introduction various factors like climatic conditions, vegetation, soil properties, topography, time, plant residue quality and crop management strategies affect the decomposition rate of organic carbon (oc) and its residence time in soil. plant residue management concerns nutrients recycling, carbon recycling in ecosystems and the increasing co2 concentration in the atmosphere. plant residue d...

residue number system (rns) is a non-weighted number system for integer number arithmetic, which is based on the residues of a number to a certain set of numbers called module set. the main characteristics and advantage of residue number system is reducing carry propagation in calculations. the elimination of carry propagation leads to the possibility of maximizing parallel processing and reduc...

residue management has a direct impact on soil physical and chemical characteristics which in turn have identical effects on sustainability of crop production in agroecosystems. the effects of wheat residual management practices (burning, plowing under and removal) on soil physical and chemical characteristics were investigated in this research. treatments were compared in a complete block desi...

For a prime p > 2 let Zp be the group of invertible elements modulo p, and let Hp denote the modular hyperbola xy ≡ 1 (mod p) where x, y ∈ Z. Following [1] we define Hp = Hp ∩ [1, p− 1], that is, Hp = {(x, y) ∈ Z : xy ≡ 1 (mod p), 1 ≤ x, y ≤ p− 1}. We note that the lines l1 : y = x and l2 : y + x = p are lines of symmetry of Hp. In this note we use these two symmetries to prove the following ba...

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, discuss some of its basic properties, and characterize the G-fuzzy congruence generated by a fuzzy relation on a semigroup. We also give certain lattice theoretic properties of Gfuzzy congruences on semigroups.

We study the distribution of spacings between squares in Z/QZ as the number of prime divisors of Q tends to infinity. In [3] Kurlberg and Rudnick proved that the spacing distribution for square free Q is Poissonian, this paper extends the result to arbitrary Q.

We show that for any fixed ε > 0, there are numbers δ > 0 and p 0 2 with the following property: for every prime p p 0 , there is an integer p δ < N p 1/(4 √ e)+ε such that the sequence 1, 2,. .. , N contains at least δN quadratic non-residues modulo p. We then apply this result to obtain a new estimate on the smallest quadratic nonresidue in a Beatty sequence.

Plots of quadratic residues display some visual features that are analyzed mathematically in this paper. The graphical patterns of quadratic residues modulo m depend only on the residues of m modulo the lowest positive integers.