The author, who has lately been David Davies Professor of Tuberculosis, Welsh National Medical School, and whose work on the epidemiology of tuberculosis is well known, has assembled in this extremely interesting book, not only his first-hand knowledge about tuberculosis in Europe, Egypt, Africa and Burma, but also extensive references on the subject from other countries. The title of the book ...

Undecidability results in rewriting have usually been proved by reduction from undecidable problems of Turing machines or, more recently, from Post’s Correspondence Problem. Another natural candidate for proofs regarding term rewriting is Recursion Theory, a direction we promote in this contribution. We present some undecidability results for “primitive” term rewriting systems, which encode pri...

This position paper presents a very simple mechanism, primitive associations, and argues that this mechanism is worth careful consideration in connection with the kind of support for program correctness that grows out of mechanisms for ownership, controlled aliasing, sharing, escape analysis, and so on.

Importantly, there is no element 1 ≤ k < p − 1 such that a ≡ 1(modp). The concepts presented in the study of primitive elements can be considered special cases of more general idea presented in group theory. Specifically, the primitve element a can be seen as a generator of Zp, we wil discuss this in more detail in the first section of the paper. Primitive elements also have applications in enc...

A set of positive integers is primitive (or 1-primitive) if no member divides another. Erd\H{o}s proved in 1935 that the weighted sum $\sum1/(n \log n)$ for $n$ ranging over a $A$ universally bounded all choices $A$. In 1988 he asked this universal bound attained by prime numbers. One source difficulty conjecture $\sum n^{-\lambda}$ maximized primes and only $\lambda$ at least critical exponent...