New laterally aromatic branched liquid crystal materials with large nematic ranges

Abstract

Three new homologous series of mesogens containing three rings in the main structure and a lateral aromatic branch have been synthesized. When the lateral aromatic branch is attached to the middle ring, monotropic phases are observed, and there is a strong tendency to form the smectic C phase. When the lateral aromatic branch is attached to an outer ring, the compounds possess purely enantiotropic nematic phases. The terminal alkoxy chain in the outer ring which has a lateral aromatic substituent can be replaced by a rigid group without disturbing the large nematic range. Selective introduction of a particular substitutent may be useful for the construction of devices possessing desirable characteristics such as non-linear optical properties.     

Gomory integer programs

 The set of all group relaxations of an integer program contains certain special members called Gomory relaxations. A family of integer programs with a fixed coefficient matrix and cost vector but varying right hand sides is a Gomory family if every program in the family can be solved by one of its Gomory relaxations. In this paper, we characterize Gomory families. Every TDI system gives a Gomory family, and we construct Gomory families from matrices whose columns form a Hilbert basis for the cone they generate. The existence of Gomory families is related to the Hilbert covering problems that arose from the conjectures of Seb?. Connections to commutative algebra are outlined at the end. Received: May 17, 2001 / Accepted: February 7, 2002 Published online: April 24, 2003 RID="⋆" ID="⋆" Research partially supported by NSF grant DMS-0100141.     

Compact Einstein warped product spaces with nonpositive scalar curvature

We study Einstein warped product spaces. As a result, we prove the following: if is an Einstein warped product space with nonpositive scalar curvature and compact base, then is simply a Riemannian product space.

     

Quantum Dynamics of Systems Connected by a Canonical Transformation

Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively.