We show that, for points along the moment curve, bar-and-joint rigidity matroid and hyperconnectivity coincide, that both coincide with \(C^{d-2}_{d-1}\)-cofactor of any (non-degenerate) conic in plane. For dimension two, having curve is no loss generality. also restricted to bipartite graphs, freer than matroid.Mathematics Subject Classifications: 52C25, 52B40Keywords: Rigidity, hyperconnectiv...

We generalize Cauchy’s celebrated theorem on the global rigidity of convex polyhedra in Euclidean 3-space E to the context of circle polyhedra in the 2-sphere S. We prove that any two convex and proper non-unitary c-polyhedra with Möbiuscongruent faces that are consistently oriented are Möbius-congruent. Our result implies the global rigidity of convex inversive distance circle packings in the ...

This approach can be carried out for other situations as well. In fact [Faltings] deals with the case of abelian varieties and shows that boundedness always holds and that for rigidity one has to impose further conditions besides non-isotriviality. Subsequently the rigidity statement has been generalized in [Peters90] and using his result, the case of K3-surfaces, resp. Abelian varieties could ...

The problem of combinatorially determining the rank of the 3-dimensional bar-joint rigidity matroid of a graph is an important open problem in combinatorial rigidity theory. Maxwell’s condition states that the edges of a graph G = (V,E) are independent in its d-dimensional generic rigidity matroid only if (a) the number of edges |E| ≤ d|V | − ( d+1 2 ) , and (b) this holds for every induced sub...

We study the rigidity properties of a class of algebraic Z-actions with entropy rank two. For this class, conditions are found which force an invariant measure to be the Haar measure on an affine subset. This is applied to show isomorphism rigidity for such actions, and to provide examples of non-isomorphic Z-actions with all their Z-sub-actions isomorphic. The proofs use lexicographic half-spa...

in this paper, by modifying cheng-yau$'$s technique to complete hypersurfaces in $s^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [h. li, hypersurfaces with constant scalar curvature in space forms, {em math. ann.} {305} (1996), 665--672].

Carbon nanotubes (CNTs) are specific structures with valuable characteristics. In general, the structure of each nanotube is defined by a unique chiral vector. In this paper, different structures of short single-walled CNTs are simulated and their mechanical properties are determined using finite element method. For this aim, a simple algorithm is presented which is able to model the geometry o...

The extent to which labour market rigidity can be beneficial for an economy is investigated in a model where technological change is non-general purpose and different types of skills are available to workers. More precisely, specific skills lock a worker into a particular technology but increases productivity. Conversely, general skills allow workers to move across technologies at the cost of l...

Elastic network models (ENM) and constraintbased, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature...

We show that positivity of energy for stationary, or strongly uniformly Schwarzschildian, asymptotically flat, non-singular domains of outer communications can be proved using Galloway’s null rigidity theorem.