Vorlesungen über Algebra.

Available on demand as hard copy or computer file from Cornell University Library.

Sur les progrès de la théorie des invariants projectifs.

Available on demand as hard copy or computer file from Cornell University Library.

Abelsche Gruppen mit abzählbaren Elementen /

Habilitationsschrift--Universität Leipzig.

Kirkman-systemen : academisch proefschrift ... /

Thesis--Rijksuniversiteit te Groningen.

Theorie der endlichen gruppen von eindeutigen transformationen in der ebene.

Available on demand as hard copy or computer file from Cornell University Library.

Les fonctions polyédriques et modulaires.

Available on demand as hard copy or computer file from Cornell University Library.

Théorie des groupes finis. Éléments de la théorie des groupes abstraits.

Available on demand as hard copy or computer file from Cornell University Library.

Groups of order pm which contain cyclic subgroups of order pm-3,

Mode of access: Internet.

Traité d'algebre supérieure /

1. Principes.--2. Racines des équations.--3. Grandeurs algébriques.

Traité d'analyse /

t. 1. Intégrales simples et multiples. Lʼéquation de Laplace et ses applications. Développments in séries. Applications géométriques du calcul infinitésimal.

Topological transformation groups

Bibliography: p. 272-279.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

Finite Groups as the Union of Proper Subgroups

2000 Mathematics Subject Classification: 20D60,20E15.

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.