This is an introduction to the algebraic theory of periodic arithmetical maps. The topic is connected with number theory, combinatorics, algebra and analysis. 1. Various Backgrounds I. Combinatorial Background. For n ∈ Z = {1, 2, 3, · · · } and a ∈ R(n) = {0, 1, · · · , n− 1}, let a(n) = a+ nZ = {x ∈ Z : x ≡ a (mod n)} = {· · · , a− n, a, a+ n, · · · } and call it a residue class with modulus n...

in this study the effect of different nitrogen source substrates on the amount of chitosan production by aspergillus niger was investigated. a. niger ptcc 5012 from the persian type culture collection (ptcc) was grown on soy bean, corn seed and canola residues at 30 °c for specified cultivation days under sterilized conditions. chitosan was extracted from the fungal mycelia using hot alkaline a...

A 3- years (2015, 2016 and 2017) field study was carried out at National Wheat Research Program, Bhirahawa, Rupandehi, Nepal to evaluate the influence of crop residues and nitrogen levels on rice. The experiment was conducted in split plot design with three replications. Main plots were two crop residue levels (with crop residues of 30 cm wheat stubble and without crop residues) and sub plots c...

Pesticides are one of the major pollutants in the environment. The residue of pesticides has been reported to be at a critical level in agricultural crops, especially in greenhouse crops. Tomato is considered as an important vegetable in Iranian food basket and is produced in fields and greenhouses. So, the current study aimed to assess diazinon and oxydemeton-methyl levels in tomatoes sampled ...

The transport of peptides to the endoplasmic reticulum by the transporter associated with antigen processing (TAP) is a necessary step towards determining CD8 T cell epitopes. In this work, we have studied the predictive performance of support vector machine models trained on single residue positions and residue combinations drawn from a large dataset consisting of 613 nonamer peptides of known...

to evaluate the sensitivity of different crops included some pulses to simulated metribuzin soil residues, an experiment was conducted in completely randomized design with factorial arrangement and four replications in research greenhouse of college of agriculture, ferdowsi university of mashhad. treatments included of 8 crops (chickpea, common bean, lentil, corn, wheat, barley, rape seed and s...

Let K be a p-adic field, R the valuation ring of K, P the maximal ideal of R and q the cardinality of the residue field R/P . Let f be a polynomial over R in n > 1 variables and let χ be a character of R×. Let Mi(u) be the number of solutions of f = u in (R/P i)n for i ∈ Z≥0 and u ∈ R/P i. These numbers are related with Igusa’s p-adic zeta function Zf,χ(s) of f . We explain the connection betwe...

The toric residue is a map depending on n + 1 semi-ample divisors on a complete toric variety of dimension n . It appears in a variety of contexts such as sparse polynomial systems, mirror symmetry, and GKZ hypergeometric functions. In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the as...