Adelic geometry and polarity

Adelic Geometry and Polarity

In the present paper we generalise transference theorems from the classical geometry of numbers to the geometry of numbers over the ring of adeles of a number field. To this end we introduce a notion of polarity for adelic convex bodies.

Adelic strings and noncommutativity

We consider adelic approach to strings and spatial noncommutativity. Path integral method to string amplitudes is emphasized. Uncertainties in spatial measurements in quantum gravity are related to noncommutativity between coordinates. p-Adic and adelic Moyal products are introduced. In particular, p-adic and adelic counterparts of some real noncommutative scalar solitons are constructed.

Geometry-Driven Polarity in Motile Amoeboid Cells

Motile eukaryotic cells, such as leukocytes, cancer cells, and amoeba, typically move inside the narrow interstitial spacings of tissue or soil. While most of our knowledge of actin-driven eukaryotic motility was obtained from cells that move on planar open surfaces, recent work has demonstrated that confinement can lead to strongly altered motile behavior. Here, we report experimental evidence...

Small Points and Adelic Metrics

On Adelic Strings

New approach to p-adic and adelic strings, which takes into account that not only world sheet but also Minkowski space-time and string momenta can be p-adic and adelic, is formulated. p-Adic and adelic string amplitudes are considered within Feynman’s path integral formalism. The adelic Veneziano amplitude is calculated. Some discreteness of string momenta is obtained. Also, adelic coupling con...