A central result in the space geometry of closed twisted ribbons is Călugăreanu’s theorem (also known as White’s formula, or the Călugăreanu-White-Fuller theorem). This enables the integer linking number of the two edges of the ribbon to be written as the sum of the ribbon twist (the rate of rotation of the ribbon about its axis) and its writhe. We show that twice the twist is the average, over...

a 30-year-old woman presented with a palpable subcutaneous nodule in the areolar region of the left breast. sonomammographic examination revealed 2 cystic lesions showing typical “filarial dance” as vigorous twirling movement of multiple curvilinear echoes with mixed red blue color doppler signals that was non-rhythmic, nonpulsatile, and the characteristic pulse doppler trace due to irregular w...

We introduce the notion of a half-ribbon Hopf algebra, which is a Hopf algebra H along with a distinguished element t ∈ H such that (H, R,C) is a ribbon Hopf algebra, where R = (t ⊗ t)∆(t) and C = t. The element t is closely related to the topological ‘half-twist’, which twists a ribbon by 180 degrees. We construct a functor from a topological category of ribbons with half-twists to the categor...

A central result in the space geometry of closed twisted ribbons is Călugăreanu’s theorem (also known as White’s formula, or the Călugăreanu-White-Fuller theorem). This enables the integer linking number of the two edges of the ribbon to be written as the sum of the ribbon twist (the rate of rotation of the ribbon about its axis) and its writhe. We show that twice the twist is the average, over...

We describe a phenomenon of ribbon-to-fiber transformation observed in the process of spinning of single wall carbon nanotubes dispersed in polymer solutions. In the process of spinning, a gel-like ribbon comprised of nanotube bundles bound by polymer is withdrawn from a solvent bath. We show that upon crossing the liquid-air interface, the ribbon may either retain its flat shape or fold into a...

Many scholars believe that notions of fault should and do pervade contract doctrine. Notwithstanding the normative and positive arguments in favor of a fault-based analysis of particular contract doctrines, I argue that contract liability is strict liability at its core. This core regime is based on two key prongs: (1) the promisor is liable to the promisee for breach, and that liability is una...

School today is caught in the dilemma of being expected to educate young people so that they can be integrated into modern industrial society. Because of structural injustices in society, not all students have equal chances in this integration process. Education in school is also expected to impart proficiency in skills which go beyond the functional skills which a productive society needs. The...

A close to native structure of bulk biological specimens can be imaged by cryo-electron microscopy of vitreous sections (CEMOVIS). In some cases structural information can be combined with X-ray data leading to atomic resolution in situ. However, CEMOVIS is not routinely used. The two critical steps consist of producing a frozen section ribbon of a few millimeters in length and transferring the...

Vermiculture is the culture of earthworms. The goal is to continually increase the number of worms in order to obtain a sustainable harvest. The worms are either used to expand a vermicomposting operation or sold to customers who use them for the same or other purposes. Vermicomposting is the process by which worms are used to convert organic materials (usually wastes) into a humus-like materia...