S-Structures for k-linear categories and the definition of a modular functor

Motivated by ideas from string theory and quantum field theory new invariants of knots and 3-dimensional manifolds have been constructed from complex algebraic structures such as Hopf algebras (Reshetikhin and Turaev), monoidal categories with additional structure (Turaev and Yetter), and modular functors (Walker and Kontsevich). These constructions are very closely related. We take a unifying categorical approach based on a natural 2-dimensional generalization of a topological field theory in the sense of Atiyah and Segal, and show that the axioms defining these complex algebraic structures are a consequence of the underlying geometry of surfaces. In particular, we show that any linear category over a field with an action of the surface category is semi-simple and Artinian.Comment: Accepted for publication in the Journal of the LMS, April 199

Divisible convex sets with properly embedded cones

In this article we construct many examples of properly convex irreducible domains divided by Zariski dense relatively hyperbolic groups in every dimension at least 3. This answers a question of Benoist. Relative hyperbolicity and non-strict convexity are captured by a family of properly embedded cones (convex hulls of points and ellipsoids) in the domain. Our construction is most flexible in dimension 3 where we give a purely topological criterion for the existence of a large deformation space of geometrically controlled convex projective structures with totally geodesic boundary on a compact 3-manifold.Comment: 90 pages. Comments are welcome

REINFORCED CONCRETE AND STONE STRUCTURES

The textbook provides main information about construction materials (concrete, reinforced concrete, stone), their physical and mechanical properties, analysis of reinforced concrete and stone structures for strength, rigidity and crack resistance

REINFORCED CONCRETE AND STONE STRUCTURES

У підручнику розглянуто загальні відомості про матеріали (бетон, арма- турну сталь, камінь) та їхні фізико-механічні властивості; основи розрахунку залізобетонних та кам’яних конструкцій за міцністю, жорсткістю, тріщино- стійкістю і способи їх конструювання. Для студентів вищих навчальних закладів авіаційного та будівельного профілю, а також спеціалістів, магістрів з проектування, будівництва аеро- портів, промислового та цивільного будівництва.The textbook provides main information about construction materials (concrete, reinforced concrete, stone), their physical and mechanical properties, resistance calculation of reinforced concrete and stone structures for strength, rigidity and crack endurance

A Geometrical Construction of Rational Boundary States in Linear Sigma Models

Starting from the geometrical construction of special Lagrangian submanifolds of a toric variety, we identify a certain subclass of A-type D-branes in the linear sigma model for a Calabi-Yau manifold and its mirror with the A- and B-type Recknagel-Schomerus boundary states of the Gepner model, by reproducing topological properties such as their labeling, intersection, and the relationships that exist in the homology lattice of the D-branes. In the non-linear sigma model phase these special Lagrangians reproduce an old construction of 3-cycles relevant for computing periods of the Calabi-Yau, and provide insight into other results in the literature on special Lagrangian submanifolds on compact Calabi-Yau manifolds. The geometrical construction of rational boundary states suggests several ways in which new Gepner model boundary states may be constructed.Comment: 45 pages, 8 Postscript figures, LaTeX2e. v2: the construction reproduces a larger set of CFT boundary states; clarified discussion of instanton contributions and moduli; other minor improvements; references added . v3: version accepted for publication in Nuclear Physics B (minor changes

In-situ deformation monitoring of aerospace qualified composites with embedded improved draw tower fibre Bragg gratings

Aerospace certified fibre reinforced plastics (FRPs) are extreme performing construction materials, which today are increasingly applied in primary structures of the new generation aircrafts (e.g. Boeing 787, Airbus 350, Bombardier C-Series), such as the fuselage, the wings and the fin. An interesting aspect on the technological point of view of sensing is that airplane manufacturers such as Airbus and Boeing are looking at incorporating health-monitoring systems (such as optical fibre sensors, especially fibre Bragg gratings) that will allow the airplane to self-monitor and report maintenance requirements to ground-based computer systems. However, one has to realize that the mechanical behaviour of anisotropic FRPs is significantly different compared to conventional isotropic construction materials. In this dissertation, the author focuses on monitoring the strain and (permanent) deformation in carbon reinforced plastic laminates with embedded fibre Bragg gratings. The research is divided in two main parts. In the first part of this research, the existing fibre draw tower technology is utilized, to manufacture an improved version of the existing in-line high quality, draw tower fibre Bragg gratings (DTG®s). With respect to accurate measurements and structural integrity, the research focuses on reducing the total diameter of the optical fibre, so the incorporation in the reinforcement fibres is enhanced and the distortion in the composite is reduced. The author elaborates in detail the methods of strain and temperature calibrations and the different setups which are applied. Additionally, with respect to the high temperatures during the composite manufacturing process, the thermal stability of the DTG®s is studied at elevated temperatures (>300°C). In the second part, the author embeds the DTG®s in specific types of thermoset and thermoplastic carbon reinforced plastic laminates. The author applies the embedded DTG®s in several stages of the composite lifetime. Starting with the monitoring of the composite manufacturing process and ending with fatigue testing until failure of the composite laminates. During the different experiments, the sensors are subjected to high temperatures, high pressures, extreme longitudinal strains and transverse strains and in the mean time, they are employed to very accurately measure (multi-axial) strains inside composites at microstrain level (~10 6)