Partially isometric dilations of noncommuting -tuples of operators

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold decomposition for partial isometries to describe the models for these dilations, and we discuss how the basic properties of a dilation depend on the row contraction.

     

Managing logical channel configurations in complex satellite architectures

As a result of the increased switching complexity of many communications satellites, often transponders are available with a variety of configuration options offering flexibility in power, bandwidth, and coverage. Many of these configurations share resources that prevent them from being simultaneously active, making it a challenge to understand and manage the satellite capacity inventory. In this paper we define the logical channel configuration (LCC) as an unambiguous unit of the inventory and present a novel method of modelling the interdependencies between these LCCs using linear algebra. In particular, a projector matrix is defined which can be used to update the activation state of all LCCs when the state of one or more of these is changed. As a result, a number of valid LCC scenarios can be easily generated and evaluated for optimal use of the satellite resources. Copyright © 2005 John Wiley & Sons, Ltd.     

Preparation of novel analgesics via diastereoselective nucleophilic addition to 1-dimethylamino-2-methylpentan-3-one

The diastereoselective synthesis of naphthyl amino alcohols via nucleophilic addition to racemic 1-dimethylamino-2-methylpentan-3-one was studied. The use of the appropriate experimental conditions allowed the synthesis of both diastereoisomers. The relative configurations were established via NOESY experiments.     

Stable Ergodicity and Frame Flows

In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to –1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher.     

Experimental Research on Erbium-doped Superfluorescent Fiber Source

The effects of the variations in fiber length, fiber mirror reflectance on efficiency and output power are experimentally investigated for erbium-doped double pass backward superfluorescent fiber sources (SFSs). The influence of fiber length on mean wavelength stability (MWS) has also been demonstrated. By incorporating a short section of un-pumped erbium-doped fiber (EDF) at the output port, the pump power dependent on MWS becomes independent of pumped EDF length. This is a novel phenomenon that hasn‘t been reported up to now,and should be helpful to SFS fabrication and theory analysis. By using a fiber Michelson interferometer as spectrum slicing component,a multi-wavelength fiber source (MWFS) with ～20 channels (from 1542nm to 1559nm) is got. The MWFS has a channel spacing of ～0. 8 nm which satisfies ITUstandard. The intensity fluctuation among channels is less than 0.5dB,and the extinction ratio of all channels is above 14dB. This kind of MWFS should be useful to wavelength division multiplexing systems.     

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hausdorff dimension of a random invariant set

The notion of random attractor for a dissipative stochastic dynamical system has recently been introduced. It generalizes the concept of global attractor in the deterministic theory. It has been shown that many stochastic dynamical systems associated to a dissipative partial differential equation perturbed by noise do possess a random attractor. In this paper, we prove that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor can be estimated by using global Lyapunov exponents. The result is obtained under very natural assumptions. As an application, we consider a stochastic reaction-diffusion equation and show that its random attractor has finite Hausdorff dimension.     

Impact of Partial Separability on Large-Scale Optimization

ELSO is an environment for the solution oflarge-scale optimization problems. With ELSO the user is required to provide only code for the evaluation of a partially separable function. ELSO exploits the partialseparability structure of the function to computethe gradient efficiently using automatic differentiation.We demonstrate ELSO's efficiency by comparing thevarious options available in ELSO.Our conclusion is that the hybrid option in ELSOprovides performance comparable to the hand-coded option, while having the significantadvantage of not requiring a hand-coded gradient orthe sparsity pattern of the partially separable function.In our test problems, which have carefully coded gradients,the computing time for the hybrid AD option is within a factor of two of thehand-coded option.     

Concerning the multiplicators of Fourier series in the trigonometric system

In this paper we prove theorems on multiplicators of Fourier series inL _p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998.