operators With Δ'Interactions And The Krein–Stieltjes String, Aleksey Kostenko, M. M. Malamud
Articles
We investigate one dimensional symmetric Schrödinger operator HX, β with δ' interactions of strength β = ⊂ on a discrete set X = ⊂ [0, b), b ≤ +∞ (xn ↑ b). We consider HX, β as an extension of the minimal operator Hmin := –d2/dx2 (\X) and study its spectral properties in the frame work of the extension theory by using the technique of boundary triplets and the corresponding Weyl functions. The construction of a boundary triplet for is given in the case d∗ := infn ∈ |xn – xn – 1| = 0. We show that spectral properties …
Heat Transfer Through The Boundary Layer On A Moving Cylindrical Fibre, Brendan Redmond, David Mcdonnell
Heat Transfer Through The Boundary Layer On A Moving Cylindrical Fibre, Brendan Redmond, David Mcdonnell
Articles
This paper applies boundary layer theory to the process of manufacturing polymer fibres known as the melt spinning process. The rate of heat loss of the fibre during this process, characterised by the local Nusselt number, is evaluated by means of a Pohlhausen integral method.
On The Socles Of Characteristic Subgroups Of Abelian P-Groups, Brendan Goldsmith, Peter Danchev
On The Socles Of Characteristic Subgroups Of Abelian P-Groups, Brendan Goldsmith, Peter Danchev
Articles
Fully invariant subgroups of an Abelian p-group have been the object of a good deal of study, while characteristic subgroups have received somewhat less attention. Recently the socles of fully invariant subgroups have been studied and this led to the notion of a socle-regular group. The present work replaces the fully invariant subgroups with characteristic ones and leads in a natural way to the notion of a strongly socle-regular group. A surprising relationship, mirroring that between transitive and fully transitive groups, is obtained.
From Permutahedron To Associahedron, Colum Watt, Thomas Brady
From Permutahedron To Associahedron, Colum Watt, Thomas Brady
Articles
For each finite real reflection group $W$, we identify a copy of the type-$W$ simplicial generalised associahedron inside the corresponding simplicial permutahedron. This defines a bijection between the facets of the generalised associahedron and the elements of the type-$W$ non-crossing partition lattice which is more tractable than previous such bijections. We show that the simplicial fan determined by this associahedron coincides with the Cambrian fan for $W$.
Poisson Structures Of Equations Associated With Groups Of Diffeomorphisms, Rossen Ivanov
Poisson Structures Of Equations Associated With Groups Of Diffeomorphisms, Rossen Ivanov
Conference papers
A class of equations describing the geodesic flow for a right-invariant metric on the group of diffeomorphisms of Rn is reviewed from the viewpoint of their Lie-Poisson structures. A subclass of these equations is analogous to the Euler equations in hydrodynamics (for n = 3), preserving the volume element of the domain of fluid flow. An example in n = 1 dimension is the Camassa-Holm equation, which is a geodesic flow equation on the group of diffeomorphisms, preserving the H1 metric.
Existence Of Infinitely Many Distinct Solutions To The Quasi-Relativistic Hartree-Fock Equations, Mattias Enstedt, Michael Melgaard
Existence Of Infinitely Many Distinct Solutions To The Quasi-Relativistic Hartree-Fock Equations, Mattias Enstedt, Michael Melgaard
Articles
We establish existence of infinitely many distinct solutions to the semilinear elliptic Hartree-Fock equations for N-electron Coulomb systems with quasirelativistic kinetic energy −α−2Δxn α−4 − α−2 for the nth electron. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge Ztot of K nuclei is greater than N − 1 and that Ztot is smaller than a critical charge Zc. The proofs are based on a new application of the Fang-Ghoussoub critical point approach to multiple solutions on a noncompact Riemannian manifold, in combination with density operator techniques.
An Analysis Of Drug Dissolution Rates In The Usp 24 Type 2 Apparatus, David Mcdonnell, Brendan Redmond, Deirdre M. D'Arcy, Anne Marie Healy, Owen Corrigan
An Analysis Of Drug Dissolution Rates In The Usp 24 Type 2 Apparatus, David Mcdonnell, Brendan Redmond, Deirdre M. D'Arcy, Anne Marie Healy, Owen Corrigan
Articles
This paper applies boundary layer theory to the process of drug dissolution in the USP 24, Type 2 Apparatus. The mass transfer rate from the top flat surface of a compact in various positions within the device is evaluated by means of a Pohlhausen integral method.
