background and objectives: with regard to the hazards of nitrite, application of natural preservatives in order to reduce the microbial load of meat and meat products is increasing. owing to their anti-bacterial properties, red barberry and the dried residue of red grape could be suitable replacers for nitrite. materials and methods: agar dilution method was employed in order to determine the m...

A prime number p is called b-elite if only finitely many generalized Fermat numbers Fb,n = b 2 + 1 are quadratic residues to p. So far, only the case b = 2 was subjected to theoretical and experimental researches by several authors. Most of the results obtained for this special case can be generalized for all bases b > 2. Moreover, the generalization allows an insight to more general structures...

By a careful analysis of the proofs of Kopparty in fields of characteristic 2, we show that the problem of powering in Fpn requires ACC(p) circuits of exponential size (in n), for any fixed prime p > 2. Similar bounds hold for quadratic residuosity. As a corollary, we obtain non-trivial bounds for exponential sums that express the correlation between the quadratic character of Fpn and n-variate...

We determine the product of the invertible quadratic residues in Zn. This is a variation on Gauss’ generalization of Wilson’s Theorem. From this we deduce that for twin primes p, p + 2, the product of the invertible quadratic residues in Zp(p+2) is ±(p+1), where the sign depends on the residue class of p modulo 4. We examine necessary and sufficient conditions for consecutive odd natural number...

In this paper, we establish a residue theorem for Malcev-Neumann series that requires few constraints, and includes previously known combinatorial residue theorems as special cases. Our residue theorem identifies the residues of two formal series that are related by a change of variables. We obtain simple conditions for when a change of variables is possible, and find that the two related forma...

We present some observations on a restricted variant of unitary Cayley graphs modulo n, and implications for a decomposition of elements of symplectic operators over the integers modulo n. We define quadratic unitary Cayley graphs Gn, whose vertex set is the ring Zn, and where residues a, b modulo n are adjacent if and only if their difference is a quadratic residue. By bounding the diameter of...

After a brief introduction to hash-coding (scatter storage) and discussion of methods described in the literature, it is shown that for hash tables of length p >2, prime, the primitive roots r of the cyclic group Z/p of prime residues mod p can be used for a simple collision strategy q(p,i) = r mod p for fi(k) = f0(k) +q(p,i) mod p. It is similar to the strategy which uses quadratic residues q(...

A non-empty family S of subsets of a finite set A has the odd (respectively, even) intersection property if there exists non-empty B ⊆ A with |B∩S| odd (respectively, even) for each S ∈ S. In characterizing sets of integers that are quadratic nonresidues modulo infinitely many primes, Wright asked for the number of such S, as a function of |A|. We give explicit formulae.

We consider the division of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we characterize the optimal allocations and we develop two exact algorithms for its search. Both the characterization and the algorithm are based on the tight relationship two geometric objects of fair division: the Individ...

Logical candidates for residue number system (RNS) implementations are applications which require very high data rates and are numerically intensive. The quadratic residue number system (QRNS) is specifically designed for fast complex arithmetic. In a previous paper by Dubois and Venetsanopoulos the use of Eisenstein complex numbers was proposed for the implementation of a radix-3 fast Fourier ...