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...

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 ...

This study was carried out to evaluate the effects of blended ash mixture on mechanical properties of concrete. In this study two reference mixtures were used. One of the mixtures was a no-fly ash mixture, and the other mixture contained 35% unblended Class C fly ash. Additional mixtures were composed of three blends of Class C and Class F fly ash while maintaining a total fly ash content of 40...

The use of fluid catalytic cracking (FCC) by-products as aluminosilicate precursors in geopolymer binders has attracted significant interest from researchers recent years owing to their high alumina and silica contents. Introduced this study is the concrete comprising FCC residue combined with fly ash requisite source aluminosilicate. Fly was replaced various contents ranging 0–100% by mass bin...

[1] Abrasion and comminution of pumice clasts during the propagation of pyroclastic flows have long been recognized as a potential source for the enhanced production of volcanic ash, however, their relative importance has eluded quantification. The amount of ash produced in situ can potentially affect runout distance, deposit sorting, the volume of ash introduced in the upper atmosphere, and in...

The emerald ash borer (Agrilus planipennis) is an invasive wood-boring beetle that has killed millions of ash trees since its accidental introduction to North America. All North American ash species (Fraxinus spp.) that emerald ash borer has encountered so far are susceptible, while an Asian species, Manchurian ash (F. mandshurica), which shares an evolutionary history with emerald ash borer, i...

The toric residue is a map depending on n + 1 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 associated po...