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...

Perennial grain production will likely present unique challenges for managing diseases that affect the productivity and longevity of crops being considered. Typical cultural practices effective at reducing soiland residue-borne pathogens, such as annual crop rotations, delayed fall planting, and tillage, are not feasible in perennial systems. Consequently, soiland residue-borne pathogens, and p...

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 ...

MANAGEMENT of post-harvest residues, produced during the green-cane harvesting of sugarcane in Louisiana, has become an increasingly important issue for producers, particularly in areas where burning of the residues is banned or restricted. If the residues, which range from 4–8 tonnes per hectare, are not removed prior to the emergence of the subsequent ratoon crop in the spring, yields may be ...

Large uncertainty exists in the estimations of greenhouse gases and aerosol emissions from crop residue burning, which could be a key source quantifying impact agricultural fire on regional air quality. In this study, we investigated burning their North China Plain (NCP) using three widely used methods, including statistical-based, burned area-based, radiative power-based methods. The impacts b...