Among the research topics are the hypergroupoid of boundary conditions for local quantum observables, the asymptotic stability of connective groups, the

K-theory of the flip automorphisms, the modular cocycle from commensuration and its Mackey range, and the classification of gapped Hamiltonians in quantum spin chains.

Acting on it categorifies acting on more conventional invariants such as cohomology or

K-theory. Unfortunately derived categories were built around the seriously flawed axiomatics of triangulated categories.

In [12] and [14], Lascoux and Schutzenberger introduced (double) Grothendieck polynomials indexed by permutations as representatives of

K-theory classes of structure sheaves of Schubert varieties in a full flag variety.

It is a major object of study in algebraic

K-theory and appears in numerous literatures.

Is the uncertain theory,

K-theory [10]solve the recent intriguing statistical problems by the power of this Neutrosophic logic ?

The motivation to study the topological properties of the space [hom.sub.st] (G, PU(H)) of stable homomorphisms from a compact Lie group G to the group of projective unitary operators on a Hilbert space H endowed with the topology of pointwise convergence, comes from realm of equivariant

K-theory.

The

K-theory functor, a covariant functor from [C.sup.*] algebras to abelian groups, gives rise to a morphism [[lambda].sub.*] of abelian groups.

And in [7], base change was interpreted as Galois-fixed points at the level of

K-theory groups.

Eleven contributions are selected from the eight working groups in the areas of elliptic surfaces and the Mahler measure, analytic number theory, number theory in functions fields and algebraic geometry over finite fields, arithmetic algebraic geometry,

K-theory and algebraic number theory, arithmetic geometry, modular forms, and arithmetic intersection theory.

The analogue of positivity in equivariant

K-theory was (again, abstractly) proven in Anderson et al.

7: Correlation plots of SW-model estimated versus observed daily transpiration for rain, non-rain and all weather conditions in the Mengcha village study area However, the SW-model is essentially derived from the PM-model and both are based on the

K-theory. The models use the gradient diffusion theory that is normally violated at canopy water transport (Federer et al., 1996).

But Nicusor Dan, a mathematician who graduated from the Sorbonne University in Paris, decided to fight back - even if this meant spending less time on his cherished research about polylogarithms and the

K-theory at the Romanian Institute for Mathematics.