The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are int...

We use the differential geometrical framework of generalized (almost) Calabi-Yau structures to reconsider the concept of mirror symmetry. It is shown that not only the metric and B-field but also the algebraic structures are uniquely mapped. As an example we use the six-torus as a trivial generalized Calabi-Yau 6-fold and an appropriate B-field.

In 1969, P. Deligne and D. Mumford compactified the moduli space of curves Mg,n. Their compactification Mg,n is a projective algebraic variety, and as such, it has an underlying analytic structure. Alternatively, the quotient of the augmented Teichmüller space by the action of the mapping class group gives a compactification of Mg,n. We put an analytic structure on this quotient and prove that ...

Let G be a complex algebraic group and L an algebraic subgroup of G. The quotient space G/L is called weakly commutative if a generic orbit of the action G : T ∗(G/L) is a coisotropic submanifold. We classify weakly commutative homogeneous spaces N L/L in the case where L is a reductive group and the natural representation L : n/[n, n], where n is the tangent algebra of the group N , is

We investigate the complexity of the lattice of local clones over a countably infinite base set. In particular, we prove that this lattice contains all algebraic lattices with at most countably many compact elements as complete sublattices, but that the class of lattices embeddable into the local clone lattice is strictly larger than that: For example, the lattice M2ω is a sublattice of the loc...

We give the general solution of three Diophantine equations in the ring of integer of the algebraic number field Q[ √ 5]. These equations are related to the problem of determination of the minimum distance in quasicrystals with fivefold symmetry.

We give a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.

A higher dimensional analogue of Kodaira's canonical bundle formula is obtained. As applications, we prove that the logcanonical ring of a klt pair with 3 is nitely generated, and that there exists an e ectively computable natural numberM such that jMK X j induces the Iitaka bering for every algebraic threefold X with Kodaira dimension = 1.

We establish new conditions ensuring that a Riemannian metric may be constructed, up to a conformal factor, from the skewsymmetries of its Riemann curvature tensor.

We investigate the arithmetic nature of special values of Thakur’s function field Gamma function at rational points. Our main result is that all linear dependence relations over the field of algebraic functions are consequences of the Anderson-Deligne-Thakur bracket relations.