This paper studies some sufficient conditions for the existence and uniqueness of a pseudo almost periodic mild solution to abstract hyperbolic differential equations with infinite delay. Applications include the existence and uniqueness of a pseudo almost periodic mild solution to the heat equation.

It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky’s theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, Bézout domain, valuation domain, Krull domain, π-domain).

An existence theorem for stationary discs of strongly pseudo-convex domains in almost complex manifolds is proved. More precisely, it is shown that, for all points of a suitable neighborhood of the boundary and for any vector belonging to certain open subsets of the tangent spaces, there exists a unique stationary disc passing through that point and tangent to the given vector. Introduction Ana...

In the study of almost hypercomplex manifolds the Hermitian metrics are well known. The parallel study of almost hypercomplex manifolds with skewHermitian metrics is in progress of development 6, 7. Let (M,H) be an almost hypercomplex manifold, i.e. M is a 4n-dimensional differentiable manifold and H is a triple (J1, J2, J3) of anticommuting almost complex structures, where J3 = J1 ◦ J2 8,2. A ...

Let G be a group acting via ring automorphisms on an integral domain R. A ring-theoretic property of R is said to G-invariant, if $$R^G$$ also has the property, where $$R^G=\{r\in \ | \sigma (r)=r \text {for all} \in G\},$$ fixed action. In this paper we prove following classes rings are invariant under operation $$R\rightarrow R^G:$$ locally pqr domains, Strong G-domains, Hilbert rings, S-stro...

Adjoining to the language of rings function symbols for splitting coefficients, relative $p$-coordinate functions, and division predicate a valuation, some theories pseudo-algebraically closed non-trivially valued fields admit quantifier elimination. It is also shown that in same theory given exponent imperfection does not elimination, due Galois theoretic obstructions.