THE TENTH-EXPONENT

The Hilbert’s-Tenth-Problem Operator

For a ring R, Hilbert’s Tenth Problem HTP (R) is the set of polynomial equations over R, in several variables, with solutions in R. We view HTP as an operator, mapping each set W of prime numbers to HTP (Z[W−1]), which is naturally viewed as a set of polynomials in Z[X1, X2, . . .]. For W = ∅, it is a famous result of Matiyasevich, Davis, Putnam, and Robinson that the jump ∅′ is Turing-equivale...

The Disinfection Concentration Exponent *

It is of course well recognized that the length of time required by a germicide to kill a given number of bacteria varies with the concentration of the substance. The relation between concentration and time can usually be expressed by the formula Ct k, often written in logarithmic form log t = log kn log c for convenience The obvious value of the concentration exponent n is that it gives direct...

On the Exponent of Triple Tensor Product of p-Groups

The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...

Tenth Annual Scientific Conference

Tenth District Economic Developments

The Tenth District economy grew at a moderate pace during 1996. The district economy expanded vigorously in early 1996 but slowed as the year progressed. Tight labor markets in many parts of the region appeared to limit job growth, particularly in the large trade and services sectors. A slumping cattle industry also curbed overall growth in parts of the district. Nonetheless, construction conti...