Substituted with four 3,4,5-tris(alkoxy)benzyl mini-dendrons, azacalix[4]pyridine (1) with the saddle-shaped core is the first liquid crystal (LC) of heteracalixaromatics. Conformational regulation of azacalix[4]pyridine by complexing with the zinc ion leads to a significant change in LC properties.

A saddle-distorted dodecaphenylporphyrin undergoes protonation followed by two-electron reduction by SnCl(2) to give a roof-shaped dodecaphenylporphodimethene which exhibits reversible one-electron reduction and oxidation behaviour in benzonitrile to allow us to observe an ESR spectrum of pi-cation radical in the course of electrochemical oxidation.

BACKGROUND Annuloplasty ring or band implantation during surgical mitral valve repair perturbs mitral annular dimensions, dynamics, and shape, which have been associated with changes in anterior mitral leaflet (AML) strain patterns and suboptimal long-term repair durability. We hypothesized that rigid rings with nonphysiological three-dimensional shapes, but not saddle-shaped rigid rings or fle...

A method is presented for finding the ridge between first order saddle points on a multidimensional surface. For atomic scale systems, such saddle points on the energy surface correspond to atomic rearrangement mechanisms. Information about the ridge can be used to test the validity of the harmonic approximation to transition state theory, in particular to verify that second order saddle points...

The problem of sampling low lying, first-order saddle points on a high dimensional surface is discussed and a method presented for improving the sampling efficiency. The discussion is in the context of an energy surface for a system of atoms and thermally activated transitions in solids treated within the harmonic approximation to transition state theory. Given a local minimum as an initial sta...

BACKGROUND Leaflet curvature is known to reduce mechanical stress. There are 2 major components that contribute to this curvature. Leaflet billowing introduces the most obvious form of leaflet curvature. The saddle shape of the mitral annulus imparts a more subtle form of leaflet curvature. This study explores the relative contributions of leaflet billowing and annular shape on leaflet curvatur...

A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. The simi...

How well do observers perceive the local shape of an object from its shaded image? This problem was addressed by first deriving a potential representation of local solid shape. The descriptor of local shape, called shape characteristic, provides a viewpoint-independent continuum between hyperbolic (saddle-shaped) and elliptic (egg-shaped) points. The ability of human observers to make categoric...

In a natural environment, cast shadows abound. Objects cast shadows both upon themselves and upon background surfaces. Previous research on the perception of 3-D shape from cast shadows has only examined the informativeness of shadows cast upon flat background surfaces. In outdoor environments, however, background surfaces often possess significant curvature (large rocks, trees, hills, etc.), a...