In this letter, we propose a novel two-way amplifyand-forward (AF) relay selection scheme over independent flat Nakagami-m fading channels. In the proposed schemes, two users first sequentially broadcast their respective information to all the relays. Then, the Nth best-relay perform AF protocol on the received signals sent from the two users and forward them to both users. The Nth best-relay i...

In this paper, the variational iteration method for solving nth-order fuzzy integro-differential equations (nth-FIDE) is proposed. In fact the problem is changed to the system of ordinary fuzzy integrodifferential equations and then fuzzy solution of nth-FIDE is obtained. Some examples show the efficiency of the proposed method.

The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R0(2m) be the minimal root discriminant for totally complex number fields of degree 2m, and put α0 = lim infmR0(2m). Define R1(m) to be the minimal root discriminant of totally real number fields of degree m and put α1 = lim infmR1(m). Assuming the Generalized Riemann Hypothesis, α...

is bijective. This sounds easy enough. One should bear in mind, however, that nobody is able to write down explicitly a basis for such innocent Q-vector spaces as the real numbers V = R or the infinite product V = ∏∞ m=1Q. Indeed, to establish the existence of a basis in infinite-dimensional vector spaces one has to use the axiom of choice, or equivalently Zorn’s Lemma, and thereby abandons all...

In this paper, the multiple solutions of Nth-order fuzzy differential equations by the equivalent integral forms are considered. Also, an Existence and uniqueness theorem of solution of Nth-order fuzzy differential equations is proved under Nth-order generalized differentiability in Banach space.

We consider with a new point of view the notion of nth powers in connection with the k-abelian equivalence of words. For a fixed natural number k, words u and v are k-abelian equivalent if every factor of length at most k occurs in u as many times as in v. The usual abelian equivalence coincides with 1-abelian equivalence. Usually k-abelian squares are defined as words w for which there exist n...

We previously showed that applying 10(-6) M of the cytokinin 6-benzylaminopurine (BAP) to uninoculated roots of Masym3, a Nod(-)Myc(-)Melilotus alba (Desr.) mutant, resulted in the accumulation of MaENOD40 transcripts to levels similar to BAP-treated wild-type roots. In contrast, inoculation with a Nod(-)S. meliloti mutant expressing the trans-zeatin synthase gene of Agrobacterium tumefaciens (...

1. Introduction. If E/F is a finite-dimensional Galois extension with Galois group G, then, by the Normal Basis Theorem, there exist elements w ∈ E such that {g(w) | g ∈ G} is an F-basis of E, a so-called normal basis, whence w is called normal in E/F. In the present paper, we study normal bases for cyclotomic fields. Let Q be the field of rational numbers; for a positive integer n, we let Q n ...