It is shown that the extended quadratic residue code of length 20 over GF(7) is a unique self-dual [20, 10, 9] code C such that the lattice obtained from C by Construction A is isomorphic to the 20-dimensional unimodular lattice D 20, up to equivalence. This is done by converting the classification of such self-dual codes to that of skew-Hadamard matrices of order 20.

The largest minimum weight of a self-dual doubly-even binary (n, k, d) code is d = 4bn/24c+ 4. Of such codes with length divisible by 24, the Golay Code is the only (24, 12, 8) code, the Extended Quadratic Residue Code is the only known (48, 24, 12) code, and there is no known (72, 36, 16) code. One may partition the search for a (48, 24, 12) self-dual doubly-even code into 3 cases. A previous ...

β-glucosidase is involved in the degradation of cellulose in soil and has the potential for monitoring biological soil quality. the objective of this study was to determine the effects of barley residue placement, burning, nitrogen fertilizer and tillage management on β-glucosidase enzyme after a period of 90 days. a field experiment was carried out based on a completely randomized design with ...

Three-dimensional cluster analysis offers a method for the prediction of functional residue clusters in proteins. This method requires a representative structure and a multiple sequence alignment as input data. Individual residues are represented in terms of regional alignments that reflect both their structural environment and their evolutionary variation, as defined by the alignment of homolo...

Scatchard analyses of erythropoietin (EPO) binding to its receptor (EPO-R) have shown that some erythroid cells display a biphasic nature of the ligand-saturation curve, indicating the presence of two classes of binding sites with different affinities. The biochemical basis accounting for this observation is unknown. We found that the culture of a human erythroleukemia cell line with tunicamyci...

of the residue field K ∼= A/A+ as an A-module. Here ∂0 : A → K is the natural augmentation, the Fi are considered graded left free A-modules whose basis elements have degree 0, and that the resolution is linear means the boundary maps ∂n, n ≥ 1, are graded of degree 1 (unless ∂n = 0). The examples we will discuss in Section 1 are variants of the polytopal semigroup rings considered in Bruns, Gu...

Hence A, B, C equal A', B', C in some order. Each of the 6 orders leads immediately to the proportionality of two rows or columns. The above theorem, in its specialization to minors of Vandermonde determinants composed of gth roots of unity in R*, was used in [l] for the proof of a theorem on power series without terms whose subscript belongs to one of 3 residue classes modulo an arbitrary inte...

Gingipains are cysteine proteinases acting as key virulence factors of the bacterium Porphyromonas gingivalis, the major pathogen in periodontal disease. The 1.5 and 2.0 A crystal structures of free and D-Phe-Phe-Arg-chloromethylketone-inhibited gingipain R reveal a 435-residue, single-polypeptide chain organized into a catalytic and an immunoglobulin-like domain. The catalytic domain is subdiv...

131 W. E. Deskins, Abstract Algebra. London: Collier-Macmillan, 1964. [4] I. Flores, The Logic of Computer Arithmetic. Englewood Cliffs, N.J.: Prentice-Hall, 1963. 151 H. L. Garner, "The residue number system," IRE Trans. Electron. Comput., vol. EC-8, pp. 140-147, June 1959. 161 N. S. Szabo and R. 1. Tanaka, Residue Arithmetic and its Applications to Computer Technology. New York: McGraw-Hill, ...

For an o-minimal expansion R of a real closed eld and a set V of Th(R)-convex valuation rings, we construct a \pseudo completion" with respect to V. This is an elementary extension S of R generated by all completions of all the residue elds of the V 2 V , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings up to ...