Fibrés Vectoriels Semi-Stables sur une Courbe de Genre Deux et Association des Points dans L’espace Projectif

2000 Mathematics Subject Classification: 14D20, 14J60.

Géométrie de direction. Application des coordonnées polyédriques. Propriété de dix points de l'ellipsoïde, de neuf points d'une courbe gauche du quatrième ordre, de huit points d'une cubique gauche.

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Analysis of exploratory eye movements in patients with schizophrenia during visual scanning of projective tests' figures

OBJECTIVE: Compare pattern of exploratory eye movements during visual scanning of the Rorschach and TAT test cards in people with schizophrenia and controls. METHOD: 10 participants with schizophrenia and 10 controls matched by age, schooling and intellectual level participated in the study. Severity of symptoms was evaluated with the Positive and Negative Syndrome Scale. Test cards were divided into three groups: TAT cards with scenes content, TAT cards with interaction content (TAT-faces), and Rorschach cards with abstract images. Eye movements were analyzed for: total number, duration and location of fixation; and length of saccadic movements. RESULTS: Different pattern of eye movement was found, with schizophrenia participants showing lower number of fixations but longer fixation duration in Rorschach cards and TAT-faces. The biggest difference was observed in Rorschach, followed by TAT-faces and TAT-scene cards. CONCLUSIONS: Results suggest alteration in visual exploration mechanisms possibly related to integration of abstract visual information.

Difference sets from projective planes

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

In search of mathematical primitives for deriving universal projective hash families

We provide some guidelines for deriving new projective hash families of cryptographic interest. Our main building blocks are so called group action systems; we explore what properties of this mathematical primitives may lead to the construction of cryptographically useful projective hash families. We point out different directions towards new constructions, deviating from known proposals arising from Cramer and Shoup's seminal work.

Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

"Vegeu el resum a l'inici del document del fitxer adjunt."

Projective modules over the Gerasimov-Sakhaev counterexample

We investigate the structure of the so-called Gerasimov- Sakhaev counterexample, which is a particular example of a universal localization, and classify (both finitely and infinitely generated) projective modules over it.

Counting polygon dissections in the projective plane

"Vegeu el resum a l'inici del document del fitxer adjunt."

Rigid flat webs on the projective plane

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.