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Articles 1 - 14 of 14
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Fixing Numbers Of Graphs And Groups, Courtney Gibbons, Joshua D. Laison
Fixing Numbers Of Graphs And Groups, Courtney Gibbons, Joshua D. Laison
Articles
The fixing number of a graph G is the smallest cardinality of a set of vertices S such that only the trivial automorphism of G fixes every vertex in S. The fixing set of a group Γ is the set of all fixing numbers of finite graphs with automorphism group Γ. Several authors have studied the distinguishing number of a graph, the smallest number of labels needed to label G so that the automorphism group of the labeled graph is trivial. The fixing number can be thought of as a variation of the distinguishing number in which every label …
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].
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.
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 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.
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.
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 …
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.
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 …
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.
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 …