This paper proposes a two-dimensional elastic shell model to characterize the deformation of single-walled carbon nanotubes using the in-plane rigidity, Poisson ratio, bending rigidity and off-plane torsion rigidity as independent elastic constants. It was found that the off-plane torsion rigidity of a single-walled carbon nanotube is not zero due to the off-plane change in the π-orbital electr...

We study the fundamental algorithmic rigidity problems for generic frameworks periodic with respect to a fixed lattice or a finite-order rotation in the plane. For fixedlattice frameworks we give an O(n) algorithm for deciding generic rigidity and an O(n) algorithm for computing rigid components. If the order of rotation is part of the input, we give an O(n) algorithm for deciding rigidity; in ...

We propose new symmetry-adapted rigidity matrices to analyze the infinitesimal rigidity of arbitrary-dimensional bar-joint frameworks with Abelian point group symmetries. These matrices define new symmetry-adapted rigidity matroids on grouplabeled quotient graphs. Using these new tools, we establish combinatorial characterizations of infinitesimally rigid two-dimensional bar-joint frameworks wh...

we introduce a homological invariant of a manifold known as Gromov’s norm. Gromov’s norm of hyperbolic manifolds will be seen to be proportional to the volume of the manifold. The first striking consequence of this result is that the volume of a hyperbolic manifold is a topological invariant. Intuitively, Gromov’s norm measures the efficiency with which multiples of a homology class can be repr...

It is a simple consequence of the maximum principle that a superharmonic function u on Rn(i. e. ∆u ≤ 0) which is 1 near infinity is identically 1 on Rn (throughout this paper, n ≥ 3). Geometrically this means that one can not conformally deform the Euclidean metric in a bounded region without decreasing the scalar curvature somewhere. In fact there is a much stronger result: one can not have an...

We study the problem of identifying conditions under which a divergence free matrix field takes values in some prescribed sets of matrices K. We treat in detail the case when K is made of two or three matrices. Our results are parallel to those on curl free matrices. In that case Ball and James showed rigidity when K is made of two matrices and Tartar proved lack of rigidity when K is made of f...

We study the implications for optimal monetary policy when declining nominal wages is not a viable margin for adjustment to adverse economic conditions. To this end, we develop a New Keynesian model where downward nominal wage rigidity arises endogenously. We show that the optimal policy response to changing economic conditions is asymmetric. Another important finding is that downward nominal r...

This paper tests the ‘morale’ theory of downward nominal wage rigidity. This theory relies on workers disliking nominal pay cuts: cuts should make workers less happy. We investigate this using panel data on individual employees’ pay and satisfaction. We confirm that nominal cuts do make workers less happy than if their pay had not fallen. But we find no difference in the effect on happiness of ...

The rigidity of a matrix measures the number of entries that must be changed in order to reduce its rank below a certain value. The known lower bounds on the rigidity of explicit matrices are very weak. It is known that stronger lower bounds would have implications to complexity theory. We consider restricted variants of the rigidity problem over the complex numbers. Using spectral methods, we ...

The ability of cancer cells to sense external mechanical forces has emerged as a significant factor in the promotion of cancer invasion. Currently there are conflicting reports in the literature with regard to whether glioblastoma (GBM) brain cancer cell migration and invasion is rigidity-sensitive. In order to address this question we have compared the rigidity-response of primary patient-deri...