Lots of string-related algorithms have applications in the field of bioinformatics. Motivations for finding palindromic substrings in bioinformatics include
Finding secondary structures in RNA folding 1
Predicting DNA breakage during gene conversion 2
Finding/analyzing clustered regularly interspaced short palindromic repeats (CRISPRs) 3
These three ...
On the surface that does not strike me as a high-quality paper. I wouldn't recommend it.
I don't think irrational/transcendental numbers are a good approach to building PRNGs. Building PRNGs is tricky business. There are standard PRNGs; I suggest using one of them, rather than trying to invent your own. They all ensure that the output is extremely ...
Assuming you work in CNF, construct "at least $k+1$-out-of-$n$" and add "or $p$" to each disjunction. Do the same for "at most $k-1$-out-of-$n$" and add "or $q$" to each disjunction.
Then add one extra term to your main conjunction, $\neg p \vee \neg q$.