Liquid-crystalline structure of poly(L-lysine) containing azobenzene units in the side chain

The structure of poly(L -lysine) containing 44% azobenzene units in the side chain was studied by X-ray diffraction between room temperature and 150°C. The polymer exhibits a mesomorphic structure of the smectic A1 type. In this structure, stable at least until 150°C, each smectic layer of thickness d results from the superposition of two layers: one of thickness d_A contains the free lysine side chains, the other of thickness d_B contains the azobenzene modified lysine side chains and the polypeptide main chains, that in their planes are arranged as in the “antiparallel” β-structure classical for polypeptides.     

Is there icosahedral ordering in liquid and undercooled metals?

The local structure of simple liquids is significantly different from that of corresponding crystalline systems. Signatures of fivefold local ordering have been previously found, but current knowledge is limited to pair distribution, leaving considerable uncertainty in the determination of the geometrical structure. New x-ray absorption experimental results on liquid and undercooled liquid copper, interpreted using an advanced data-analysis method based on multiple-scattering simulations, are shown to contain direct information on triplet correlations making feasible a reliable determination of the bond-angle distribution and fraction of nearly icosahedral configurations in liquids.     

Combinatorial methods in the theory of Cohen-Macaulay rings

Characterizations of Cohen-Macaulay posets are given in terms of the nonsingularity of certain incidence matrices. These results are applied to derive a purely combinatorial construction of basic systems for Stanley-Reisner rings of shellable posets. A procedure for transferring identities from one polynomial ring to another is then used to obtain basic systems for partition rings.     

On surfaces with a rectilinear geodesic circle

Summary We say that a surface has a “rectilinear geodesic circle“ if it contains a straight line segment AB and a point F whose geodesic distance from a variable point of AB is a constant. The problem of generating such surfaces is solved here by constructing families of cones which behave locally (along a curce) like solutions, and then taking their envelopes. This method generates a class of solutions which depend on an arbitrary curve. This is an excerpt from a thesis presented in partial fulfillment of the Ph. D. Requirements of the Mathematics Department of Stanford University. It was supported in part by the Ballistics Research Laboratory of the Ordnance Department, U. S. Army, under Contract No. DA-04-200-ORD-294.