The following theorems on the structure inside nonrecursive truth-table degrees are established: D egtev's result that the number of bounded truth-table degrees inside a truth-table degree is at least two is improved by showing that this number is innnite. There are even innnite chains and an-tichains of bounded truth-table degrees inside the truth-table degrees which implies an aarmative answe...

We study generalizations of Demuth’s Theorem, which states that the image of a Martin-Löf random real under a tt-reduction is either computable or Turing equivalent to a Martin-Löf random real. We show that Demuth’s Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the stat...

We prove that there exist sets of natural numbers A and B such that A and B form a minimal pair with respect to Turing reducibility, enumeration reducibility, hyperarithmetical reducibility and hyperenumer-ation reducibility. Relativized versions of this result are presented as well. 1. Introduction In the present paper we consider four kinds of reducibilities among sets of natural numbers: Tur...

We investigate the following modification of the well known irregularity strength of graphs. Given a total weighting w of a graph G = (V,E) with elements of a set {1, 2, . . . , s}, denote wtG(v) = ∑ e3v w(e)+w(v) for each v ∈ V . The smallest s for which exists such a weighting with wtG(u) 6= wtG(v) whenever u and v are distinct vertices of G is called the total vertex irregularity strength of...

A Turing degree a is said to be almost everywhere dominating if, for almost all X ∈ 2 with respect to the “fair coin” probability measure on 2, and for all g : ω → ω Turing reducible to X, there exists f : ω → ω of Turing degree a which dominates g. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly defined classes of Turing degrees. We r...

In this paper, we study the noise-reduction problem in the KarhunenLoève expansion domain. We develop two classes of optimal filters. The first class estimates a frame of speech by filtering the corresponding frame of the noisy speech. We will show that several well-known existing methods belong or are closely related to this category. The second class, which has not been studied before, obtain...

Mixed-microbial assemblages enriched from a septic tank, coastal sediment samples, the digester sludge of a brewery wastewater treatment plant and acidic sulfate soil samples were compared on the basis of growth rate, waste and sulfate reduction rate under sulfate reducing conditions at 30 degrees C. The specific growth rate of various cultures was in the range 0.0013-0.0022 hr(-1). Estimates o...

We prove that there exists a noncappable enumeration degree strictly below 0 0 e. Two notions of relative computability, Turing and enumeration re-ducibility, are basic to any natural ne-structure theory for the classes of computable and incomputable objects. Of the theories for the corresponding degree structures (D D D and D D D e), that for the Turing degrees is the better developed, mainly ...

A computable structure A is x-computably categorical for some Turing degree x, if for every computable structure B ∼= A there is an isomorphism f : B → A with f ≤T x. A degree x is a degree of categoricity if there is a computable structure A such that A is x-computably categorical, and for all y, if A is y-computably categorical then x ≤T y. We construct a Σ2 set whose degree is not a degree o...