the biobreeding- diabetes prone (bb-dp) rat spontaneously develops an autoimmune diabetic syndrome that is dependent on the rt1 u major histocompatibility complex (mhc) haplotype and homozygosity for an allele at the lymphopenia (lyp) locus. lyp mutation is responsible for a peripheral t -lymphopenia. there are other genetic loci contributing to diabetes susceptibility in this strain. bb rats c...

let $alpha$ be an automorphism of a ring $r$. the authors [on skewinverse laurent-serieswise armendariz rings, comm. algebra 40(1)(2012) 138-156] applied the concept of armendariz rings to inverseskew laurent series rings and introduced skew inverselaurent-serieswise armendariz rings. in this article, we study on aspecial type of these rings and introduce strongly armendariz ringsof inverse ske...

Suppose that p, q, r, s are non-negative integers with m = p+ q+ r+ s. The class X(p, q, r, s) of permutations that contain no pattern of the formαβγ where |α| = r, |γ| = s and β is any arrangement of {1, 2, . . . , p}∪{m−q+1,m− q+2, . . . ,m} is considered. A recurrence relation to enumerate the permutations of X(p, q, r, s) is established. The method of proof also shows that X(p, q, r, s) = X...