On Modules Which Are Self-Slender, R. Gobel, Brendan Goldsmith, O. Kolman
On Modules Which Are Self-Slender, R. Gobel, Brendan Goldsmith, O. Kolman
Articles
This paper is an examination of the dual of the fundamental isomorphism relating homomorphism groups involving direct sums and direct products over arbitrary index sets. Recall that a module G is said to be self-slender if every homomorphism from a countable product of copies of G into G, vanishes on all but finitely many of the components of the product. Modules of this type are investigated. The simplest version of the results obtained is that under weak cardinality restrictions, there exist non-slender but self-slender Abelian groups.
Two Component Integrable Systems Modelling Shallow Water Waves: The Constant Vorticity Case, Rossen Ivanov
Two Component Integrable Systems Modelling Shallow Water Waves: The Constant Vorticity Case, Rossen Ivanov
Articles
In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of mass conservation, the simplest bottom and surface conditions and the constant vorticity condition. The approximate model equations are generated by introduction of suitable scalings and by truncating asymptotic expansions of the quantities to appropriate order. The so obtained equations can be related to three different integrable systems: a two component generalization of the Camassa-Holm equation, the Zakharov-Ito system and the Kaup-Boussinesq system. The …
1-D Schrödinger Operators With Local Point Interactions On A Discrete Set, Aleksey Kostenko, Mark M. Malamud
1-D Schrödinger Operators With Local Point Interactions On A Discrete Set, Aleksey Kostenko, Mark M. Malamud
Articles
Spectral properties of 1-D Schrödinger operators HX,α := − d2 dx2 + xn∈X αnδ(x − xn) with local point interactions on a discrete set X = {xn}∞ n=1 are well studied when d∗ := infn,k∈N |xn − xk| > 0. Our paper is devoted to the case d∗ = 0. We consider HX,α in the framework of extension theory of symmetric operators by applying the technique of boundary triplets and the corresponding Weyl functions.
Phase Transitions In Materials With Thermal Memory: The Case Of Unequal Conductivities, John Murrough Golden
Phase Transitions In Materials With Thermal Memory: The Case Of Unequal Conductivities, John Murrough Golden
Articles
A model for thermally induced phase transitions in materials with thermal memory was recently proposed, where the equations determining heatflow were assumed to be the same in both phases. In this work, the model is generalized to the case of phase dependent heatflow relations. The temperature (or coldness) gradient is decomposed into two parts, each zero on one phase and equal to the temperature (or coldness) gradient on the other. However, they vary smoothly over the transition zone. These are treated as separate independent quantities in the derivation of field equations from thermodynamics. Heat flux is given by an integral …
On The Socles Of Fully Invariant Abelian P-Groups, Brendan Goldsmith, P. V. Danchev
On The Socles Of Fully Invariant Abelian P-Groups, Brendan Goldsmith, P. V. Danchev
Articles
The classification of the fully invariant subgroups of a reduced Abelian p-group is a difficult long-standing problem when one moves outside of the class of fully transitive groups. In this work we restrict attention to the socles of fully invariant subgroups and introduce a new class of groups which we term socle-regular groups; this class is shown to be large and strictly contains the class of fully transitive groups. The basic properties of such groups are investigated but it is shown that the classification of even this simplified class of groups, seems extremely difficult.
Converging Flow Between Coaxial Cones, O. Hall, A. D. Gilbert, C. P. Hills
Converging Flow Between Coaxial Cones, O. Hall, A. D. Gilbert, C. P. Hills
Articles
Fluid flow governed by the Navier-Stokes equation is considered in a domain bounded by two cones with the same axis. In the first, 'non-parallel' case, the two cones have the same apex and different angles θ = α and β in spherical polar coordinates (r, θ, φ). In the second, 'parallel' case, the two cones have the same opening angle α, parallel walls separated by a gap h and apices separated by a distance h/sinα. Flows are driven by a source Q at the origin, the apex of the lower cone in the parallel case. The Stokes solution for the …
Nonaxisymmetric Stokes Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert
Nonaxisymmetric Stokes Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert
Articles
We study the fully three-dimensional Stokes flow within a geometry consisting of two infinite cones with coincident apices. The Stokes approximation is valid near the apex and we consider the dominant flow features as it is approached. The cones are assumed to be stationary and the flow to be driven by an arbitrary far-field disturbance. We express the flow quantities in terms of eigenfunction expansions and allow for the first time for nonaxisymmetric flow regimes through an azimuthal wave number. The eigenvalue problem is solved numerically for successive wave numbers. Both real and complex sequences of eigenvalues are found, their …
