ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

Eigenvalues of Casimir operators for gl(m/infinity)

A full set of Casimir operators for the Lie superalgebra gl(m/infinity) is constructed and shown to be well defined in the category O-FS generated by the highest-weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(m/infinity) are also determined.

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

On the loss of regularity for a class of weakly hyperbolic operators

In this paper we determine bounds for the optimal loss of regularity in the Sobolev scale for a class of weakly hyperbolic operators. (C) 2009 Elsevier Inc. All rights reserved.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Eigenvalue computations in the context of data-sparse approximations of integral operators

In this work, we consider the numerical solution of a large eigenvalue problem resulting from a finite rank discretization of an integral operator. We are interested in computing a few eigenpairs, with an iterative method, so a matrix representation that allows for fast matrix-vector products is required. Hierarchical matrices are appropriate for this setting, and also provide cheap LU decompositions required in the spectral transformation technique. We illustrate the use of freely available software tools to address the problem, in particular SLEPc for the eigensolvers and HLib for the construction of H-matrices. The numerical tests are performed using an astrophysics application. Results show the benefits of the data-sparse representation compared to standard storage schemes, in terms of computational cost as well as memory requirements.

Application of Gage R&R methodology for improving the training and evaluation of automatic optical inspection machine operators

The current level of demand by customers in the electronics industry requires the production of parts with an extremely high level of reliability and quality to ensure complete confidence on the end customer. Automatic Optical Inspection (AOI) machines have an important role in the monitoring and detection of errors during the manufacturing process for printed circuit boards. These machines present images of products with probable assembly mistakes to an operator and him decide whether the product has a real defect or if in turn this was an automated false detection. Operator training is an important aspect for obtaining a lower rate of evaluation failure by the operator and consequently a lower rate of actual defects that slip through to the following processes. The Gage R&R methodology for attributes is part of a Six Sigma strategy to examine the repeatability and reproducibility of an evaluation system, thus giving important feedback on the suitability of each operator in classifying defects. This methodology was already applied in several industry sectors and services at different processes, with excellent results in the evaluation of subjective parameters. An application for training operators of AOI machines was developed, in order to be able to check their fitness and improve future evaluation performance. This application will provide a better understanding of the specific training needs for each operator, and also to accompany the evolution of the training program for new components which in turn present additional new difficulties for the operator evaluation. The use of this application will contribute to reduce the number of defects misclassified by the operators that are passed on to the following steps in the productive process. This defect reduction will also contribute to the continuous improvement of the operator evaluation performance, which is seen as a quality management goal.

Using an ambient intelligent architecture for developing an intelligent tutoring system for training operators of power system control centres

This paper describes an architecture conceived to integrate Power Sys-tems tools in a Power System Control Centre, based on an Ambient Intelligent (AmI) paradigm. This architecture is an instantiation of the generic architecture proposed in [1] for developing systems that interact with AmI environments. This architecture has been proposed as a consequence of a methodology for the inclu-sion of Artificial Intelligence in AmI environments (ISyRAmI - Intelligent Sys-tems Research for Ambient Intelligence). The architecture presented in the paper will be able to integrate two applications in the control room of a power system transmission network. The first is SPARSE expert system, used to get diagnosis of incidents and to support power restoration. The second application is an Intelligent Tutoring System (ITS) incorporating two training tools. The first tutoring tool is used to train operators to get the diagnosis of incidents. The second one is another tutoring tool used to train operators to perform restoration procedures.

Combining artificial intelligence techniques for the training of power system control centre operators

Control Centre operators are essential to assure a good performance of Power Systems. Operators’ actions are critical in dealing with incidents, especially severe faults, like blackouts. In this paper we present an Intelligent Tutoring approach for training Portuguese Control Centre operators in incident analysis and diagnosis, and service restoration of Power Systems, offering context awareness and an easy integration in the working environment.

Testing native speakers of German and Portuguese on the understanding of topological operators-line-region relations in gvSIG

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Incremental Recomputation of Pig Latin’s Nest and Unnest Operators

This master’s thesis addresses the maintenance of pre-computed structures, which store a frequent or expensive query, for the nested bag data type in the high level work-flow language Pig Latin. This thesis defines a model suitable to accommodate incremental expressions over nested bags on Pig Latin. Afterwards, the partitioned normal form for sets is extended with further restrictions, in order to accommodate the nested bag model, allow the Pig Latin nest and unnest operators revert each other, and create a suitable environment to the incremental computations. Subsequently, the extended operators – extended union and extended difference – are defined for the nested bag data model with the partitioned normal form for bags (PNF Bag) restriction, and semantics for the extended operators are given. Finally, incremental data propagation expressions are proposed for the nest and unnest operators on the data model proposed with the PNF Bag restriction, and the proof of correctness is given.

Semigroup operators and applications

Dissertação de mestrado em Matemática