New results and open problems on Toeplitz operators in Bergman spaces

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems -- concerning boundedness, compactness and Fredholm properties -- which was presented at the conference "Recent Advances in Function Related Operator Theory'' in Puerto Rico in March 2010.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.

Necessary conditions of optimality for vector-valued impulsive control problems

A vector-valued impulsive control problem is considered whose dynamics, defined by a differential inclusion, are such that the vector fields associated with the singular term do not satisfy the so-called Frobenius condition. A concept of robust solution based on a new reparametrization procedure is adopted in order to derive necessary conditions of optimality. These conditions are obtained by taking a limit of those for an appropriate sequence of auxiliary standard optimal control problems approximating the original one. An example to illustrate the nature of the new optimality conditions is provided. © 2000 Elsevier Science B.V. All rights reserved.

DOCPAL at nineteenth months: an outline of activities, problems and promises (with a complete set of flow diagrams, worksheets, forms, etc)

Includes bibliography

Enhancing skills in solving open-ended problems using game-based exercises

Some requirements for engineering programmes, such as an ability to use the techniques, skills and modern engineering tools necessary for engineering practice, as well as an understanding of professional and ethical responsibility or an ability to communicate effectively, need new activities designed for measuring students’ progress. Negotiations take place continuously at any stage of a project and, so, the ability of engineers and managers to effectively carry out a negotiation is crucial for the success or failure of projects and businesses. Since it involves communication between individuals motivated to come together in an agreement for mutual benefit, it can be used to enhance these personal abilities. The main objective of this study was to evaluate the adequacy of mixing playing sessions and theory to maximise the students’ strategic vision in combination with negotiating skills. Results show that the combination of playing with theoretical training teaches students to strategise through analysis and discussion of alternatives. The outcome is then more optimised.

Knowledge-based analysis of microarray gene expression data by using support vector machines

We introduce a method of functionally classifying genes by using gene expression data from DNA microarray hybridization experiments. The method is based on the theory of support vector machines (SVMs). SVMs are considered a supervised computer learning method because they exploit prior knowledge of gene function to identify unknown genes of similar function from expression data. SVMs avoid several problems associated with unsupervised clustering methods, such as hierarchical clustering and self-organizing maps. SVMs have many mathematical features that make them attractive for gene expression analysis, including their flexibility in choosing a similarity function, sparseness of solution when dealing with large data sets, the ability to handle large feature spaces, and the ability to identify outliers. We test several SVMs that use different similarity metrics, as well as some other supervised learning methods, and find that the SVMs best identify sets of genes with a common function using expression data. Finally, we use SVMs to predict functional roles for uncharacterized yeast ORFs based on their expression data.

The major range problems and their solution, résumé of a report prepared in response to Senate resolution 29, together with letters of transmittal, table of contents, etc., from "The western range,a great but neglected natural resource,"

Mode of access: Internet.

Arbor day manual : an aid in preparing programs for Arbor day exercises ; containing choice selections on trees, forests, flowers, and kindred subjects ; Arbor day music, specimen programs, etc. /

Mode of access: Internet.

Prevention and control of vector problems.

Mode of access: Internet.

A biochemic basis for the study of problems of taxonomy, heredity, evolution, etc., with especial reference to the starches and tissues of parent-stocks and hybrid-stocks and the starches and hemoglobins of varieties, species, and genera.

Mode of access: Internet.

The first six books of the Elements of Euclid, and propositions I.-XXI. of book XI., and an appendix on the cylinder, sphere, cone, etc., with copious annotations and numerous exercises,

Available on demand as hard copy or computer file from Cornell University.

Problems and exercises in accounting,

Mode of access: Internet.