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The symmetries of a function are considered that takes as its argument an arbitrary two‐dimensional Bravais lattice, represented by a 2×2 matrix. Rotating the lattice corresponds to multiplying its matrix on the right by an element of SO(2). Matrices related by left multiplication of an...
Using a combination of Hamiltonian reduction under continuous and discrete symmetry groups, the Lax equations for the motion of generalized tops are derived as part of a general approach to moment map embeddings of integrable Hamiltonian systems in loop algebras.
The combination of Synge’s approach to Einstein’s equations with energy conditions and the Segré classification of the energy‐momentum tensor is used in the examination of Einstein’s space‐time. An alternative physical interpretation for the Einstein static model is discussed. An...
A representation is found for the finite Fourier series of a vector whereby any constant constraint on its magnitude is completely solved and automatically satisfied. The representation is a product of rotations, one set for each harmonic, such that the independent degrees of freedom are...
The expression for the determinant of the Laplace operator is used in terms of functional integration to compute the asymptotic behavior on degenerating Riemann surfaces. In the case of the Arakelov metric, the information is sufficiently precise to give a value for the absolute constants...
The effective conductivity of a two‐phase two‐dimensional composite with diamond‐shaped tiling is considered. This analysis, based on a projection of the boundary conditions on linear combinations of solutions to the electrostatic equation that are orthonormal on the boundary, generalizes...
A class of noninvertible Bogoliubov transformations in an abstract Boson Fock space is used to construct in the Fock space a family of self‐adjoint operators H which are quadratic in the annihilation and the creation operators and are of the form H = H 0 + H I with the property that the...
Properties of the Euler–Lagrange differential equation for cos F , where F is the chiral angle of the classical Skyrme soliton in the hedgehog ansatz, are investigated. The power series solution for y =cos F , is obtained that presents the behavior of an almost geometric series, and the...
Practical implementation of two important methods of constructing integrable dynamical systems, the Lax pair method and the Adler–Konstant–Symes theorem, is studied. General considerations are illustrated by several examples that contain multiwave interaction systems and interacting Garnier...
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