Assuming that the underlying probability space is non-atomic we prove that products of random matrices (linear cocycles) with simple Lyapunov spectrum form an L p-dense set (1 p < 1) in the space of all cocy-cles satisfying the integrability conditions of the multiplicative ergodic theorem. However, the linear cocycles with one-point spectrum are also L p-dense. Further, in any L 1-neighborhood...

Communication schemes employing quantum entanglement open a wide field of possible applications with properties outperforming their classical counterparts. Promising examples are quantum key distribution, quantum dense coding, and quantum state teleportation. We investigate the potential of quantum cryptography, i.e. quantum key distribution (QKD), with special emphasis on the demands and oppor...

We compare two examples of random dense countable sets, Brownian local minima and unordered uniform infinite sample. They appear to be identically distributed. A framework for such notions is proposed. In addition, random elements of other singular spaces (especially, reals modulo rationals) are considered. Introduction For almost every Brownian path ω = (bt)t∈[0,1] on [0, 1], the set (0.1) Mω ...

As the Internet autonomous sytem (AS)-level topology grows over time, some of its structural properties remain unchanged. Such time-invariant properties are generally interesting because they tend to reflect some fundamental processes or constraints behind Internet growth. As has been shown before, the time-invariant structural properties of the Internet include some most basic ones, such as th...

There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow P (k) ∝ k−γ with γ ∈ (1, 2]. Models of growing networks have been successfully employed to produce scale-free networks using preferential attachment, however these...

Model calculations for the photon-dominated region S 140 are presented. The overall geometry and an inhomogeneous density distribution are incorporated and the chemical and thermal balance is solved in two and three dimensions. The observed widespread neutral carbon emission in the extended molecular cloud is investigated for a range in clump size and volume filling factor. It is found that the...

Over the last twenty years, dense linear algebra libraries have gone through three generations of public domain general purpose packages. In the seventies, the rst generation of packages were EISPACK and LINPACK, which implemented a broad spectrum of algorithms for solving dense linear eigenproblems and dense linear systems. In the late eighties, the second generation package called LAPACK was ...

The morphology and kinematics of molecular clouds (MCs) are best explained as the consequence of super–sonic turbulence. Super–sonic turbulence fragments MCs into dense sheets, filaments and cores and large low density “voids”, via the action of highly radiative shocks. We refer to this process as turbulent fragmentation. In this work we derive the mass distribution of dense cores due to turbul...

Solving a system of equations of the form Tx = y, where T is a sparse triangular matrix, is required after the factorization phase in the direct methods of solving systems of linear equations. A few parallel formulations have been proposed recently. The common belief in parallelizing this problem is that the parallel formulation utilizing a two dimensional distribution of T is unscalable. In th...