We consider a vector field in a half-space which vanishes at . If a vector field is invariant under rotation around axis, we say that it is axially symmetric, in other words, for every rotation about the axis. If, moreover, an axially symmetric vector field is invariant under reflection by every plane containing axis, we say it is axially symmetric with no swirl, that is to say, is axially symm...

We rigorously establish some exact properties of reflection symmetric spin systems with antiferromagnetic crossing bonds: At least one ground state has total spin zero and a positive semidefinite coefficient matrix. The crossing bonds obey an ice rule. This augments some previous results which were limited to bipartite spin systems and is of particular interest for frustrated spin systems. c ©1...

2. The Freudenthal theorem for symmetric spaces Our primary interest is in the classical compact groups; nevertheless, it is essential for our method to consider the larger family of compact symmetric spaces. A compact homogeneous Riemannian manifold M is called symmetric if it admits an 'inverse operation', i.e. if M admits an isometry, keeping a point P e M fixed, and whose differential at P ...

The reflection and transmission of thermoelastic plane waves at an imperfect boundary of two dissimilar fibre-reinforced transversely isotropic thermoelastic solid half-spaces under hydrostatic initial stress has been investigated. The appropriate boundary conditions are applied at the interface to obtain the reflection and transmission coefficients of various reflected and transmitted waves wi...

This paper deals with some universal spaces. For every topological space $X$, the $T_1$ is viewed as bottom element of lattice $\mathcal{L}_X$. The class morphisms in $\mathrm{\mathbf{Top}}$ orthogonal to all spaces characterized. Also, we introduce new separation axioms and characterize them. Moreover, $X$ for which associated a spectral space. Finally, give characterizations such that their $...

In this paper we use elementary geometrical and topological methods to study some questions about the coarse geometry of symmetric spaces. Our results are powerful enough to apply to noncocompact lattices in higher rank symmetric spaces, such as SL(n,Z), n ≥ 3 : Theorem 8.1 is a major step towards the proof of quasiisometric rigidity of such lattices ([E]). We also give a different, and effecti...

In this paper, we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple Lie algebras. These solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type. We show that the Ricci curvatures of our solvmanifolds coincide with the restrictions of the Ricci curvatures of the ambient symmetric spaces. Consequently, all of our solvmanifolds...