Quantale Modules and their Operators, with Applications

The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined. Such operators - that turn out to be precisely the homomorphisms between free objects in those categories - find concrete applications in two different branches of image processing, namely fuzzy image compression and mathematical morphology

Main clause external constituents and the derivation of subject-initial verb Second

This paper discusses V3-patterns with a sentence-initial adverbial clause in Standard Dutch (StD) and West-Flemish (WF), which appear to violate the V2 restriction which normally regulates word order in these languages. V3-patterns occur in both languages; they can be interpreted as complying with the V2 constraint provided they are analyzed as the result of merging a regular root clause with V2 order with an extra-sentential adverbial clause. The paper shows that the distribution of V3-patterns is slightly wider in WF than in StD: StD requires that the root clause which combines with the extra-sentential constituent either exhibits subject-verb inversion (XP-V-S) or, in the case of subject initial V2 clauses, that the subject has a distinguished information-structural status such as contrastive focus/topic; WF allows V3-structures more freely, regardless of whether they display subject-verb inversion and regardless of the informational-structural status of the subject. The analysis takes as its point of departure the earlier claim that V2-languages can be symmetric in the sense that the finite verb always leaves the TP domain and occupies the highest head position in the root clause, the complementizer position C in the traditional generative analysis, or asymmetric in the sense that the position of the finite verb varies in that it occupies the C-position when the root clause exhibits subject-verb inversion or a lower TP internal tense position (T) in root clauses without inversion. The hypothesis is that V3-patterns with a sentence-initial adverbial clause are only possible if the initial adverbial clause attains a local relation with the finite verb, and that this requires the finite verb to be in the (higher) C-position. By assuming that StD is an asymmetric V2-language while WF is a symmetric V2-language the variation with respect to the distribution of V3-patterns in these languages can be captured

On Cremona contractibility of unions of lines in the plane

We discuss the concept of Cremona contractible plane curves, with an historical account on the development of this subject. We then classify Cremona contractible unions of d > 11 lines in the plane.Comment: 14 pages; removed section 5 which contained an incomplete proof; accepted for publication on Kyoto Journal of Mathematic