Monomial, Gorenstein and Bass Orders

In this article we study a class of orders called {\it monomial orders} in a central simple algebra over a non-Archimedean local field. Monomial orders are easily represented and they may be also viewed as a direct generalization of Eichler orders in quaternion algebras. A criterion for monomial orders to be Gorenstein or to be Bass is given. It is shown that a monomial order is Bass if and only if it is either a hereditary or an Eichler order of period two.Comment: 13 pages; fix typos in the proof of Theorem 3.

CONSUMER PREFERENCES AND EVALUATIONS OF A PROCESSED MEAT PRODUCT

Consumer/Household Economics,

RAG-1 Mutations Associated with B-Cell-Negative SCID Dissociate the Nicking and Transesterification Steps of V(D)J Recombination

Some patients with B-cell-negative severe combined immune deficiency (SCID) carry mutations in RAG-1 or RAG-2 that impair V(D)J recombination. Two recessive RAG-1 mutations responsible for B-cell-negative SCID, R621H and E719K, impair V(D)J recombination without affecting formation of single-site recombination signal sequence complexes, specific DNA contacts, or perturbation of DNA structure at the heptamer-coding junction. The E719K mutation impairs DNA cleavage by the RAG complex, with a greater effect on nicking than on transesterification; a conservative glutamine substitution exhibits a similar effect. When cysteine is substituted for E719, RAG-1 activity is enhanced in Mn2+ but remains impaired in Mg2+, suggesting an interaction between this residue and an essential metal ion. The R621H mutation partially impairs nicking, with little effect on transesterification. The residual nicking activity of the R621H mutant is reduced at least 10-fold upon a change from pH 7.0 to pH 8.4. Site-specific nicking is severely impaired by an alanine substitution at R621 but is spared by substitution with lysine. These observations are consistent with involvement of a positively charged residue at position 621 in the nicking step of the RAG-mediated cleavage reaction. Our data provide a mechanistic explanation for one form of hereditary SCID. Moreover, while RAG-1 is directly involved in catalysis of both nicking and transesterification, our observations indicate that these two steps have distinct catalytic requirements

Supersingular abelian surfaces and Eichler class number formula

Let $F$ be a totally real field with ring of integers $O_F$, and $D$ be a totally definite quaternion algebra over $F$. A well-known formula established by Eichler and then extended by K\"orner computes the class number of any $O_F$-order in $D$. In this paper we generalize the Eichler class number formula so that it works for arbitrary $\mathbb{Z}$-orders in $D$. The motivation is to count the isomorphism classes of supersingular abelian surfaces in a simple isogeny class over a prime finite field $\mathbb{F}_p$. We give explicit formulas for the number of these isomorphism classes for all primes $p$.Comment: 29 pages, 3 numerical tables, shortened revised version with same results, Sections 7-9 of v2 are remove