N be a rational map, where f 0 ,. .. , f N are homogeneous polynomials of degree d with no common factors. Then φ is defined at all points not in the indeterminacy locus Z(φ) = { P ∈ P N : f 0 (P) = · · · = f N (P) = 0 }. The map φ is said to be dominant if the image φ (P N Z(φ)) is Zariski dense, i.e., does not lie in a proper algebraic subset of P N. Alternatively, the map φ is dominant if th...

In this paper, following [W.A. Kirk, P.S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory. 4 (2003) 79-89], we give a fixed point result for cyclic weak φ-contractions on partial metric space. A Maia type fixed point theorem for cyclic weak φ-contractions is also given.

Generation of a quasi-contractive semigroup by generalized Ornstein-Uhlenbeck operators ℒ = −∆ + ∇Φ · ∇ − G V c|x|−2 in the weighted space L2(RN, e−Φ(x)dx) is proven, where Φ ∈ C2(RN, R), C1(RN, RN), 0 ≤ C1(RN) and c > 0. The proofs are carried out an application L2-weighted Hardy inequality bilinear form techniques.

We prove: For all n and all n-cylic isometriesφ : ΛQ → ΛQ of the rational K3 lattice there exists an algebraic realization of φ, i.e. marked algebraic K3 surfaces (S,ηS) and (M,ηM), whereM is a moduli space of sheaves on S, and a Hodge isometry ψ : H2(S,Q)→ H2(M,Q) such that φ = ηM ◦ψ ◦ η−1 S . 1 Facts about cyclic isometries We need the existence of a triple ((S,ηS), (M,ηM),ψ) to have a point ...

Abstract Let $\mathcal {A} \subset{\mathcal {B}}(\mathcal {H})$ A ⊂ B ( H ) be a row contraction and $\Phi _{\mathcal {A}}$ Φ determined by {A}$ completely positive map on ${\mathcal . ...