Let π(x; d, a) denote the number of primes p ≤ x with p ≡ a(mod d). Chebyshev’s bias is the phenomenon that ‘more often’ π(x; d, n) > π(x; d, r), than the other way around, where n is a quadratic non-residue mod d and r is a quadratic residue mod d. If π(x; d, n) ≥ π(x; d, r) for every x up to some large number, then one expects that N(x; d, n) ≥ N(x; d, r) for every x. Here N(x; d, a) denotes ...

The ring Zk(+, .) mod p k with prime power modulus (prime p > 2) is analysed. Its cyclic group Gk of units has order (p − 1)p, and all p-th power n residues form a subgroup Fk with |Fk| = |Gk|/p. The subgroup of order p − 1, the core Ak of Gk, extends Fermat’s Small Theorem (FST ) to mod p, consisting of p − 1 residues with n ≡ n mod p. The concept of carry, e.g. n in FST extension n ≡ np + 1 m...

In sorghum and mungbean – lentil cropping system, field experiments were conducted for three successive years to assess the effect of mung bean residue incorporation on sorghum and succeeding lentil productivity along with different doses of phosphorus (P; 0, 30, 60 kg ha−1) applied to these crops. The level of soil fertility was also tested with or without incorporation of mung bean residue. T...

An extraction method based on matrix solid phase dispersion (MSPD) and high performance liquid chromatography with UV detection for quantification of two widely used pesticides (Malathion and α-Endosulfan) in Khazar rice from north of Iran were investigated. The ratio of solid phase (adsorbent) to sample, types of eluting solvent and its volume were optimized to achieve the highest recoveries f...

Removal of corn residue for biofuels can decrease soil organic carbon1,2 (SOC) and increase CO2 emissions3 because residue C in biofuels is oxidized to CO2 at a faster rate than when added to soil.4,5 Net CO2 emissions from residue removal are not adequately characterized in biofuel life cycle assessment (LCA).6–8 Here we used a model to estimate CO2 emissions from corn residue removal across t...

1. Ficin and stem-bromelain are irreversibly inhibited by 1,3-dibromoacetone, a reagent designed to react first with the active-site cysteine residue and subsequently with a second nucleophile. Evidence is presented that establishes that a histidine residue is within a 5A locus of the active-site cysteine residue in both enzymes. The histidine residue in both enzymes is alkylated at N-1 by dibr...

background: chlorinated pesticides have been used in pest control for several decades in the world. these compounds are still applied in many regions, and their continuous usage has resulted in their bioaccumulation and residue in the food chain. these residues could transfer to food products and accumulate in fat tissues. undoubtedly, the breast milk could be a significant biomarker for estima...