Equations Of The Camassa-Holm Hierarchy, Rossen Ivanov
Equations Of The Camassa-Holm Hierarchy, Rossen Ivanov
Articles
The squared eigenfunctions of the spectral problem associated with the CamassaHolm (CH) equation represent a complete basis of functions, which helps to describe the inverse scattering transform for the CH hierarchy as a generalized Fourier transform (GFT). All the fundamental properties of the CH equation, such as the integrals of motion, the description of the equations of the whole hierarchy, and their Hamiltonian structures, can be naturally expressed using the completeness relation and the recursion operator, whose eigenfunctions are the squared solutions. Using the GFT, we explicitly describe some members of the CH hierarchy, including integrable deformations for the CH …
Algebraic Entropy For Abelian Groups, Dikran Dikranjan, Brendan Goldsmith, Luigi Salce, Paolo Zanardo
Algebraic Entropy For Abelian Groups, Dikran Dikranjan, Brendan Goldsmith, Luigi Salce, Paolo Zanardo
Articles
The theory of endomorphism rings of algebraic structures allows, in a natural way, a systematic approach based on the notion of entropy borrowed from dynamical systems. Here we study the algebraic entropy of the endomorphisms of Abelian groups, introduced in 1965 by Adler, Konheim and McAndrew. The so-called Addition Theorem is proved; this expresses the algebraic entropy of an endomorphism $ \phi$ of a torsion group as the sum of the algebraic entropies of the restriction to a $ \phi$-invariant subgroup and of the endomorphism induced on the quotient group. Particular attention is paid to endomorphisms with zero algebraic entropy …
Daemon Decay And Inflation, Emil Prodanov
Daemon Decay And Inflation, Emil Prodanov
Articles
In 1971, Hawking suggested [1] that there may be a very large number of gravitationally collapsed charged objects of very low masses, formed as a result of fluctuations in the early Universe. A mass of of these objects could be accumulated at the centre of a star like the Sun. The masses of these collapsed objects are from and above and their charges are up to ±30 electron units [1].
On The Socles Of Characteristic Subgroups Of Abelian P-Groups, P. V. Danchev, Brendan Goldsmith
On The Socles Of Characteristic Subgroups Of Abelian P-Groups, P. V. Danchev, Brendan Goldsmith
Articles
Fully invariant subgroups of an Abelian p-group have been the object of a good deal of study, while characteristic subgroups have received somewhat less attention. Recently the socles of fully invariant subgroups have been studied and this led to the notion of a socle-regular group. The present work replaces the fully invariant subgroups with characteristic ones and leads in a natural way to the notion of a strongly socle-regular group. A surprising relationship, mirroring that between transitive and fully transitive groups, is obtained.
Langer's Method For The Calculation Of Escape Rates And Its Application To Systems Of Ferromagnets, Gerard Duff
Langer's Method For The Calculation Of Escape Rates And Its Application To Systems Of Ferromagnets, Gerard Duff
Doctoral
This work is a study of the application of a theory proposed by J. S. Langer (J.S. Langer, Statistical Theory of the Decay of Metastable States, Annals of Physics 54, 258-275 (1969)) for the calculation of the decay rate (relaxation rate) of a metastable state. The theory is set in the context of statistical mechanics, where the dynamics of a system with a large number of degrees of freedom (order 1023) are reduced to N degrees of freedom, where N is small, when a steady state or equilibrium position is maintained by the entire system. In this thesis N equals …
Environmental Limits On The Nonresonant Cosmic-Ray Current-Driven Instability, Brian Reville, John Kirk, Peter Duffy, Stephen O'Sullivan
Environmental Limits On The Nonresonant Cosmic-Ray Current-Driven Instability, Brian Reville, John Kirk, Peter Duffy, Stephen O'Sullivan
Articles
We investigate the so-called nonresonant cosmic-ray streaming instability, first discussed by Bell (2004). The extent to which thermal damping and ion-neutral collisions reduce the growth of this instability is calculated. Limits on the growth of the nonresonant mode in SN1006 and RX J1713.7-3946 are presented.
Some Rather Mechanical Reflections On Symmetry: In Art, Science, Engineering, Mathematics, Etc., Jim Mcgovern
Some Rather Mechanical Reflections On Symmetry: In Art, Science, Engineering, Mathematics, Etc., Jim Mcgovern
Articles
This Inaugural Lecture consists of some of my rather mechanical, being an engineer, reflections on symmetry in diverse areas such as art, science, engineering, mathematics, etc. I explain what symmetry is to me, giving examples with lots of images and mentioning or at least barely referencing art, science, architecture, engineering, heritage, cosmology, bicycles, flight, invention, ingenuity, history, wallpaper, mathematics, typography, structures, regular shapes, coordinate systems, spacetime, thermodynamics and suchlike.
