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 ...

This thesis investigates architectures for high speed signal convolution using residue number system techniques. The focus is on VLSI implementations, a choice that gives two parameters by which judge different architectures: speed and hardware size. Although the focus is on the standard residue number system, the same concepts can be directly applied to quadratic residue number system architec...

The Hamming weight enumerator function of the formally self-dual even, binary extended quadratic residue code of prime p = 8m + 1 is given by Gleason’s theorem for singly-even code. Using this theorem, the Hamming weight distribution of the extended quadratic residue is completely determined once the number of codewords of Hamming weight j Aj , for 0 ≤ j ≤ 2m, are known. The smallest prime for ...

to investigate the changes in yield and yield components of dry land wheat (triticum aestivum l. cv agosta), under the influence of residue and nitrogen levels and different tillage practices, a field experiment was conducted during the 2006-2007 growing season, in the agricultural research station of the college of agriculture, shiraz university, iran. the experiment was designed as a split-sp...

Every year lots of black tea (Camellia sinensis (L.) Kuntze) residue will produce in the factories. These residue are unusable whereas the bio active compounds can be extracted and used in the drag and food industries. Due to mentioned problems, this project was conducted years 2011 - 2012 with the aim to make a study on consecutive isolation of all bio active compounds from tea residu...