Characterizations of locally testable events

Let Σ be a finite alphabet, Σ^* the free monoid generated by Σ and χ the length of χ ∈ Σ^*. For any integer k0, f_k(χ) (t_k(χ)) is χ if χ < k + 1, and it is the prefix (suffix) of χ of length k, othewise. Also let m_k+1(χ) = {νχ = uνw and ν = k+1}. For χ, y ε Σ^* define χ ～ _k+1y iff f_k(χ) = f_k(y), t_k(χ) = t_k(y) and m_k+1(χ) = m_k+1(y). The relation ～_k+1 is a congruence of finite index over Σ^*. An event E ? Σ^* is (k+1)-testable iff it is a union of congruence classes of ～_k+1. E is locally testable (LT) if it is k+1-testable for some k. (This definition differs from that of [6] but is equivalent.)We show that the family of LT events is a proper sub-family of star-free events of dot-depth 1. LT events and k-testable events are characterized in terms of (a) restricted star-free expressions based on finite and cofinite events; (b) finite automata accepting these events; (c) semigroups; and (d) structural decomposition of such automata. Algorithms are given for deciding whether a regular event is (a) LT and (b) k+1-testable. Generalized definite events are also characterized.     

Consensus of opinion

In a decision analysis, it is often necessary to combine a group of individuals' beliefs into a consensus probability distribution. This paper addresses the question whether it is possible to base such consensus distributions only upon the information present within the group or must some arbitrary rule be used to resolve disagreement. Some earlier work on modifying beliefs in the light of another's opinion is developed to apply to groups of n people. Using this as a “benchmark of rationality”, standard methods of forming group consensus probability distributions are found somewhat arbitrary. Furthermore it is argued that the possibility of constructing better procedures is remote.     

The theory of melting in heteropolymers. II. Correlated chains

Equations are derived for the calculation of the ground-state melting curves for polynucleotide sequences with correlation between the nearest neighbors. The case of arbitrary correlated sequences is also considered. The effect of correlations in the sequence on the width and on the intrinsic fine structure of melting curves is discussed.Work supported in part by NSF Material Research Laboratory at Case Western Reserve University.     

Proprietes electrogalvaniques et electroniques du sulfure d'argent β: Domaine d'existence

The study of electrogalvanic and electronic properties of the form β of silver sulfide has been performed on polycrystalline samples whose non stoichiometry is controled by coulometric titration with the cell Ag/RbAg₄I₅/Ag₂₊?S/Pt.The data obtained lead to the adoption of an electronic model according to which the Frenkel defects of the silver sublattice are completly ionized. The variation with temperature of the electronic properties near the stoichiometric composition between 23 and 176°C, the temperature of transition between the two forms β and α of Ag₂S, enables the forbidden gap E_i = (1,35?1,5 × 10^?3T) eV to be computed. The existence range has been drawn between 69°C and the α ? β transition temperature.The study of the ionic conductivity has made it possible to detect two ranges of preferential conduction and to determine the mechanism of migrations of the intersticial silver ions.