The classical Szegö theorems study the asymptotic behaviour of the determinants of the finite sections PnT (a)Pn of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results to operators which have almost periodic functions on their diagonals.

Almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr’s fundamental theorem for almost periodic functions which we then generalize to almost periodic functions on general topological groups.

By means of the exponential dichotomy method and the properties of the weighted pseudo almost periodic functions, sufficient conditions are obtained for the existence of weighted pseudo almost periodic solutions of functional differential equations with finite delay.

A sequence {un}n∈ω in abstract additively-written Abelian group G is called a T -sequence if there is a Hausdorff group topology on G relative to which limn un = 0. We say that a subgroupH of an infinite compact Abelian groupX is T -characterized if there is a T -sequence u = {un} in the dual group of X , such that H = {x ∈ X : (un, x) → 1}. We show that a closed subgroupH ofX is T -characteriz...

We study strong solutions u : R → X, a Banach space X, of the nth-order evolution equation u(n) −Au(n−1) = f , an infinitesimal generator of a strongly continuous group A : D(A) ⊆ X → X, and a given forcing term f : R → X. It is shown that if X is reflexive, u and u(n−1) are Stepanov-bounded, and f is Stepanov almost periodic, then u and all derivatives u′, . . . ,u(n−1) are strongly almost per...

We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain Ω with nonhomogeneous boundary conditions. We apply the so-called uniformly ω-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming f ∈ Lloc 0, T ;L2 Ω , which is translation compact and φ ∈ C1 b R ;H2 R1 × {±L} asymptotically alm...

We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type. It is proved that under suitable conditions every positive solution is asymptotically almost periodic. Moreover, all positive almost periodic solutions are harmonic and uniformly stable, and if one of them is spatially homogeneous, then so are others. The existence of an alm...

Since the conventional esterification method requires longer processing time and obtain low yield, the intensification of this process is still interesting subject to be investigated. To reduce the oil extraction cost from seeds which almost 70% of total processing cost, in situ esterification has been recently introduced. The objective of study was to produce biodiesel from rubber seeds oil th...

where | ∗ |v is the v from among the normalization of norms so that the product formula holds. A vector x ∈ VA is primitive if it is of the form xog where g ∈ GL(n,A) and xo ∈ VQ. That is, it is an image of a rational point of the vectorspace by an element of the adele group. For x = (x1, . . . , xn) ∈ VQ, at almost all non-archimedean primes v the xi’s are in Zv and have greatest common diviso...

The aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎It is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...