The Tardy Convalescent

The Convalescent Mental Patient

cases helped and a substantial increase in the amount refunded by patients and their friends. The main difficulty, however, in securing an increase in our subscriptions (said Sir Charles) is that the appeal to the imagination?so necessary in all cases, and so simple and successful in pleading for, say, work amongst children?is not easy to frame in the case of mental after-care. The little orpha...

On n-tardy sets

Harrington and Soare introduced the notion of an n-tardy set. They showed that there is a nonempty E property Q(A) such that if Q(A) then A is 2tardy. Since they also showed no 2-tardy set is complete, Harrington and Soare showed that there exists an orbit of computably enumerable sets such that every set in that orbit is incomplete. Our study of n-tardy sets takes off from where Harrington and...

Tardy DCs to the (Th1) rescue

Like a tourist without a map, tumor-fighting T cells have a hard time finding their destination without directions. According to Clark et al. (page 2221), dismantling these directions helps skin cancer cells hide from killer T cells. To enter the skin, T cells must grab on to the adhesive molecule E-selectin, which is expressed on the endothelial cells lining blood vessels in the skin. The auth...

Minimizing the Number of Tardy Jobs

Residue Classes Having Tardy Totients

We show, in an effective way, that there exists a sequence of congruence classes ak (mod mk) such that the minimal solution n = nk of the congruence φ(n) ≡ ak (mod mk) exists and satisfies log nk/ logmk → ∞ as k → ∞. Here, φ(n) is the Euler function. This answers a question raised in [3]. We also show that every congruence class containing an even integer contains infinitely many values of the ...