We investigate the connections between the complexity of a c.e. set, as calibrated by its strength as an oracle for Turing computations of functions in the Ershov hierarchy, and how strong reducibilities allows us to compute such sets. For example, we prove that a c.e. degree is totally ω-c.e. iff every set in it is weak truth-table reducible to a hypersimple, or ranked, set. We also show that ...

In this letter we consider higher-dimensional Yang–Mills theories and examine their consistent coset space dimensional reduction. Utilizing a suitable ansatz and imposing a simple set of constraints we determine the four-dimensional gauge theory obtained from the reduction of both the higher-dimensional Lagrangian and the corresponding equations of motion. The two reductions yield equivalent re...

If a, b and n are positive integers with b ≥ a and n ≥ 3, then the equation of the title possesses at most one solution in positive integers x and y, with the possible exceptions of (a, b, n) satisfying b = a + 1, 2 ≤ a ≤ min{0.3n, 83} and 17 ≤ n ≤ 347. The proof of this result relies on a variety of diophantine approximation techniques including those of rational approximation to hypergeometri...

The Simple Network Management Protocol (SMMP) was introduced in the late 1980s. Since then, several evolutionary protocol changes have taken place, resulting in the SNMP version 3 framework (SNMPv3). Extensive use of SNMP has led to significant practical experience by both network operators and researchers. Since recently, researchers are in the possession of real world SNMP traces. This allows...

A core issue in the cognitive sciences is understanding how people acquire conceptual knowledge. One way that people can acquire this knowledge is through the inference of missing feature information. Recent studies have proposed a shift away from the idea that inference learning results in knowledge of the internal structure of the categories being learned. The current study varies the inferen...

We define and investigate the computational complexity of the query containment problem for data that support both uncertainty and lineage. Query containment depends on the definition of database containment which, for traditional databases, is defined as a simple set containment for each relation. As this is not the case in the presence of uncertainty and lineage, we revisit the notion of data...

We apply Padé approximation techniques to deduce lower bounds for simultaneous rational approximation to one or more algebraic numbers. In particular, we strengthen work of Osgood, Fel’dman and Rickert, proving, for example, that max {∣∣∣√2− p1/q∣∣∣ , ∣∣∣√3− p2/q∣∣∣} > q−1.79155 for q > q0 (where the latter is an effective constant). Some of the Diophantine consequences of such bounds will be d...

If a, b and n are positive integers with b ≥ a and n ≥ 3, then the equation of the title possesses at most one solution in positive integers x and y, with the possible exceptions of (a, b, n) satisfying b = a + 1, 2 ≤ a ≤ min{0.3n, 83} and 17 ≤ n ≤ 347. The proof of this result relies on a variety of diophantine approximation techniques including those of rational approximation to hypergeometri...

In this study a simple and general chemical association theory is introduced. The concept of infinite equilibrium model is re-examined and true mole fractions of associated species are calculated. The theory is applied to derive the distribution function of associated species. As a severe test the application of presented theory to the van der Waals mixture model is introduced in order to p...