Print ISSN: 0022-1767 Online ISSN: 1550-6606. Immunologists, Inc. All rights reserved. Copyright © 2013 by The American Association of 9650 Rockville Pike, Bethesda, MD 20814-3994. The American Association of Immunologists, Inc., is published twice each month by The Journal of Immunology at U niersity of N rth D aota L ib of H ealth Scences on O cber 9, 2013 hp://w w w jim m unl.org/ D ow nlade...

Let p be the characteristic of Fq and let q be a primitive root modulo a prime r = 2n + 1. Let β ∈ Fq2n be a primitive rth root of unity. We prove that the multiplicative order of the Gauss period β + β−1 is at least (log p)c logn for some c > 0. This improves the bound obtained by Ahmadi, Shparlinski and Voloch when p is very large compared with n. We also obtain bounds for ”most” p.

Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive rth root of unity, one obtains under certain conditions a normal basis for Fqn over Fq, where r is a prime and nk = r− 1 for some integer k. We generalize this construction by allowing arbitrary integers r with nk = φ(r), and find in many cases smaller values of k than i...

The coefficients of g(s) in expanding the rth derivative of the composite function g ◦ f by Faà di Bruno’s formula, is determined by a Diophantine linear system, which is proved to be equivalent to the problem of enumerating partitions of a finite set of integers attached to r and s canonically. © 2005 Elsevier B.V. All rights reserved. MSC: primary 11D04; secondary 05A17; 11D45; 11Y50; 15A36; ...

This paper uses rth-order categorical Markov chains to model the probability of precipitation. Several stationary and non-stationary high order Markov models are proposed and compared using BIC. The number of parameters increases exponentially by adding the Markov order. Several classes of high-order Markov models are proposed which their increase of number of parameters are modest. The theory ...

We prove a version of Schur–Weyl duality over finite fields. We prove that for any field k, if k has at least r + 1 elements, then Schur– Weyl duality holds for the rth tensor power of a finite dimensional vector space V . Moreover, if the dimension of V is at least r + 1, the natural map kSr → EndGL(V )(V ) is an isomorphism. This isomorphism may fail if dimk V is not strictly larger than r.

The logsum formula, which provides the expected maximum utility for the multinomial logit model, is often used as a measure of welfare. We provide here a closed form formula of the welfare measure of an individual who has not access to his first-best choice, but has access to his rth-best choice, r = 2, ...n, where n is the number of alternatives. The derivation is based on a standard identity ...

I shaH that in a monetary grol.,rth model Edgel..'Orthsubstitutability betl.,reen consumption and real balances do not in general imply multiple steady state solutions as has been Hidely believed following Drock (1974). I then show that when the government budget constraint is explicit and the deficit is money-financed with fixed real coupons on outstanding bonds, it is not possible to rule out...