14,345 research outputs found
Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]
Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so
contains a \textit{universal -matrix} in the tensor product algebra which
satisfies the Yang-Baxter equation. Applying the vector representation ,
which acts on the vector module , to one side of a universal -matrix
gives a Lax operator. In this paper a Lax operator is constructed for the
-type quantum superalgebras . This can in turn be used to
find a solution to the Yang-Baxter equation acting on
where is an arbitrary module. The case is included
here as an example.Comment: 15 page
Using constraint preconditioners with regularized saddle-point problems
The problem of finding good preconditioners for the numerical solution of a certain important class of indefinite linear systems is considered. These systems are of a 2 by 2 block (KKT) structure in which the (2,2) block (denoted by -C) is assumed to be nonzero. In Constraint preconditioning for indefinite linear systems , SIAM J. Matrix Anal. Appl., 21 (2000), Keller, Gould and Wathen introduced the idea of using constraint preconditioners that have a specific 2 by 2 block structure for the case of C being zero. We shall give results concerning the spectrum and form of the eigenvectors when a preconditioner of the form considered by Keller, Gould and Wathen is used but the system we wish to solve may have C \neq 0 . In particular, the results presented here indicate clustering of eigenvalues and, hence, faster convergence of Krylov subspace iterative methods when the entries of C are small; such situations arise naturally in interior point methods for optimization and we present results for such problems which validate our conclusions.\ud
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The first author's work was supported by the OUCL Doctorial Training Accoun
On implicit-factorization constraint preconditioners
Recently Dollar and Wathen [14] proposed a class of incomplete factorizations for saddle-point problems, based upon earlier work by Schilders [40]. In this paper, we generalize this class of preconditioners, and examine the spectral implications of our approach. Numerical tests indicate the efficacy of our preconditioners
Alternative criterion for two-dimensional wrapping percolation
Based on the differences between a spanning cluster and a wrapping cluster,
an alternative criterion for testing wrapping percolation is provided for
two-dimensional lattices. By following the Newman-Ziff method, the finite size
scaling of estimates for percolation thresholds are given. The results are
consistent with those from Machta's method.Comment: 4 pages, 2 figure
A dc to dc converter
The object of the invention is to provide an improved converter for converting one direct current voltage to another. A plurality of phased square wave voltages are provided from a ring counter through amplifiers to a like plurality of output transformers. Each of these transformers has two windings, and S(1) winding and an S(2) winding. The S(1) windings are connected in series, then the S(2) windings are connected in series, and finally, the two sets of windings are connected in series. One of six SCRs is connected between each two series connected windings to a positive output terminal and one of diodes is connected between each set of two windings of a zero output terminal. By virtue of this configuration, a quite high average direct current voltage is obtained, which varies between full voltage and two-thirds full voltage rather than from full voltage to zero. Further, its variation, ripple frequency, is reduced to one-sixth of that present in a single phase system. Application to raising battery voltage for an ion propulsion system is mentioned
A Bramble-Pasciak-like method with applications in optimization
Saddle-point systems arise in many applications areas, in fact in any situation where an extremum principle arises with constraints. The Stokes problem describing slow viscous flow of an incompressible fluid is a classic example coming from partial differential equations and in the area of Optimization such problems are ubiquitous.\ud
In this manuscript we show how new approaches for the solution of saddle-point systems arising in Optimization can be derived from the Bramble-Pasciak Conjugate Gradient approach widely used in PDEs and more recent generalizations thereof. In particular we derive a class of new solution methods based on the use of Preconditioned Conjugate Gradients in non-standard inner products and demonstrate how these can be understood through more standard machinery. We show connections to Constraint Preconditioning and give the results of numerical computations on a number of standard Optimization test examples
Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras
The Perk--Schultz model may be expressed in terms of the solution of the
Yang--Baxter equation associated with the fundamental representation of the
untwisted affine extension of the general linear quantum superalgebra
, with a multiparametric co-product action as given by
Reshetikhin. Here we present analogous explicit expressions for solutions of
the Yang-Baxter equation associated with the fundamental representations of the
twisted and untwisted affine extensions of the orthosymplectic quantum
superalgebras . In this manner we obtain generalisations of the
Perk--Schultz model.Comment: 10 pages, 2 figure
Statistics of Cosmological Black Hole Jet Sources: Blazar Predictions for GLAST
A study of the statistics of cosmological black-hole jet sources is applied
to EGRET blazar data, and predictions are made for GLAST. Black-hole jet
sources are modeled as collimated relativistic plasma outflows with radiation
beamed along the jet axis due to strong Doppler boosting. The comoving rate
density of blazar flares is assumed to follow a blazar formation rate (BFR),
modeled by analytic functions based on astronomical observations and fits to
EGRET data. The redshift and size distributions of gamma-ray blazars observed
with EGRET, separated into BL Lac object (BL) and flat spectrum radio quasar
(FSRQ) distributions, are fit with monoparametric functions for the
distributions of the jet Lorentz factor \Gamma, comoving directional power
l'_e, and spectral slope. A BFR factor ~10 x greater at z ~ 1 than at present
is found to fit the FSRQ data. A smaller comoving rate density and greater
luminosity of BL flares at early times compared to the present epoch fits the
BL data. Based on the EGRET observations, ~1000 blazars consisting of ~800
FSRQs and FR2 radio galaxies and ~200 BL Lacs and FR1 radio galaxies will be
detected with GLAST during the first year of the mission. Additional AGN
classes, such as hard-spectrum BL Lacs that were mostly missed with EGRET,
could add more GLAST sources. The FSRQ and BL contributions to the EGRET
gamma-ray background at 1 GeV are estimated at the level of ~10 - 15% and ~2 -
4%, respectively. EGRET and GLAST sensitivities to blazar flares are considered
in the optimal case, and a GLAST analysis method for blazar detection is
outlined.Comment: 17 pages, 9 figures, ApJ, in press, v.660, May 1, 2007 (minor changes
from previous version
Punctuated Equilibrium in Software Evolution
The approach based on paradigm of self-organized criticality proposed for
experimental investigation and theoretical modelling of software evolution. The
dynamics of modifications studied for three free, open source programs Mozilla,
Free-BSD and Emacs using the data from version control systems. Scaling laws
typical for the self-organization criticality found. The model of software
evolution presenting the natural selection principle is proposed. The results
of numerical and analytical investigation of the model are presented. They are
in a good agreement with the data collected for the real-world software.Comment: 4 pages, LaTeX, 2 Postscript figure
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