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...

Colloidal nanocrystal gels can be assembled using a difunctional “linker” molecule to mediate bonding between nanocrystals. The conditions for gelation and the structure of gel are controlled macroscopically by linker concentration microscopically linker’s molecular characteristics. Here, we demonstrate toy model colloid–linker mixture that flexibility plays key role in determining both phase b...

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...

In a previous paper, a control Iaw has been developed fix passive bilateral teleoperator to achieve theoretically perfect coordination in the presence of arbitrary environment forcing, and to enable the teleoperator to behave like a passive rigid mechanical tool. In this paper, we develop an adaptive control law to relax the need far the precise knowledge of inertia parameters, and a robust con...

Consider an irreducible component of the Hilbert scheme whose general point parameterizes a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such components when X is P, P or a smooth quadric threefold in P, respectively. Those bounds make sense from the asymptotic viewpoint if we fix d and let g vary. Some examples...