30,751 research outputs found
The exterior degree of a pair of finite groups
The exterior degree of a pair of finite groups , which is a
generalization of the exterior degree of finite groups, is the probability for
two elements in such that . In the present paper,
we state some relations between this concept and the relative commutatively
degree, capability and the Schur multiplier of a pair of groups.Comment: To appear in Mediterr. J. Mat
Integrability of irrotational silent cosmological models
We revisit the issue of integrability conditions for the irrotational silent
cosmological models. We formulate the problem both in 1+3 covariant and 1+3
orthonormal frame notation, and show there exists a series of constraint
equations that need to be satisfied. These conditions hold identically for
FLRW-linearised silent models, but not in the general exact non-linear case.
Thus there is a linearisation instability, and it is highly unlikely that there
is a large class of silent models. We conjecture that there are no spatially
inhomogeneous solutions with Weyl curvature of Petrov type I, and indicate
further issues that await clarification.Comment: Minor corrections and improvements; 1 new reference; to appear Class.
Quantum Grav.; 16 pages Ioplpp
Dynamics of Inflationary Universes with Positive Spatial Curvature
If the spatial curvature of the universe is positive, then the curvature term
will always dominate at early enough times in a slow-rolling inflationary
epoch. This enhances inflationary effects and hence puts limits on the possible
number of e-foldings that can have occurred, independently of what happened
before inflation began and in particular without regard for what may have
happened in the Planck era. We use a simple multi-stage model to examine this
limit as a function of the present density parameter and the epoch
when inflation ends.Comment: 9 Pages RevTex4. Revised and update
Consistency of dust solutions with div H=0
One of the necessary covariant conditions for gravitational radiation is the
vanishing of the divergence of the magnetic Weyl tensor H_{ab}, while H_{ab}
itself is nonzero. We complete a recent analysis by showing that in
irrotational dust spacetimes, the condition div H=0 evolves consistently in the
exact nonlinear theory.Comment: 3 pages Revte
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