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Reliability modeling of a 1-out-of-2 system: Research with diverse Off-the-shelf SQL database servers
Fault tolerance via design diversity is often the only viable way of achieving sufficient dependability levels when using off-the-shelf components. We have reported previously on studies with bug reports of four open-source and commercial off-the-shelf database servers and later release of two of them. The results were very promising for designers of fault-tolerant solutions that wish to employ diverse servers: very few bugs caused failures in more than one server and none caused failure in more than two. In this paper we offer details of two approaches we have studied to construct reliability growth models for a 1-out-of-2 fault-tolerant server which utilize the bug reports. The models presented are of practical significance to system designers wishing to employ diversity with off-the-shelf components since often the bug reports are the only direct dependability evidence available to them
Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)
A Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor
representations of the Lie superalgebra gl(m|n). Explicit expressions for the
generators of the Lie superalgebra acting on this basis are determined.
Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of
any covariant tensor representation of gl(m|n) with the natural representation
V ([1,0,...,0]) of gl(m|n) with highest weight (1,0,. . . ,0) are computed.
Both results are steps for the explicit construction of the parastatistics Fock
space.Comment: 16 page
Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)
The goal of this paper is to give an explicit construction of the Fock spaces
of the parafermion and the paraboson algebra, for an infinite set of
generators. This is equivalent to constructing certain unitary irreducible
lowest weight representations of the (infinite rank) Lie algebra so(\infty) and
of the Lie superalgebra osp(1|\infty). A complete solution to the problem is
presented, in which the Fock spaces have basis vectors labelled by certain
infinite but stable Gelfand-Zetlin patterns, and the transformation of the
basis is given explicitly. We also present expressions for the character of the
Fock space representations
Hopf algebras and characters of classical groups
Schur functions provide an integral basis of the ring of symmetric functions.
It is shown that this ring has a natural Hopf algebra structure by identifying
the appropriate product, coproduct, unit, counit and antipode, and their
properties. Characters of covariant tensor irreducible representations of the
classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur
functions, and the Hopf algebra is exploited in the determination of
group-subgroup branching rules and the decomposition of tensor products. The
analysis is carried out in terms of n-independent universal characters. The
corresponding rings, CharGL, CharO and CharSp, of universal characters each
have their own natural Hopf algebra structure. The appropriate product,
coproduct, unit, counit and antipode are identified in each case.Comment: 9 pages. Uses jpconf.cls and jpconf11.clo. Presented by RCK at
SSPCM'07, Myczkowce, Poland, Sept 200
Integrity bases for local invariants of composite quantum systems
Unitary group branchings appropriate to the calculation of local invariants
of density matrices of composite quantum systems are formulated using the
method of -function plethysms. From this, the generating function for the
number of invariants at each degree in the density matrix can be computed. For
the case of two two-level systems the generating function is . Factorisation of such series leads
in principle to the identification of an integrity basis of algebraically
independent invariants. This note replaces Appendix B of our paper\cite{us} J
Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in
corrected and conclusions modified accordingl
Angular momentum decomposition of the three-dimensional Wigner harmonic oscillator
In the Wigner framework, one abandons the assumption that the usual canonical
commutation relations are necessarily valid. Instead, the compatibility of
Hamilton's equations and the Heisenberg equations are the starting point, and
no further assumptions are made about how the position and momentum operators
commute. Wigner quantization leads to new classes of solutions, and
representations of Lie superalgebras are needed to describe them. For the
n-dimensional Wigner harmonic oscillator, solutions are known in terms of the
Lie superalgebras osp(1|2n) and gl(1|n). For n=3N, the question arises as to
how the angular momentum decomposition of representations of these Lie
superalgebras is computed. We construct generating functions for the angular
momentum decomposition of specific series of representations of osp(1|6N) and
gl(1|3N), with N=1 and N=2. This problem can be completely solved for N=1.
However, for N=2 only some classes of representations allow executable
computation
Pinning and depinning of a classic quasi-one-dimensional Wigner crystal in the presence of a constriction
We studied the dynamics of a quasi-one-dimensional chain-like system of
charged particles at low temperature, interacting through a screened Coulomb
potential in the presence of a local constriction. The response of the system
when an external electric field is applied was investigated. We performed
Langevin molecular dynamics simulations for different values of the driving
force and for different temperatures. We found that the friction together with
the constriction pins the particles up to a critical value of the driving
force. The system can depin \emph{elastically} or \emph{quasi-elastically}
depending on the strength of the constriction. The elastic (quasi-elastic)
depinning is characterized by a critical exponent
(). The dc conductivity is zero in the pinned regime, it has
non-ohmic characteristics after the activation of the motion and then it is
constant. Furthermore, the dependence of the conductivity with temperature and
strength of the constriction was investigated in detail. We found interesting
differences between the single and the multi-chain regimes as the temperature
is increased.Comment: 18 pages, 16 figures, accepted for publication in PR
Normal Form and Nekhoroshev stability for nearly-integrable Hamiltonian systems with unconditionally slow aperiodic time dependence
The aim of this paper is to extend the results of Giorgilli and Zehnder for
aperiodic time dependent systems to a case of general nearly-integrable convex
analytic Hamiltonians. The existence of a normal form and then a stability
result are shown in the case of a slow aperiodic time dependence that, under
some smallness conditions, is independent on the size of the perturbation.Comment: Corrected typo in the title and statement of Lemma 3.
Correlated singlet phase in the one-dimensional Hubbard-Holstein model
We show that a nearest-neighbor singlet phase results (from an effective
Hamiltonian) for the one-dimensional Hubbard-Holstein model in the regime of
strong electron-electron and electron-phonon interactions and under
non-adiabatic conditions (). By mapping the system of
nearest-neighbor singlets at a filling onto a hard-core-boson (HCB)
- model at a filling , we demonstrate explicitly that
superfluidity and charge-density-wave (CDW) occur mutually exclusively with the
diagonal long range order manifesting itself only at one-third filling.
Furthermore, we also show that the Bose-Einstein condensate (BEC) occupation
number for the singlet phase, similar to the for a HCB tight
binding model, scales as ; however, the coefficient of in
the for the interacting singlet phase is numerically demonstrated to be
smaller.Comment: Corrected a few reference
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