abstractthe liquid crystal director distribution is determined for a confined chiral nematic slab. the molecular director distribution of the field-controlled chiral nematic slab is directly calculated. the director profiles for the tilt and the twist angles, under different applied fields, are calculated in the slab with weak boundary conditions. then, the dependence of the threshold field on ...

We study twisted Spin-manifolds over a paracompact Hausdorff space X with a twisting α : X → K(Z, 3). We introduce the topological index and the analytical index on the bordism group of α-twisted Spin-manifolds over (X,α), taking values in topological twisted K-homology and analytical twisted K-homology respectively. The main result of this paper is to establish the equality between the topolog...

Braided textile materials are widely used in many industries and agriculture. tapes for domestic purposes, the food industry, construction, medicine, aircraft manufacturing, electrical engineering, etc. Every braided product must correspond to a unique group of parameters properties, depending on initial manufacturing parameters. The production is still insufficiently explored. In process desig...

We present a generalization of standard Turing machines based on allowing unusual tapes. We present a set of reasonable constraints on tape geometry and classify all tapes conforming to these constraints. Surprisingly, this generalization does not lead to yet another equivalent formulation of the notion of computable function. Rather, it gives an alternative definition of the recursively enumer...