This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.

Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in Rd if every generic realization in Rd as a tensegrity framework is...

A direction-length framework is a pair (G, p), where G = (V ;D,L) is a ‘mixed’ graph whose edges are labeled as ‘direction’ or ‘length’ edges, and p is a map from V to R for some d. The label of an edge uv represents a direction or length constraint between p(u) and p(v). Let G be obtained from G by adding, for each length edge e of G, a direction edge with the same end vertices as e. We show t...

Various coarse graining schemes have been proposed to speed up computer simulations of the motion within large biomolecules, which can contain hundreds of thousands of atoms. We point out here that there is a very natural way of doing this, using the rigid regions identified within a biomolecule as the coarse grain elements. Subsequently, computer resources can be concentrated on the flexible c...

some considerable damage to steel structures during the hyogo-ken nanbu earthquake occurred. among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. the lessons from these phenomena led to the need for improved understanding of column base...

An ideal I on a cardinal κ is called rigid if all automorphisms of P (κ)/I are trivial. An ideal is called μ-minimal if whenever G ⊆ P (κ)/I is generic and X ∈ P (μ)V [G] \ V , it follows that V [X] = V [G]. We prove that the existence of a rigid saturated μ-minimal ideal on μ+, where μ is a regular cardinal, is consistent relative to the existence of large cardinals. The existence of such an i...

An incremental symmetric boundary integral formulation for the problem of many domains connected by non-linear cohesive interfaces is here presented. The problem of domains with traction-free cracks and/or rigid connections are particular instances of the proposed cohesive formulation. The numerical approximation of the considered problem is achieved by the symmetric Galerkin boundary element m...