A Tardy Uptake

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...

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 ...

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

An exact approach to early/tardy scheduling with release dates

In this paper, we consider the single machine earliness/tardiness scheduling problem with di/erent release dates and no unforced idle time. The problem is decomposed into weighted earliness and weighted tardiness subproblems. Lower bounding procedures are proposed for each of these subproblems, and the lower bound for the original problem is the sum of the lower bounds for the two subproblems. ...