Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Geometry and kinematics of the Roisan-Cignana Shear Zone, and the orogenic evolution of the Dent Blanche Tectonic System (Western Alps)

The Dent Blanche Tectonic System (DBTS) is a composite thrust sheet derived from the previously thinned passive Adriatic continental margin. A kilometric high-strain zone, the Roisan-Cignana Shear Zone (RCSZ) defines the major tectonic boundary within the DBTS and separates it into two subunits, the Dent Blanche s.s. nappe to the northwest and the Mont Mary nappe to the southeast. Within this shear zone, tectonic slices of Mesozoic and pre-Alpine meta-sediments became amalgamated with continental basement rocks of the Adriatic margin. The occurrence of high pressure assemblages along the contact between these tectonic slices indicates that the amalgamation occurred prior to or during the subduction process, at an early stage of the Alpine orogenic cycle. Detailed mapping, petrographic and structural analysis show that the Roisan-Cignana Shear Zone results from several superimposed Alpine structural and metamorphic stages. Subduction of the continental fragments is recorded by blueschist-facies deformation, whereas the Alpine collision is reflected by a greenschist facies overprint associated with the development of large-scale open folds. The postnappe evolution comprises the development of low-angle brittle faults, followed by large-scale folding (Vanzone phase) and finally brittle extensional faults. The RCSZ shows that fragments of continental crust had been torn off the passive continental margin prior to continental collision, thus recording the entire history of the orogenic cycle. The role of preceding Permo-Triassic lithospheric thinning, Jurassic rifting, and ablative subduction processes in controlling the removal of crustal fragments from the reactivated passive continental margin is discussed. Results of this study constrain the temporal sequence of the tectono-metamorphic processes involved in the assembly of the DBTS, but they also show limits on the interpretation. In particular it remains difficult to judge to what extent precollisional rifting at the Adriatic continental margin preconditioned the efficiency of convergent processes, i.e. accretion, subduction, and orogenic exhumation.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

SrGAP2-Dependent Integration of Membrane Geometry and Slit-Robo-Repulsive Cues Regulates Fibroblast Contact Inhibition of Locomotion

Migrating fibroblasts undergo contact inhibition of locomotion (CIL), a process that was discovered five decades ago and still is not fully understood at the molecular level. We identify the Slit2-Robo4-srGAP2 signaling network as a key regulator of CIL in fibroblasts. CIL involves highly dynamic contact protrusions with a specialized actin cytoskeleton that stochastically explore cell-cell overlaps between colliding fibroblasts. A membrane curvature-sensing F-BAR domain pre-localizes srGAP2 to protruding edges and terminates their extension phase in response to cell collision. A FRET-based biosensor reveals that Rac1 activity is focused in a band at the tip of contact protrusions, in contrast to the broad activation gradient in contact-free protrusions. SrGAP2 specifically controls the duration of Rac1 activity in contact protrusions, but not in contact-free protrusions. We propose that srGAP2 integrates cell edge curvature and Slit-Robo-mediated repulsive cues to fine-tune Rac1 activation dynamics in contact protrusions to spatiotemporally coordinate CIL.

Effects of Strand Geometry on Selected Properties of Long-Stand Structural Composite Lumber Made from Northeastern Hardwoods

Structural composite lumber (SCL) products often possess significantly higher design values than the top grades of solid lumber, making it a popular choice for both residential and commercial applications. The enhanced mechanical properties of SCL are mainly due to defect randomization and densification of the wood fiber, both largely functions of the size, shape and composition (species) of the wood element. Traditionally, SCL manufacturers have used thin, rectangular elements produced from either moderate density softwoods or low density hardwoods. Higher density hardwood species have been avoided, as they require higher pressures to adequately densify and consolidate the wood furnish. These higher pressures can lead to increased manufacturing costs, damage to the wood fiber and/or a product that is too dense, making it heavy and unreceptive to common mechanical fastening techniques. In the northeastern United States high density, diffuse-porous hardwoods (such as maple, beech and birch) are abundant. Use of these species as primary furnish for a SCL product may allow for a competitive advantage in terms of resource cost against products that rely on veneer grade logs. Proximity to this abundant and relatively inexpensive resource may facilitate entry of SCL production facilities in the northeastern United States, where currently none exist. However, modifications to current strand sizes, geometries or production techniques will likely be required to allow for use of these species. A new SCL product concept has been invented allowing for use of these high density hardwoods. The product, referred to as long-strand structural composite lumber (LSSCL), uses strands of significantly larger cross sectional areas and volumes than existing SCL products. In spite of the large strand size, satisfactory consolidation is achieved without excessive densification of the wood fiber through use of a symmetrical strand geometric cross-section. LSSCL density is similar to that of existing SCL products, but is due mainly to the inherent density of the species, rather than through densification. An experiment was designed and conducted producing LSSCL from both large (7/16”) and small (1/4”) strands, of both square and triangular geometric cross sections. Testing results indicate that the large, triangular strands produce LSSCL beams with projected design values of: Modulus of elasticity (MOEapp) – 1,750,000 psi; Allowable bending stress (Fb) – 2750 psi; Allowable shear stress (Fv) – 260 psi. Several modifications are recommended which may lead to improvement of these values, likely allowing for competition against existing SCL products.

Pseudo-Juden und zweifelhafte Autoren

Moritz Steinschneider

Geist des Jeruschalmi (Pseudo-Jonathan)

Seligman Bär

Die Abfassungszeit des Pseudo-Aristeas

Heinrich Graetz

Die Abfassungszeit des Pseudo-Aristeas

Heinrich Graetz

Der Pseudo-Messias im 14. Jahrhundert

Heinrich Graetz

Pseudo-Kimchi (Müller) [Nachricht] : (zu S. 384)

Moritz Steinschneider

Pseudo-Saadja's und Elasar Rokeach's Commentare zum Jezira-Buche. Die Recension Saadja's

Abraham Epstein

Pseudo-Saadja's und Elasar Rokeach's Commentare zum Jezira-Buche. Die Recension Saadja's

Abraham Epstein