We study here the degree-theoretic structure of set-theoretical splittings of recursively enumerable (r.e.) sets into differences of r.e. sets. As a corollary we deduce that the ordering of wtt–degrees of unsolvability of differences of r.e. sets is not a distributive semilattice and is not elementarily equivalent to the ordering of r.e. wtt–degrees of unsolvability.

Mindfulness has been studied as a momentary state and an enduring trait, yet little research reconciled these accounts. We draw from Whole Trait Theory (WTT) to conceptualize (the descriptive side of) trait mindfulness person-specific density distribution of mindful states. In preregistered secondary analyses three samples – daily diaries with adolescents (1,505 observations) experience samplin...

We study the classes of hypersimple and semicomputable sets as well as their intersection in the weak truth table degrees. We construct degrees that are not bounded by hypersimple degrees outside any non-trivial upper cone of Turing degrees and show that the hypersimple-free c.e. wtt degrees are downwards dense in the c.e. wtt degrees. Moreover, we consider the sets that are both hypersimple an...

Formation of turbulence of capillary waves is studied in laboratory experiments. The spectra show multiple exponentially decreasing harmonics of the parametrically excited wave which nonlinearly broaden with the increase in forcing. Spectral broadening leads to the development of the spectral continuum which scales as ∝ f, in agreement with the weak turbulence theory (WTT). Modulation instabili...

Aim: To detect pathological brain conditions early is a core procedure for patients so as to have enough time for treatment. Traditional manual detection is either cumbersome, or expensive, or time-consuming. We aim to offer a system that can automatically identify pathological brain images in this paper. Method: We propose a novel image feature, viz., Fractional Fourier Entropy (FRFE), which i...

Computability theorists have studied many different reducibilities between sets of natural numbers including one reducibility (≤1), many-one reducibility (≤m), truth table reducibility (≤tt), weak truth table reducibility (≤wtt) and Turing reducibility (≤T ). The motivation for studying reducibilities stronger that Turing reducibility stems from internally motivated questions about varying the ...

This paper examines the constructive Hausdorff and packing dimensions of weak truth-table degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dimH(S) and constructive packing dimension dimP(S) is weak truth-table equivalent to a sequence R with dimH(R) ≥ dimH(S)/dimP(S)− ǫ, for arbitrary ǫ > 0. Furthermore, if dimP(S) > 0, then dimP(R) ≥ 1− ǫ. The re...

We study the approximation properties of computably enumerable reals. We deal with a natural notion of approximation representation and study their wtt-degrees. Also, we show that a single representation may correspond to a quite diverse variety of reals.

We show that Sacks’ and Shoenfield’s analogs of jump inversion fail for both ttand wttreducibilities in a strong way. In particular we show that there is a ∆2 set B >tt ∅ ′ such that there is no c.e. set A with A′ ≡wtt B . We also show that there is a Σ 0 2 set C >tt ∅ ′ such that there is no ∆2 set D with D′ ≡wtt C . §

It has long been understood that availability of thermophysical and thermochemical property data is vital to scientific research and industrial design. For over 65 years, the Thermodynamics Research Center (TRC) has been publishing tables of critically evaluated data covering physical and thermodynamic properties of pure compounds, TRC Tables-Hydrocarbons and TRC Tables-Non-Hydrocarbons. Over t...