A hypergraph H = (V,E) is called (1, k)-sparse, for some integer k, if each subset X ⊆ V with |X| ≥ k spans at most |X| − k hyperedges. If we also have |E| = |V | − k then H is (1, k)-tight. Hypergraphs of this kind occur in several problems of combinatorial rigidity, where the goal is to analyse the generic rigidity properties of point sets equipped with geometric constraints involving subsets...

In this paper we establish a rigid connection between two classical objects: the R.Thompson group (the group of all piece-wise linear homeomorphisms of the unit interval with finitely many dyadic break points and all slopes powers of 2) and the Dunce hat (the topological space obtained from the triangle ABC by gluing AB, BC and AC). We prove that a diagram group of a directed 2-complex contains...

High-K isomer decay rates are compared and interpreted, with an emphasis on the spin degree of freedom. It is argued that high-K values do not in themselves lead to K mixing. Rather, evidence is presented that the most important consideration is the isomer energy relative to a rotor whose moment of inertia is approximately 85% of the rigid-body value. The high-spin limit to the occurrence of hi...

We present a new method for describing the kinematics of the rotational motion of a rigid body The new kinematic formulation provides a three dimensional parameterization of the rotation group using two perpendicular rotations thus it complements the Eulerian angles three rotations and Euler Rodrigues parameters one rotation The di erential equations can be described by two scalar equations We ...

In this paper we further investigate some applications of Nambu mechanics in hydrodynamical systems. Using the Euler equations for a rotating rigid body Névir and Blender [J. Phys. A 26 (1993), L1189–L1193] had demonstrated the connection between Nambu mechanics and noncanonical Hamiltonian mechanics. Nambu mechanics is extended to incompressible ideal hydrodynamical fields using energy and hel...

Rigidity theory has helped in our understanding of the properties of network glasses. We analyze the connection between rigidity and various non-random features in the network structure. Lack of small rings in the network can lead to a sharper rigidity transition. We review a model of network self-organization that we have proposed, in which the existence of an intermediate phase that is rigid,...

Category theoretic aspects of non-rational conformal field theories are discussed. We consider the case that the category C of chiral sectors is a finite tensor category, i.e. a rigid monoidal category whose class of objects has certain finiteness properties. Besides the simple objects, the indecomposable projective objects of C are of particular interest. The fusion rules of C can be block-dia...

The specific and selective detection of Salmonella typhymurium based on the use of a polyclonal antibody immobilized by the Langmuir-Blodgett method on the surface of a quartz crystal acoustic wave device was demonstrated in liquid samples. These biosensors were selective to S. typhymurium in the presence of large concentrations of Escherichia coli O157:H7. They were also specific to S. typhymu...

This Chapter expounds the modern theory of symplectic reduction in finitedimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether’s theorem. It also illustrates one of mechanics’ grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emp...