We prove that there is a full and faithful nerve functor defined on the category 2-Cat lax of 2-categories and (normal) lax 2-functors. This functor extends the usual notion of nerve of a category and it coincides on objects with the so-called geometric nerve of a 2-category or of a 2-groupoid. We also show that (normal) lax 2-natural transformations produce homotopies of a special kind, and th...

Korean has two types of voiceless alveolar fricatives One is called aspirated and the other tense (Kagaya, 1974) The aspirated fricatives have also been called lax fricatives because phonolog1cally they act hke a lax obstruent, undergomg a set of processes that lax stops do For example, Korean lax stops and Isl undergo post-obstruent tensmg {Sohn 1999) Aspirated stops (e g, ch), however, do not...

The entropy solutions of the compressible Euler equations satisfy a minimum principle for the specific entropy [10]. First order schemes such as Godunov-type and Lax-Friedrichs schemes and the second order kinetic schemes [6] also satisfy a discrete minimum entropy principle. In this paper, we show an extension of the positivity-preserving high order schemes for the compressible Euler equations...

The universal character is a generalization of the Schur function attached to a pair of partitions. We study an integrable system of q-difference equations satisfied by the universal characters, which is an extension of the q-KP hierarchy and is called the lattice q-UC hierarchy. We describe the lattice q-UC hierarchy as a compatibility condition of its associated linear system (Lax formalism) ...

In this paper the scattering matrix of a scattering system consisting of two selfadjoint operators with finite dimensional resolvent difference is expressed in terms of a matrix Nevanlinna function. The problem is embedded into an extension theoretic framework and the theory of boundary triplets and associated Weyl functions for (in general nondensely defined) symmetric operators is applied. Th...

The entropy solutions of the compressible Euler equations satisfy a minimum principle for the specific entropy [11]. First order schemes such as Godunov-type and Lax-Friedrichs schemes and the second order kinetic schemes [6] also satisfy a discrete minimum entropy principle. In this paper, we show an extension of the positivity-preserving high order schemes for the compressible Euler equations...

Despite playing a central role in tolerance, little is known regarding the mechanism by which intracellular CTLA-4 is shuttled from the trans-Golgi network to the surfaces of T cells. In this context, Ras-related GTPase Rab8 plays an important role in the intracellular transport, while we have previously shown that CTLA-4 binds to the immune cell adaptor TRIM in T cells. In this study, we demon...

The work continues a presentation of modern quantum mathematics backgrounds started in [3]. A general approach to quantum holonomic computing based on geometric Lie algebraic structures on Grassmann manifolds and related with them Lax type flows is proposed. Making use of the differential geometric techniques like momentum mapping reduction, central extension and connection theory on Stiefel bu...