Consider a stationary, linear Hilbert space valued process. We establish Berry-Essen type results with optimal convergence rates under sharp dependence conditions on the underlying coefficient sequence of the linear operators. The case of non-linear Bernoulli-shift sequences is also considered. If the sequence is m-dependent, the optimal rate (n/m)1/2 is reached. If the sequence is weakly geome...

Abstract In this study, by using definition of ρ -statistical convergence which was defined Çakallı [5], we introduce the concepts pointwise w α ( f )-summability, order and uniform sequences real-valued functions. Also, give some inclusion relations between these concepts.

3D quasiperiodic tilings derived from deformed cuboctahedra are obtained by projection from 7D or 6D lattice space to 3D tile-space. Lattice matrices defining the projections from 7D or 6D lattice space to tileand test-space are given by introducing a deformation parameter. Two types of lattice matrices are considered, orthonormal and row-wise orthogonal, both are corresponding to deformation o...

We show that if X is a Σ 1 separable metrizable space which is not σ-compact then C p (X), the space of bounded real-valued continuous functions on X with the topology of pointwise convergence, is Borel-Π 1 -complete. Assuming projective determinacy we show that if X is projective not σ-compact and n is least such that X is Σ1n then Cp(X), the space of real-valued continuous functions on X with...

L-sets over a base set X are generalizations of classical sets where subsets are not specified by characteristic functions from X to {0, 1} but rather by functions from X to a lattice L. For an L-set a ∈ L and an element x ∈ X, a(x) is interpreted as the grade of membership of x in a. Stratified L-topological spaces are generalizations of topological spaces to the L-set case [1]. In [2], strati...

ACVF is the theory of non-trivially valued algebraically closed valued f ields. This theory is the model companion of the theory of valued fields. ACVF does not have elimination of imaginaries in the home sort (the valued field sort). Nevertheless, Haskell, Hrushovski, and Macpherson in [2] were able to find a collection of “geometric sorts” in which elimination of imaginaries holds. Let K be a...

We give the quantum subset construction of orthomodular lattice-valued finite automata, then we show the equivalence between orthomodular lattice-valued finite automata, orthomodular lattice-valued deterministic finite automata and orthomodular lattice-valued finite automata with empty string-moves. Based on these equivalences, we study the algebraic operations on orthomodular lattice-valued re...

Let (Ω,Σ,μ) be a σ -finite complete measure space and C be the field of complex numbers. By L(μ ,CN), we denote the linear space of all equivalence classes of CN-valued Σ-measurable functions on Ω that are identified μ-a.e. and are considered as column vectors. Let M◦ denote the linear space of all functions in L(μ ,CN) that are finite a.e. With the topology of convergence in measure on the set...