Sequence entropy pairs and complexity pairs for a measure

Metric-Entropy Pairs on Lattices

We introduce the notion of ∧and ∨-pairs of functions on lattices as an abstraction of the notions of metric and its related entropy for probability distributions. This approach allows us to highlight the relationships that exist between various properties of metrics and entropies and opens the possibility of extending these concepts to other algebraic structures.

Wavelength Isolation Sequence Pairs

In the early 1950s, Golay studied binary sequence pairs whose autocorrelation properties are ideal for use in the design of multislit spectrometers. He found examples for some small lengths, but, unable to find more, he suggested that perhaps further examples do not exist and turned his attention to an alternative solution to the design problem (involving what are now called Golay complementary...

Entropy, area, and black hole pairs.

We clarify the relation between gravitational entropy and the area of horizons. We first show that the entropy of an extreme Reissner-Nordström black hole is zero, despite the fact that its horizon has nonzero area. Next, we consider the pair creation of extremal and nonextremal black holes. It is shown that the action which governs the rate of this pair creation is directly related to the area...

The Constructions of Almost Binary Sequence Pairs and Binary Sequence Pairs with Three-Level Autocorrelation

ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS

Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...