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Articles 211 - 240 of 320
Full-Text Articles in Mathematics
On Socle-Regularity And Some Notions Of Transitivity For Abelian P-Groups, Brendan Goldsmith, Peter Danchev
On Socle-Regularity And Some Notions Of Transitivity For Abelian P-Groups, Brendan Goldsmith, Peter Danchev
Articles
In the present work the interconnections between various notions of transitivity for Abelian p-groups and the recently introduced concepts of socle-regular and strongly socle-regular groups are studied.
Bayesian Inference For Exponential Random Graph Models, Alberto Caimo, Nial Friel
Bayesian Inference For Exponential Random Graph Models, Alberto Caimo, Nial Friel
Articles
Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can be carried out in a Bayesian framework using a MCMC algorithm, which circumvents the need to calculate the normalising constants. We use a population MCMC approach which accelerates convergence and improves mixing of the Markov chain. This approach improves performance with respect to the Monte Carlo maximum likelihood method of Geyer and Thompson (1992).
Extended Green-Liouville Asymptotics And Vacuum Polarization For Lukewarm Black Holes, Cormac Breen, Adrian Ottewill
Extended Green-Liouville Asymptotics And Vacuum Polarization For Lukewarm Black Holes, Cormac Breen, Adrian Ottewill
Articles
We consider a quantum field on a lukewarm black hole spacetime. We introduce a new uniform approximation to the radial equation, constructed using an extension of Green-Liouville asymptotics. We then use this new approximation to construct the renormalized vacuum polarization in the Hartle-Hawking vacuum. Previous calculations of the vacuum polarization rely on the WKB approximation to the solutions of the radial equation, however the nonuniformity of the WKB approximations obscures the results of these calculations near both horizons. The use of our new approximation eliminates these obscurities, enabling us to obtain explicitly finite and easily calculable values of the vacuum …
Inverse Scattering Transform For The Degasperis–Procesi Equation, Adrian Constantin, Rossen Ivanov, Jonatan Lenells
Inverse Scattering Transform For The Degasperis–Procesi Equation, Adrian Constantin, Rossen Ivanov, Jonatan Lenells
Articles
We develop the Inverse Scattering Transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method are presented.
The Maximal Pure Spectrum Of An Abelian Group, Brendan Goldsmith, Ruediger Goebel
The Maximal Pure Spectrum Of An Abelian Group, Brendan Goldsmith, Ruediger Goebel
Articles
This paper introduces the notion of the maximal pure spectrum of an Abelian group - this is the set of isomorphism classes of maximal proper pure subgroups - and focuses on the situation in which this spectrum is small. The converse situation is also examined i.e. given a collection of isomorphism classes of groups, can one find an Abelian group having precisely this collection as its maximal pure spectrum. Finally, it is shown that in some familiar situations, the answers to these questions may be undecidable.
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 Aassociahedron, Colum Watt, Thomas Brady
From Permutahedron To Aassociahedron, 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 $W$.
The Similarity Problem For Indefinite Sturm-Liouville Operators With Periodic Coefficients, Aleksey Kostenko
The Similarity Problem For Indefinite Sturm-Liouville Operators With Periodic Coefficients, Aleksey Kostenko
Articles
We investigate the problem of similarity to a self-adjoint operator for $J$-positive Sturm-Liouville operators $L=\frac{1}{\omega}(-\frac{d^2}{dx^2}+q)$ with $2\pi$-periodic coefficients $q$ and $\omega$. It is shown that if 0 is a critical point of the operator $L$, then it is a singular critical point. This gives us a new class of $J$-positive differential operators with the singular critical point 0. Also, we extend the Beals and Parfenov regularity conditions for the critical point $\infty$ to the case of operators with periodic coefficients.
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 $W$.
Climbing Eements In Finite Coxeter Groups, Colum Watt, Thomas Brady, Aisling Kenny
Climbing Eements In Finite Coxeter Groups, Colum Watt, Thomas Brady, Aisling Kenny
Articles
We define the notion of a climbing element in a finite real reflection group relative to a total order on the reflection set and we characterise these elements in the case where the total order arises from a bipartite Coxeter element.
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.
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.
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 …
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 …
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 …
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.
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].
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.
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.
Non-Existence Of A Minimizer To The Hartree-Fock Functional, Michael Melgaard, Mattias Enstedt
Non-Existence Of A Minimizer To The Hartree-Fock Functional, Michael Melgaard, Mattias Enstedt
Articles
In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization
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.
Existence Of A Solution To Hartree-Fock Equations With Decreasing Magnetic Field, Mattias Enstedt, Michael Melgaard
Existence Of A Solution To Hartree-Fock Equations With Decreasing Magnetic Field, Mattias Enstedt, Michael Melgaard
Articles
In the presence of an external magnetic field, we prove existence of a ground state within the Hartree–Fock theory of atoms and molecules. The ground state exists provided the magnetic field decreases at infinity and the total charge of nuclei exceeds , where is the number of electrons. In the opposite direction, no ground state exists if .