Let C be a smooth, connected, projective non-hyperelliptic curve of genus g ≥ 2 over the complex numbers and let Pic(C) be the connected component of its Picard variety parametrizing degree d line bundles, for d ∈ Z. The variety Pic(C) carries a naturally defined divisor, the Riemann theta divisor Θ, whose support consists of line bundles that have nonzero global sections. The Riemann singulari...

The image of the principal minor map for n×n-matrices is shown to be closed. In the 19th century, Nansen and Muir studied the implicitization problem of finding all relations among principal minors when n = 4. We complete their partial results by constructing explicit polynomials of degree 12 that scheme-theoretically define this affine variety and also its projective closure in P15. The latter...

The use of 3D laser scanner in documenting heritage sites has increased significantely over the past few years. This is maily due to advances of such systems which allow for the fast and reliable generation of millions of 3D points. Despite the considerable progress of these approaches, the highest possible degree in efficiency and flexibility of data collection will be possible, if other techn...

A new approach, the projective system approach, is proposed to realize modified projective synchronization between two different chaotic systems. By simple analysis of trajectories in the phase space, a projective system of the original chaotic systems is obtained to replace the errors system to judge the occurrence of modified projective synchronization. Theoretical analysis and numerical simu...

We characterize semiperfect modules, semiperfect rings, and perfect rings using locally projective covers and generalized locally projective covers, where locally projective modules were introduced by Zimmermann-Huisgen and generalized locally projective coves are adapted from Azumaya’s generalized projective covers.

In this paper, embeddings φ : M → P from a linear space (M,M) in a projective space (P,L) are studied. We give examples for dimM > dimP and show under which conditions equality holds. More precisely, we introduce properties (G) (for a line L ∈ L and for a plane E ⊂ M it holds that |L ∩ φ(M)| 6 = 1) and (E) (φ(E) = φ(E) ∩ φ(M), whereby φ(E) denotes the by φ(E) generated subspace of P ). If (G) a...

27 Using projective and objective measures, effects of rock music on emotion were investigated. Sixty students were randomly assigned to three conditions: hard rock, soft rock, and no music. One group listened to hard rock music while taking a projective test with five ink blots and an objective test with an Emotional Assessment Scale (EAS). The same procedure was used for the second group whil...

Menu systems are a standard interface technique in 2D desktop systems. Using menu systems in virtual reality systems however, is often problematic. In this paper, we present five techniques for menu selection in a 3D desktop virtual reality system: a 3D ray-casting technique, two projective techniques, one technique based on 3D positioning, and one technique based on the standard 2D desktop mou...

Art therapy has been applied in a variety of settings and with a large number of different client groups. It has been used for aesthetic, educational and clinical reasons. One of the main applications in the past has been to measure intelligence. However, the test-retest reliability was found to be poor. For example, intelligence or projective tests in clinical psychology, like the 'Rorschach i...

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