Three-dimensional Schwarzschild spacetimes

In the following we find all of the three-dimensional flat spacetimes which are static and rotationally symmetric.     

Graphs that admit square 1-factorizations are hamiltonian Cayley graphs

A square 1-factorization of a graph is a 1-factorization in which the union of any two distinct 1-factors is a disjoint union of 4-cycles. We show that a graph admits a square 1-factorization if and only if it is a Cayley graph with group (₂) ⁿ for somen. The rest of the title follows since Cayley graphs of abelian groups are known to be hamiltonian.     

Every finite solvable group with a unique element of order two,except the quaternion group,has a symmetric sequencing

All finite solvable groups that have symmetric sequencings are characterized. Let G be a finite solvable group. It is shown that G has a symmetric sequencing if and only if G has a unique element of order two and is not the quaternion group. All finite groups with a unique element of order two such that the order of the group is not divisible by three are solvable and thus, except for the quaternion group, have symmetric sequencings. A crucial step used in the proof of these facts is a construction showing that if a finite group H has a normal subgroup C of odd order such that H/C admits a 2-sequencing, then H admits a 2-sequencing. The results of this article can be viewed as generalizing a theorem of Gordon about Abelian groups and as extending the idea of a starter, suitably modified, to a large class of groups of even order by showing the existence of the required object. © 1993 John Wiley & Sons, Inc.     

Symmetries inT ij related to nonuniqueness of solutions to Einstein's equations

A symmetry principle is proposed which in the case whenT _ij enjoys sufficient symmetry helps to pick out the physically relevant solution to Einstein's equations.     

Influence of the martensitic structure transformation in LaAg x In1−x on the magnetic properties of substituted Ce

The martensitic phase transformation has no observable effect on the magnetic susceptibility of Ce in LaAg _x In_1–x which agrees with the assumption of a crystal field splitting by 300 K of the² F _5/2 ground state of Ce³⁺ ions. The magnetic ordering temperature and the Kondo minimum move to higher temperatures together with the martensitic phase transformation when the Ag concentration is reduced. This behavior can be related qualitatively to the lowering of the 5d – e _g levels in the center of the Brillouin-zone with increasing In content.