An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance (Revised Version) 2008, Jim Mcgovern
An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance (Revised Version) 2008, Jim Mcgovern
Conference Papers
A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent cuboctahedral lattices are denoted by four colours and the composite lattice is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour lattice can be referenced by an integer 4-tuple containing only the positive non-zero integers (the counting numbers). The relationship between the discrete rhombohedral lattice and a discrete Cartesian lattice is explained. Some interesting aspects of the lattice and of the counting-number 4-tuple coordinate system are pointed …
Metrology And Proportion In The Ecclesiastical Architecture Of Medieval Ireland, Avril Behan, Rachel Moss
Metrology And Proportion In The Ecclesiastical Architecture Of Medieval Ireland, Avril Behan, Rachel Moss
Conference Papers
The aim of this paper is to examine the extent to which detailed empirical analysis of the metrology and proportional systems used in the design of Irish ecclesiastical architecture can be analysed to provide historical information not otherwise available. Focussing on a relatively limited sample of window tracery designs as a case study, it will first set out to establish what, if any, systems were in use, and then what light these might shed on the background, training and work practices of the masons, and, by association, the patrons responsible for employing them.
An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance, Jim Mcgovern
An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance, Jim Mcgovern
Conference Papers
A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral or cubic point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent lattices are denoted by four colours and the composite lattice is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour lattice can be referenced by an integer 4-tuple containing only the positive non-zero integers (the counting numbers). The relationship between the discrete rhombohedral lattice and a discrete Cartesian lattice is explained. Some interesting aspects of the lattice and of the counting-number 4-tuple coordinate system are …
The Dublin Institute Of Technology And University Status: A Case Study Of The Application By Dit For Designation As A University (1996-99), Colm Garvey
Other resources
Section 9 of the Universities Act 1997 set out, for the first time, a statutory mechanism for the establishment of a new university in Ireland. The Dublin Institute of Technology (DIT) was the first institution to be granted a review under this legislation. This thesis presents an account and analysis of how the application for university title was handled by an international review group, by the Higher Education Authority (HEA) and by the Irish Government. This case study is based on access to files held by the HEA and on interviews with some of the leading players in the Review …
Nearly-Hamiltonian Structure For Water Waves With Constant Vorticity, Adrian Constantin, Rossen Ivanov, Emil Prodanov
Nearly-Hamiltonian Structure For Water Waves With Constant Vorticity, Adrian Constantin, Rossen Ivanov, Emil Prodanov
Articles
We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.
Higher Derivatives Of Spectral Functions Associated With One-Dimensional Schrodinger Operators, Daphne Gilbert, B.J. Harris, S.M. Riehl
Higher Derivatives Of Spectral Functions Associated With One-Dimensional Schrodinger Operators, Daphne Gilbert, B.J. Harris, S.M. Riehl
Articles
We investigate the existence and asymptotic behaviour of higher derivatives of the spectral function in the context of one-dimensional Schr¨odinger operators on the half-line with integrable potentials. In particular, we identify sufficient conditions on the potential for the existence and continuity of the n-th derivative, and outline a systematic procedure for estimating numerical upper bounds for the turning points of such derivatives. Explicit worked examples illustrate the development and application of the theory.
A Study Of Boundary Layer Fflow With No-Slip And Slip Boundary Conditions, Sandra B. Spillane
A Study Of Boundary Layer Fflow With No-Slip And Slip Boundary Conditions, Sandra B. Spillane
Doctoral
This thesis involves solving the two-dimensional boundary layer equations for axially symmetric fluid flow along a circular cylinder using the no-slip and slip boundary condition, and along a flat plate with the slip boundary condition. Initially, historical results in both areas are summarised. The research section of this thesis is concerned with extending these historical results. In the first research chapters, a Pade approximation and an Euler transformation are used to greatly extend the region of validity of the historical results. Following that is an investigation of the relaxation of the traditional no-slip boundary condition, which usually occurs when there …
On An Integrable Two-Component Camassa-Holm Shallow Water System, Adrian Constantin, Rossen Ivanov
On An Integrable Two-Component Camassa-Holm Shallow Water System, Adrian Constantin, Rossen Ivanov
Articles
The interest in the Camassa-Holm equation inspired the search for various generalizations of this equation with interesting properties and applications. In this letter we deal with such a twocomponent integrable system of coupled equations. First we derive the system in the context of shallow water theory. Then we show that while small initial data develop into global solutions, for some initial data wave breaking occurs. We also discuss the solitary wave solutions. Finally, we present an explicit construction for the peakon solutions in the short wave limit of system.
Algebraic Discretization Of The Camassa-Holm And Hunter-Saxton Equations, Rossen Ivanov
Algebraic Discretization Of The Camassa-Holm And Hunter-Saxton Equations, Rossen Ivanov
Articles
The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H1 and H.1 right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a right-invariant metric on the infinitedimensional group of diffeomorphisms preserving the volume element of the domain of fluid flow and to the Euler equations of rigid body whith a fixed point, describing geodesics for a left-invariant metric on SO(3). The CH and HS equations are integrable bi-hamiltonian equations and one of their Hamiltonian structures is associated to the …