In this paper residue number system (RNS) arithmetic and redundant residue number system (RRNS) based codes as well as their properties are reviewed. We propose a number of applications for RRNS codes and demonstrate how RRNS codes can be employed in global communication systems, in order to simplify the associated systems by unifying the entire encoding and decoding procedure across global com...

We have shown that Rpl3, a protein of the large ribosomal subunit from baker's yeast (Saccharomyces cerevisiae), is stoichiometrically monomethylated at position 243, producing a 3-methylhistidine residue. This conclusion is supported by top-down and bottom-up mass spectrometry of Rpl3, as well as by biochemical analysis of Rpl3 radiolabeled in vivo with S-adenosyl-l-[methyl-(3)H]methionine. Th...

Acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE) catalyze the hydrolysis of the neurotransmitter acetylcholine and, thereby, function as coregulators of cholinergic neurotransmission. For both enzymes, hydrolysis takes place near the bottom of a 20 Å deep active site gorge. A number of amino acid residues within the gorge have been identified as important in facilitating efficient ...

This paper explores the role of group theory in providing a proof for the Law of Quadratic Reciprocity, which states that for distinct odd primes pand q, q is a quadratic residue mod p if and only if p is a quadratic residue mod q, unless p and q are both congruent to 3 mod 4. The Law of Quadratic Reciprocity is an important result in number theory; it provides us with a simple method to determ...

In this paper we study elementary approaches to classical theorems on representations of primes of the form ax2 + by2, in particular the two squares theorem. While most approaches make use of quadratic residues, we study a route initiated by Liouville, and simplified by Heath-Brown and Zagier.

We point out that off-shell four-dimensional spacetime-supersymmetry implies strange hermiticity properties for the N=1 RNS superstring. However, these hermiticity properties become natural when the N=1 superstring is embedded into an N=2 superstring.

(where χ (mod q) is a Dirichlet character) arise naturally in many classical problems of analytic number theory, from estimating the least quadratic nonresidue (mod p) to bounding L-functions. Recall that for any character χ (mod q) , |Sχ(x)| is trivially bounded above by φ(q). A folklore conjecture (which is a consequence of the Generalized Riemann Hypothesis) predicts that for nonprincipal ch...

We construct a class of codes of length such that the minimum distance outside of a certain subcode is, up to a constant factor, bounded below by the square root of , a well-known property of quadratic residue codes. The construction, using the group algebra of an Abelian group and a special partition or splitting of the group, yields quadratic residue codes, duadic codes, and their generalizat...

The prolyl aminopeptidase complexes of Ala-TBODA [2-alanyl-5-tert-butyl-(1, 3, 4)-oxadiazole] and Sar-TBODA [2-sarcosyl-5-tert-butyl-(1, 3, 4)-oxadiazole] were analyzed by X-ray crystallography at 2.4 angstroms resolution. Frames of alanine and sarcosine residues were well superimposed on each other in the pyrrolidine ring of proline residue, suggesting that Ala and Sar are recognized as parts ...

despite of beneficial effects of antibiotics in treatments of infectious diseases, antibiotic residues in meat, milk, eggs and another products can cause serious side effects for human health. it is clear that, antibiotic residues in food stuff, cause bacterial resistance, allergic reactions, toxicity, carcinogenic effects and change of natural micro flora of intestine in consumers. so, the aim...