The role of B cells and autoimmunity as contributing factors to poor neurological outcomes following spinal cord injury (SCI) is poorly understood. The study by Ankeny et al., in this issue of the JCI, identifies a new immunopathological mechanism arising after SCI in mice (see the related article beginning on page 2990). The study shows that B cells produce pathogenic antibodies that impair le...

The well-known “H conjecture” (see [HaR]) states that n + 1 is prime infinitely many often. This is equivalent to the existence of infinitely many primes p satisfying {p1/2} < p. The current methods of analytic number theory are far from being sufficient to prove these conjectures. However, Kubilius [Kub] and Ankeny [Ank] proved already about fifty years ago that, assuming the truth of the Riem...

Let p(z) = ?n?=0 a?z? be a polynomial of degree n, M(p,R) := max|z|=R?0 |p(z)|, and M(p,1) ||p||. Then according to well-known result Ankeny Rivlin, we have for R ? 1, (Rn+1/2) This inequality has been sharpened among others by Govil, who proved that ||p||-n/2 (||p||2-4|an|2/||p||) {(R-1)||p||/||p||+2|an|- ln (1+ (R-1)||p||/||p||+2|an|)}. In this paper, sharpen the above which in turn sharpens ...

In the literature there has been considerable attention given to the exploration of relationships between certain diophantine equations and class numbers of quadratic fields. In this paper we provide criteria for the insolvability of certain diophantine equations. This result is then used to determine when related real quadratic fields have class number bigger than 1. Moreover, based on criteri...

Let p be an odd prime with p ⌘ 1 (mod 4) and " = (t + upp)/2 > 1 be the fundamental unit of the real quadratic field K = Q(pp) over the rationals. The Ankeny-Artin-Chowla conjecture asserts that p u, which still remains unsolved. In this paper, we investigate various kinds of congruences equivalent to its negation p | u by making use of Dirichlet’s class number formula, the products of quadrati...