We prove that a weakly convex almost Kähler 4-manifold contains a compact, non-constant J-holomorphic curve if the corresponding monopole invariant is not zero and if the corresponding line bundle is non-trivial.

A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G. The notion of density arises naturally both in connection with the theory of uniform distribution and with the theory of almost periodic functions. Our main result effectively answers the question "when are all densities on G induced by measures on some compactification of G?...

In this note we communicate some important remarks about the concepts of almost periodic time scales and almost periodic functions on time scales that are proposed by Wang and Agarwal in their recent papers ( see [7]-[10]).

For a compact Hausdorff space X , the space SC(X ×X) of separately continuous complex valued functions on X can be viewed as a C∗-subalgebra of C(X)∗∗⊗C(X)∗∗, namely those elements which slice into C(X). The analogous definition for a non-commutative C∗-algebra does not necessarily give an algebra, but we show that there is always a greatest C∗-subalgebra. This thus gives a noncommutative notio...

The best known constructions for arrays with low bias are those from [1] and the exponential sum method based on the WeilCarlitz-Uchiyama bound. They all yield essentially the same parameters. We present new efficient coding-theoretic constructions, which allow farreaching generalizations and improvements. The classical constructions can be described as making use of Reed-Solomon codes. Our rec...

The one-to-one relation between the points fulfilling the KKT conditions of an optimization problem and the zeros of the corresponding Kojima function is well-known. In the present paper we study the interplay between metric regularity and strong regularity of this a priori nonsmooth function in the context of semidefinite programming. Having in mind the topological structure of the positive se...

Let $mathcal{A}$ be a Banach algebra with BAI and $E$ be an introverted subspace of $mathcal{A}^prime$. In this paper we study the quotient Arens regularity of $mathcal{A}$ with respect to $E$ and prove that the group algebra $L^1(G)$ for a locally compact group $G$, is quotient Arens regular with respect to certain introverted subspace $E$ of $L^infty(G)$. Some related result are given as well.

We consider Markov decision processes (MDP) as generators of sequences of probability distributions over states. A probability distribution is psynchronizing if the probability mass is at least p in a single state, or in a given set of states. We consider four temporal synchronizing modes: a sequence of probability distributions is always p-synchronizing, eventually p-synchronizing, weakly psyn...