A note on smoothing properties of the Bergman projection

Recently Herbig, McNeal, and Straube have showed that the Bergman projection of conjugate holomorphic functions is smooth up to the boundary on smoothly bounded domains that satisfy condition R. We show that a further smoothing property holds on a family of Reinhardt domains; namely, the Bergman projection of conjugate holomorphic functions is holomorphic past the boundary.

On modules and rings satisfy condition (𝒞)

A right [Formula: see text]-module [Formula: see text] is called to satisfy condition [Formula: see text] if, for every [Formula: see text] and [Formula: see text], there exists [Formula: see text] such that [Formula: see text] and if [Formula: see text] is a direct summand of [Formula: see text], then [Formula: see text] is a direct summand of [Formula: see text]. In this paper, we give some properties of rings and modules to satisfy condition [Formula: see text]. Moreover, their connections with von Neumann regular rings, Hereditary rings, Noetherian rings and (semi)artinian rings are addressed.

New examples of partial samples from the uniform AR(1) process and asymptotic distributions of extremes

The joint limiting distribution of maximum of the specific sub-sample and maximum of the complete sample from the first-order auto-regressive process with uniform marginal distributions is obtained in this article. There are considered several examples of partial samples, consisted of non-randomly selected terms of the full sample. It is well known that the uniform AR(1) process is strictly stationary random sequence; it doesn?t satisfy condition of weak dependency, that prohibits clustering of extremes. As a consequence of this property, some interesting conclusions about joint asymptotic distributions are reached.

Random affine code tree fractals and Falconer–Sloan condition

We calculate the almost sure dimension for a general class of random affine code tree fractals in $\mathbb{R}^{d}$. The result is based on a probabilistic version of the Falconer–Sloan condition $C(s)$ introduced in Falconer and Sloan [Continuity of subadditive pressure for self-affine sets. Real Anal. Exchange 34 (2009), 413–427]. We verify that, in general, systems having a small number of maps do not satisfy condition $C(s)$. However, there exists a natural number $n$ such that for typical systems the family of all iterates up to level $n$ satisfies condition $C(s)$.

On the Gauss Map of Surfaces of Revolution with Lightlike Axis in Minkowski 3-Space

By studying the Gauss mapGand Laplace operatorΔhof the second fundamental formh, we will classify surfaces of revolution with a lightlike axis in 3-dimensional Minkowski space and also obtain the surface of Enneper of the 2nd kind, the surface of Enneper of the 3rd kind, the de Sitter pseudosphere, and the hyperbolic pseudosphere that satisfy conditionΔhG=ΛG, Λbeing a3×3real matrix.

ON RINGS R WHOSE GRAPHS Γ(R) SATISFY CONDITION (Kp)

Let p be a prime number. Let G = Γ(R) be a ring graph, i.e. the zero-divisor graph of a commutative ring R. For an induced subgraph H of G, let CG(H) = {z ∈ V(G) ∣N(z) = V(H)}. Assume that in the graph G there exists an induced subgraph H which is isomorphic to the complete graph Kp-1, a vertex c ∈ CG(H), and a vertex z such that d(c, z) = 3. In this paper, we characterize the finite commutative rings R whose graphs G = Γ(R) have this property (called condition (Kp)).

Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces

Let (𝑋, 𝑑) be a convex metric space, 𝐶 be a closed and convex subset of 𝑋 and let 𝐵(𝐶) be the family of all nonempty bounded subsets of 𝐶. In this paper some results are obtained on the convergence of the Ishikawa iterates associated with a pair of multi-valued mappings 𝑆,𝑇 : 𝐶 → 𝐵(𝐶) which satisfy condition (2.1) below.

Non-commutative Noetherian Unique Factorization Domains often have stable range one

Let R be a Noetherian ring. If R is commutative then (a) every non-unit is contained in a height-1 prime ideal - this is the Krull principal ideal theorem - but (b) R can have an arbitrarily large stable range. The main aim of this paper is to show that if certain non-commutative rings satisfy condition (a) then they have stable range one. We shall prove theTheorem. Let R be a Noetherian domain which is not commutative. Suppose that every non-unit of R lies in at least one height-1 prime ideal and that every height-1 prime is completely prime. Then the stable range of R is one.