URL decay is a serious problem in health care management journals. In addition to using website archiving tools like WebCite, publishers should require authors to both keep copies of Internet-based information they used and deposit copies of data with the publishers.

We introduce three formal theories of increasing strength for linear algebra in order to study the complexity of the concepts needed to prove the basic theorems of the subject. We give what is apparently the first feasible proofs of the Cayley-Hamilton theorem and other properties of the determinant, and study the propositional proof complexity of matrix identities such as AB = I → B A = I .

In this study, we provide mathematical and practice-driven justification for using [0, 1] normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization, are presented. A new type of paradox of infinity is described.

This study has been inspired by numerous requests from researchers who often confuse Saaty's AHP with the Pairwise Comparisons (PC) method, taking AHP as the only representation of PC. Most formal

A shuffle of two strings is formed by interleaving the characters into a new string, keeping the characters of each string in order. A string is a square if it is a shuffle of two identical strings. There is a known polynomial time dynamic programming algorithm to determine if a given string z is the shuffle of two given strings x, y; however, it has been an open question whether there is a polynomial time algorithm to determine if a given string z is a square. We resolve this by proving that this problem is NP-complete via a many-one reduction from 3-Partition.