We give a diagrammatic definition of Uq(sl2) when q is not a root of unity, including the Hopf algebra structure and relationship with the Temperley-Lieb category. Quantum groups, knot diagrams, skein theory.

We develop a skein exact sequence for knot Floer homology, involving singular knots. This leads to an explicit, algebraic description of knot Floer homology in terms of a braid projection of the knot.

We introduce a truncated addition operation on pairs of N-bit binary numbers that interpolates between ordinary addition mod 2 N and bitwise addition in (Z/2Z) N. We use truncated addition to analyze hash functions that are built from the bit operations add, rotate, and xor, such as Blake, Skein, and Cubehash. Any ARX algorithm can be approximated by replacing ordinary addition with truncated a...

PURPOSE To define the corneal optics of conductive keratoplasty (CK) and assess the clinical implications for hyperopia and presbyopia management. METHODS Four analyses were done. (1) Multifocal effects: In a prospective study of CK, uncorrected visual acuity (UCVA) for a given refractive error in 72 postoperative eyes was compared to control eyes. (2) Surgically induced astigmatism (SIA): 20...

Discovering the mechanical properties of biological composite structures at the Nano-scale is much interesting today. Top Neck mollusk shells are amongst biomaterials Nano-Composite that their layered structures are composed of organic and inorganic materials. Since the Nano indentation process is known as an efficient method to determine mechanical properties like elastic modulus and hardness ...

A simple and modular synthetic approach, based on miniemulsion polymerization, has been developed for the fabrication of composite polymer-metal nanoparticle materials. The procedure produces well-defined composite structures consisting of gold, silver or MnFe(2)O(4) nanoparticles (∼10 nm in diameter) encapsulated within larger spherical nanoparticles of poly(divinylbenzene) (∼100 nm in diamete...

We have studied the effective response of composites of spherical particles with a dielectric profile which varies along the radius of the particles. We developed a differential effective dipole theory to compute the dipole moment of individual spherical particle and hence the effective dielectric response of a dilute suspension. The theory has been applied to two model dielectric profiles. Mor...