ON JORDAN CLASSES FOR VINBERG’S θ-GROUPS

On Pre-θ-Open Sets and Two Classes of Functions

Complexity Classes between Θ

We give different characterizations of the classes Plogi(NP), which are located between Θ2 and ∆2 . First we show that these classes are equal to the classes AC i−1(NP). Second we prove that they are also equivalent to certain binary search classes over NP. Third we show that they can be characterized as the classes defined by circuits of size O(log n) with NP oracle gates. All the proofs given...

On Jordan ideals and left (θ, θ)-derivations in prime rings

Let R be a ring and S a nonempty subset of R. Suppose that θ and φ are endomorphisms of R. An additive mapping δ : R → R is called a left (θ,φ)-derivation (resp., Jordan left (θ,φ)derivation) on S if δ(xy) = θ(x)δ(y)+φ(y)δ(x) (resp., δ(x2) = θ(x)δ(x)+φ(x)δ(x)) holds for all x,y ∈ S. Suppose that J is a Jordan ideal and a subring of a 2-torsion-free prime ring R. In the present paper, it is show...

On Invariant Theory of Θ-groups

The ground field k is algebraically closed and of characteristic zero. Throughout, G is a connected and simply connected semisimple algebraic group, g is its Lie algebra, and Φ is the Cartan–Killing form on g; l = rk g. Int g (resp. Aut g) is the group of inner (resp. all) automorphisms of g; N is the nilpotent cone in g. For x ∈ g, z(x) is the centraliser of x in g. Let g = ⊕i∈Zmgi be a period...

Semi-θ-Open Sets and New Classes of Maps