∗Note The theorems in sections 5.1 and 5.2 each have two versions, one stated in terms of linear operators, one in terms of matrices. The book states most of them in terms of linear operators, whilst in the lecture notes, they are mostly stated in terms of matrices. For example, compare Theorem 5.5 and its corollary in the book with Theorem 5 and its corollary in the lecture notes; also compare...

In this paper, by using the geometric construction of linear blocking sets as projections of canonical subgeometries, we determine all the GF (q)linear blocking sets of the plane PG(2, q).

The groups of high dimensional knots have been characterized by Kervaire [7], but there is still no general description of all 2-knot groups. Kervaire identified a large class of groups that are natural candidates to serve as 2-knot groups and proved that each of these groups is the group of the complement of a smooth 2-sphere in a homotopy 4-sphere. Freedman’s solution to the 4-dimensional Poi...

The goal of this homework assignment was to use linear regression to predict users’ ratings of books sold on Amazon.com. To construct the feature matrix, we tokenized the written review texts in several different ways: With and without stemming, as well as using either single words as tokens or bigrams. The dependent variable is a star rating given by reviewers, ranging from 1 star (very unsati...

University of Caifornia/Davis 93.

IMAGE ENHANCEMENT V. Pahor, G. Ramponi, G.L. Sicuranza D.E.E.I., University of Trieste via A. Valerio, 10, 34127 Trieste, Italy Tel: +39 40 6767140; fax: +39 40 6763460 e-mail: [email protected] ABSTRACT A two-dimensional adaptive nonlinear lter, called 2{ D FIR{PWL lter is introduced for noise cancellation from images. It is based on the cascade of a linear FIR lter and a piecewise...

holds for all open sets U ⊆ Σ in a sufficiently small neighbourhood of the origin. We have already seen that (1) holds for non-trivial values of p only if the family Xπ of associated vector fields satisfies the Hörmander condition. A deeper fact is that the converse of this statement is true. This converse may be expressed in a very precise fashion which relates the range of Lebesgue exponents ...

If φ is an analytic function mapping the unit disk D into itself, the composition operator Cφ is the operator on H 2 given by Cφf = f ◦φ. The structure of the composition operator Cφ is usually complex, even if the function φ is fairly simple. In this paper, we consider composition operators whose symbol φ is a linear fractional transformation mapping the disk into itself. That is, we will assu...